Ch4_OringerR


 * Ross Oringer Chapter 4 Wikilog toc**

Chapter 4- Section 1
This image shows the kids motion path. The kid is unsure of what will happen next because he is sliding in the wheeling chair blindfolded. The person pushing is creating the track, and the person riding the ride is not sure what to expect.
 * What Do You See?**

The part that creates the loudest screams is the initial drop after slowly and gradually moving up the first giant hill. Speed/velocity picks up rapidly. This creates screams because the rider doesn't know what to expect, and the feeling of fear is great. Stomachs drop and different feelings are within the person, creating excitement and screams throughout the rest of the ride.
 * What Do You Think?**

2/28/11
 * Roller Coaster Design **

456 feet maximum height with a maximum speed of 128 mph. Launched horizontally from 0-128 mph in 3.5 seconds, then vertically 90 degrees into a quarter degree turn. Reach a 270 degree spiral, eventually reaching a second hill of 129 feet.
 * Kingda Ka: Six Flags Great Adventure Jackson, NJ **

120 foot first drop twists 180 degrees. It then hits a 98 foot vertical loop leading into a rapid horizontal launch. The ride has various helixes, in which the first helix is an upward spin providing ample positive g-forces.
 * Talon: Dorney Park Allentown, PA **

3/1/11
 * Physics Talk **

**Summary**: Scalar is a quantity that has magnitude, but no direction. Displacement is a measured distance with a direction included. A vector is a quantity that has both magnitude and direction. Speed is the distance traveled divided by the elapsed time. Velocity is the displacement divided by time. Delta is represented by final minus initial. Acceleration is the change in velocity divided by time. Acceleration is a vector quantity, and is in the direction of the change in velocity.

1. Displacement is the measured distance with a direction included. Distance, or scalar, doesn't include direction. 2. The displacement is 0 kilometers. It is 2km to get to the school, and 2km to get back to the house. 2-2=0. 3. Speed is the distance traveled divided by the elapsed time. Speed is scalar. and velocity is the displacement divided by elapsed time. It is a vector quantity. 4. Acceleration can be found with the equation: A=change in velocity/elapsed time.
 * Checking Up Questions **

3/1/11 1. *See Images* 2. The biggest thrill is atop the first hilltop. It is the tallest, making it the biggest drop. After gradually climbing up the big hill, the coaster will reach the top, slowly, then pick up very rapid speed, leaving the person who is riding with screams. Stomachs will drop as well. Any points of acceleration, including the back curve and horizontal circle will also be thrilling. 3a. La Paz, Bolivia travels the greatest speed. This is because it has the biggest radius in a 24 hour time period. Time is the constant. 3b. v=d/t =4,000km/24hr =1,667 km/hr 3c. Although the speed may be the greatest, there is clearly no acceleration, and you wouldn't really notice. 4. a= change in V/elapsed time =16m/s-4m/s / 3s =4m/s^2 5a. car going at 50 km/hr is SPEED 5b. student riding bike 4 m/s going home- VELOCITY 5c. coaster whips around a left turn at 5m/s- ACCELERATION 5d. coaster going up 12 meters at 3 m/s- DISPLACEMENT, VELOCITY 5e. train ride NW 150 km- DISPLACEMENT 6. v=d/t =.1 meter/2 seconds =.05 m/s 7. v=d/t .05 m/s=.05 m/ (time) 1 s= time 8. a=delta V/delta t = 25m/s / 10 s  =2.5m/s^2 10. If I were to make two changes, I would make the biggest lift shorter. Preschool children aren't physically and psychologically able to face such a task. Also, I would add more short hills to make the ride have some reasonable thrills, adding some excitement. 10b.
 * PTG**

3/2/11 The constant changes in direction and points of acceleration create the loudest screams and produce the thrilling sensation. The big drops, the back curves, and the constant turns create the screams.
 * What Do You Think Now?**

Chapter 4- Section 2
There are two different carts on the track. One cart is making crazy noises as seen in the image because that group is going down a steep hill. The other group has bored looks on faces as seen in the image because they are traveling on the horizontal track traveling a constant speed.
 * What Do You See? **

The roller coaster with the biggest thrill is the 90 degree angle because it is more steep. No matter what material the track is, the bigger the angle, the steeper the angle of descent.
 * What Do You Think?**

3/5/11 **Summary**: GPE is the resulting energy based on its position in a gravitational field. KE is the energy an object posses because of its motion, due to its speed. Both KE and GPE depend on the mass of the object. GPE=mgh. G is a constant of 9.8 m/s^2. The unit of energy is joules, represented by a J symbol. Mechanical energy is the sum of kinetic and potential energy. The sum of GPE and KE are constant. When GPE increases, KE decreases. KE (bottom) + GPE (bottom) = KE (top) + GPE (top)
 * Physics Talk **

1. The higher a ball is released, the greater the speed of the ball at the bottom of the run. 2. When height increases, GPE does as well. The mass has the same impact. GPE decreases as the mass decreases. 3. KE increases as the velocity increases. When mass increases, KE also increases. 4. As a cart on a coaster rolls down a hill, all the lost energy that is from the decreasing GPE goes to the increase due to the increase in velocity. 5. **SEE CHART ABOVE** 30,000 J of KE
 * Checking Up Questions **

3/7/11 1. The speeds of the carts are the same. The initial height is the same, even though the inclines are different. 3. 4.   *AT TOP AND BOTTOM THE LITTLE BUMP IS SUPPOSED TO BE 0** 5. 6.   LITTLE STUMP AT TOP AND BOTTOM IS SUPPOSED TO BE 0 7a. GPE=mgh =(.2)(9.8)(.75) =1.47J 7b. GPE=KE 1.47=1.47 KE 7c. h=.375m which is half way 8. Whether 6 or 26 passengers, the speed will not change either way. GPE at the top is equal to KE at the bottom. *Always, the masses cancel out. 9a. It is traveling fastest at point B because it is at the lowest possible position. Highest KE=lowest GPE. 9b. C and F, the coaster is traveling at the same speed. The heights are the same, and GPE is equal to KE in this sense. 9c. The coaster is traveling faster at point D. It has more kinetic and less gravitational potential. 10b. The coaster can not reach point H. The original GPE height is less than H. There is not enough KE. The highest hill is always the first one. The coaster could roll back down because there is not enough KE to go with the GPE. 11.
 * PTG**
 * height (m) || KE=1/2mv^2 || GPE=mgh || combined GPE and KE ||
 * top 30 || 0 || 60,000 || 60,000 ||
 * bottom 0 || 60,000 || 0 || 60,000 ||
 * half 15 || 30,000 || 30,000 || 60,000 ||
 * 3/4 down 7.5 || 45,000 || 15,000 || 60,000 ||
 * height (m) || KE || GPE || combined GPE and KE ||
 * top 25 || 0 || 75,000 || 75,000 ||
 * bottom 0 || 75,000 || 0 || 75,000 ||
 * half 12.5 || 37,500 || 37,500 || 75,000 ||
 * 3/4 (5) || 60,000 || 15,000 || 75,000 ||
 * Position || Height (m) || GPE || KE || Combined ||
 * bottom hill || 0 || 0 || 50,000 || 50,000 ||
 * top hill || 25 || 50,000 || 0 || 50,000 ||
 * top loop || 15 || 30,000 || 20,000 || 50,000 ||
 * horiz. loop || 0 || 0 || 50,000 || 50,000 ||

3/10/11 The initial height is the same on both tracks. The higher the initial height, the greater the velocity at the bottom. The greater thrill would be B because the change in speed (acceleration) is greater due to the steeper slope of the track.
 * What Do You Think Now?**

Chapter 4- Section 3
One kid launched the frog spring toy into the air. A lab partner is standing up with a ruler attempting to eye how high the toy goes into the air. There is also a photo gate towards the bottom of the launch immediately after the frog launches to get its velocity. Another kid is getting ready to launch another toy.
 * What Do You See? **

To get to its highest point, the roller coaster slowly and gradually climbs up a large hill. No, it does not cost more to lift the people on the roller coaster. No matter how many passengers, the cart is going to make it to the highest point of the roller coaster track.
 * What Do You Think? **

3/14/11 **Summary**: Conservation of Energy: all energy in a system balances between KE EPE and GPE. Elastic Potential Energy (EPE) equals spring potential energy (SPE). SPE is the energy stored in a spring due to its compression or stretch A bouncy ball loses height after each bounce because some of the energy is converted to sound/heat energy. The total energy of an object can be GPE, SPE, or KE. THE SUM OF THE ENERGIES IS ALWAYS THE SAME. When using the table, the total number all the way to the right must be the same throughout in joules. A pop toy with a greater mass won't go as a high as one with lower mass, but SPE is the same. For a pop-up toy, GPE at the bottom and KE & GPE (just after leaving table) = KE & GPE (half way) and GPE (at the top). THEY BALANCE OUT. GPE = mgh. Mass has a direct impact: the larger the mass, the shorter the height and visa versa. When energy is transformed in a roller coaster, all GPE is at the highest point before the big drop, and it is transformed into rapid KE as it goes down the drop. After the cars are pulled up to the top of the hill, GPE and KE remains the same. As the cart breaks stop the Kinetic converts into thermal energy. If the brakes did not work then a large and strong spring can stop the car when the spring compresses. SPE has the same equation as EPE (=1/2kx^2.) GPE + KE + SPE is constant.
 * Physics Talk **

1. As it bounces off of the table, all of the SPE transfers into gravitational potential energy and kinetic energy. 2. Because it has 2J of potential energy, the kinetic energy will be 2J as well. 3. When reaching maximum height, the GPE will be 2J. 4. EPE=1/2kx^2. K is the spring constant and x is the distance compressed/stretched.
 * Checking Up Questions **

3/15/11 5. The second hill can't be higher than the first. It won't have enough gravitational potential energy to reach the top of the second hill. At most, you can get up to the same height as what you started with. 6. The roller coaster doesn't travel forever. As it continues to move, it loses its kinetic energy and gravitational potential which turns into heat and sound energy. Work due to friction turns into thermal energy. Some turns to therman, and you have less available to make kinetic and GPE. 7. GPE=electric energy (300)(9.8)(15)= electric energy =44,100J 8a. KE= 1/2 mv^2 KE=1/2(400)(15)^2 =45,000J 8b. GPE=KE =45,000 J 8c. 45,000= (400)(9.8)(h) height=11.5 meters 9. As a ball is thrown upwards, the height is increasing, which means that the GPE also increases. 10. It is the same because it is independent. They are all going up to the same height so they will all have the same gravitational potential energy at the end. 11a. They should have similar results because they are the same. 1/2mv^2=mgh. Should be about the same as the GPE and KE. . 078 11b. KE=SPE 1/2 mv^2=SPE SPE= 1/2(0.020)(2.7)^2 SPE=0.073 J 11c. KE=GPE 1/2mv^2=mgh 1/2(.006)(2.7)^2= (.006)(9.8)h 4 m/ 3 (because its tripled) height=.13 meters 12a. SPE= 1/2 kx^2 52,920J= 1/2k(4)^2 x= 6,615 Nm/s 12b. GPE= SPE GPE=mgh GPE=70,560 J 1/2(6,615)x^2=70,560 x= 4.62m 13. KE= SPE KE=1/2kx^2 KE=1/2(40)(.3)^2 KE= 1.8 J
 * Physics To Go **

3/16/11 As mass increased, the height decreased. They compensate. EPE=GPE=KE. They are all under the conservation of energy. Roller coasters are pulled by electric cables. As mass increases, height decreases. More electric energy is needed because the mass is heavier and the people need to get to the top of the roller coaster. Therefore, the costs is greater to life the roller coaster if its full of people. GPE gets bigger. If GPE gets bigger,it takes more work to get to the top.
 * What Do You Think Now? **

Chapter 4- Section 4
The roller coaster rider on the left is bored on the ride because there isn't much of a thrill. It is not a steep first drop, as you can see from their sleeping facial expressions. This one takes place on the moon and it is slower. The next picture on the right shows a bigger thrill of a roller coaster. The first drop is steep, and the riders are ecstatic on the roller coaster as seen with the exclamation point. They are on Jupiter and the gravity on Jupiter is greater.
 * What Do You See?**

Gravity has direction. The direction is downward. Gravity is always pushing down to the core of the Earth, and that is why the people all over the world (including Australia) are standing up on their feet.
 * What Do You Think?**

3/16/11 **Summary**: A gravitational field is the gravitational influence in the space around a massive object. Earth is the source of its gravitational field. The test object is a part of the Earth's field. This is called the response or test object. The lines on the field show direction of the force on a mass. The closer the lines, the stronger the field. Acceleration due to gravity is greater when closer to Earth. The inverse square relationship is the relationship between the magnitude of a gravitational force and the distance from the mass. This also describes how electrostatic forces depend on the distance from an electrical charge. Newton's law of universal gravitation describes the gravitational attraction of objects for one another. The law states all bodies with mass attract to all other bodies with mass. Force is proportional to the product of two masses and force increases as mass increases. Galileo (late 1500s): Earth moves around sun in a circular path Kepler (1600s): Tycho Brahe Law of Ellipses: the planets orbit the sun in an elliptical path; Sun is the focus eccentricity; e=0, circle earth's orbit: e=.07 Law of Equal Areas: the closer to the sun, the faster you go Law of Harmonies: period of a planet^2 divided by the distance from sun^3 is constant for all planets in the solar system (T^2/R^3) Newton (late 1600s): force of gravity is inversely proportional to the distance squared between two objects mass of earth is 6*10^24; mass of a person is 1*10^2 bigger the mass, more overwhelming the force force of gravity is proportional to mass one times mass two Cavendish (late 1700s): Fg= __ (m1*m2)/d^2 G= universal gravitational constant=6.67*10^-11 Force of gravity=gravitational attraction=gravitational force=weight: w;Fg in newtons
 * Physics Talk **

1. The direction of the gravitational field is towards the ground pointing downward. 2. The field lines are strongest towards the bottom near the Earth's core. 3. If you triple the distance between two masses, the force is 1/9 of the original. 4. The force that holds the moon in its orbit around the Earth is gravity. 5. The shape of the planets orbit around the sun is in a circle (elliptical).
 * Checking Up Questions **

3/17/11 1. Originally, the gravitational force between two asteroids is 500 N. If the distance between them is doubled, the force would be 125 N (1/4 the original). 2a. Fg would be 1/4 of the original 2b. Fg is 1/9 original 2c. Fg is 1/16 original 3. Gravity is always trusted because it does its job of keeping all humans standing on their feet on the Earth. Gravity is always there because we never see floating objects. 4. Acceleration due to gravity (g) is less at the top, but negligible. 5a. Water on the Earth's side facing the moon is closer to the moon than the center of Earth. This is where there is high tide, and on the opposite side of Earth away from the moon is low tide. 5b. Water moves independently to Earth. There are high tides on those bodies of water facing the moon. The gravitational field of the moon is attracted to the water, making the water rise to the forces. Water does not have as much mass as an entire planet (Earth). 5c. There is not an even distribution of water on the Earth's surface because there are bits of land scattered (islands) throughout the waters. All bodies of water are different distances from the moon and therefore, have different (stronger, weaker) impacted forces of the gravitational field of the moon. This is the inverse-square relationship. The further away from the moon, the more subtle the waves. 6a. If a fish was not impacted by gravity, it would be moved away from the water and into the air, becoming a floating object, and eventually, it will die. 6b. Gravity holds the water down so the fish can swim in the water. Gravity holds the fish in the water because the mass of a fish is much less than the mass of the Earth. Because masses attract, the large mass of Earth attracts to the small mass of the fish. 7a. 1/4 the force 7b. 1/9 the force 7c. 1/16 the force 7d. 4 times 8a. 2 times 8b. 3 times 8c. 4 times 8d. 1/2 times 9a. quadruple (4) 9b. 9 times 9c. 16 times 9d. 1/4 times (half times half) 10a. 2 times 10b. 9 times 10c. 6 times
 * Physics To Go**

3/18/11
 * Physics Plus**

1. Ac=v^2/r

2. v=d/t (2*pi*3.84*10^8))/2440800 v=998.505 m/s

3. a=v^2/r =998.505^2/3.84*10^8 =.0025m/s^2

3/18/11 Gravity has a downward direction, or facing the center core of the Earth. Its the direction of the force on the mass. The earth is acting on the human. People in Australia are still held down to the ground even though gravity is supposed to have them upside down. Gravity attracts the mass of the people to the mass of the Earth. People are therefore forced to the surface of Earth.
 * What Do You Think Now?**

Chapter 4- Section 5
One side shows a butcher's shop weighing a block of meat. At the deli, it is in pounds. The picture on the right is a more scientific approach to how much it is measured. The picture shows its measured in newtons.
 * What Do You See? **

Yes, you can use the same scale. Both of the animals are on the Earth, and it can give measurements of weight for both animals. A bathroom scale is a measurement of weight. When stepping on the scale, the weight from your body is balanced by the weight of the scale pushing up towards the feet.
 * What Do You Think?**

3/28/11 **Summary**: Hooke's law is the restoring force exerted by a spring is directly proportional to the distance of stretch or compression of the spring. Fs=-kx. K is the spring constant and x is the distance stretched or compressed. The negative indicates the opposite direction of compression/stretching. A large value of K means the spring is stiff, and a small value of k means the spring is weaker. Weight=mg. M equals mass. G equals gravity. Weight is a force. Mass stays the same, but weight changes due to the change in the gravitational field. For a bathroom scale, there is a spring inside the scale. When stepping on the scale, the spring compresses enough to provide an equal force which is equal to the weight.
 * Physics Talk **

1. If the force of the spring is increased 5 times, the stretch of the spring increases 5 times as well (direct relation) 2. Spring constant (k) displays the strength of a spring. The greater value of k, the stiffer the spring. The smaller, the weaker. 3. Mass (in kg) is a part of the weight equation. N=kg*m/s^2. Acceleration must equal 0. 4. The more weight that steps onto the scale, the more compression of the spring inside the scale.
 * Checking Up Questions **

3/28/11 1a. w=mg =(100kg)(9.8m/s^2) =980 N 1b. w=mg =(10kg)(9.8m/s^2) =98 N 1c. w=mg =(60)(9.8) =588 N  2a. .25/130=1/x x=578.5 N 2b. 4.45(1000) x= 4,450 N  2c. 4.45(50) x=222.5 N  3a. 3b. see above trend lines 3c. The slope of the graph is 14.913 N/m, which is the k (spring constant) value. 3d. The slope represents the k value. This shows the strength/stiffness or weakness of the spring. 3e. I purposefully made the second spring more weak. The slope is 1.8667 N/m. This is the k value, and it is weaker because it has a less steep slope. The spring is weaker than the other one. 4. Fs=-kx 12=k(.03) k=400N/m 5. As the force of the spring increases, the stretch distance also increases. It is a direct relationship. When clearing the side that K is on, the equation becomes k=Force of spring divided by stretch distance. The greater the value of k, the greater the stiffness of the spring. Therefore, the more force, the less distance it stretches. When weight is added, the stretch distance will increases, but it may not be a dramatic increase. Negative sign indicates that the force is going in the opposite direction of the stretch distance. 6. The greater value of k, the more stiff the spring is. Therefore, 15.0 N/cm is more difficult to stretch. 7. slope= 150N/m *points of slope (.03,4.5)(.01,1.5) 8. A spring scale displays weight in newtons. When attaching masses, the scale stretches, and you can read the scale to determine the weight. It incorporates the mass added and the stretch distance that is created from adding mass. Therefore, it follows the y=-kx formula.
 * Physics To Go**

The same scale can not weigh both a canary and an elephant. The scale works by the compression of a spring. The spring can only hold so much. The scale would be only able to read the maximum number of weight on it, and that will not be the full weight of the elephant. There is not enough distance for the spring to compress for the elephant to go onto the scale. The spring can only be so stiff. The more stiff the scale, the more weight it can hold without reaching the maximum. The distances of compression between a canary and an elephant are much different. Bathroom scale results occur by the spring's compression. The scale is able to provide a force that balances the force of the body on the scale. The spring is connected to a scale that has been calibrated to provide a weight. As weight increases, the scale compresses more.
 * What Do You Think Now?**

Chapter 4- Section 6
In this image, the man on the left who is not as high in the air in the elevator has a scale reading of 0. As the man to the right is higher in the air, he can't seem to realize why the scale reads such a large number, as seen with the ? above his head.
 * What Do You See? **

Weight will not change when you are on a roller coaster. At all times, the formula for calculating weight is mass times gravity. Gravity is a constant, and the mass is not going to change. Therefore, weight will remain the same, but the person riding may feel heavier or lighter at certain points on the coaster. The bathroom scale, when sitting on it, will spit out different results based on location on the roller coaster. This is because it calculates the force that rests on the scale.
 * What Do You Think? **

4/5/11
 * Physics Talk **

**Summary**: According to Newton's first law, an object at rest has no net force acting on it. According to the second law, an object at rest has zero acceleration and no net force acting on it. The same goes for an object in constant velocity. When sitting on a scale on a leveled roller coaster, the scale reading would be equal to the actual weight of the person. When accelerating up, there is a net force pushing you up. When moving up on the scale, the magnitude reading is greater than weight. The magnitude of the force of Earth would be less tahn the force of the compressed spring in the scale. The net force of a person is down if an elevator/person are accelerating downward. Weight readings are identical when the elevator is in constant motion or at rest. When accelerating up, the person accelerates up. The Earth pulls down on you with a smaller force than the scale goes upward, therefore, the scale reads a larger force. The forces make weight feel greater/less (force hold stomach in place against gravitational forces.) When elevators accelerate down, the reading is smaller force than originally because the force of the scale is up on the person and less than the force of weight down. Air resistance can't be ignored on a roller coaster. A roller coaster in a free fall accelerates 9.8m/s^2.

// Types Of Motion // Increasing, constant, decreasing when increasing, velocity and acceleration point in the same direction. Net force: sum of all forces acting on that object for increasing, net force must be in the same direction as acceleration (∑F=ma) The bigger force always points in direction of the net force

1. When moving at constant speed, all of the forces are a net force of zero. 2. When accelerating up, the scale reading is greater because a points up, and ∑f points in the same direction. 3. Object at rest stays at rest. An unbalanced force is going to get you moving. That force is the scale. The force of you on the scale is equal and opposite. To get you moving, you put a bigger force on the scale. 4. If the cable were to break, all forces would go down. The only force would be the weight of you pushing down. The force reading on the scale would be zero. It is a free fall. Your falling at the same rate as the scale is falling. You won't push down on it. 5. Air resistance slows a falling raindrop. We normally ignore air resistance.
 * Checking Up Questions **

4/6/11 1a. vf=vi+at =0+(9.8)(2) = 19.6 m/s 1b. vf=vi+at (9.8)(5) = 49 m/s 1c. vf=vi+at =(9.8)(10) =98 m/s 2a. vf=vi+at =(1.6)(2) =3.2 m/s 2b. vf=vi+at =(1.6)(5) =7.5 m/s 2c.vf=vi+at =(1.6)(10) =16 m/s 4. 5. Because you feel lighter, it means that it is increasing down. Acceleration must be negative because if the reading is less than what it is at rest, than acceleration and force are down. Decreasing up is also an option. Normal force is less than weight. 6. Velocity and acceleration are both pointing up. Net force points in the direction of acceleration. The force is pointing up. The normal force has to be bigger. 7a. Once the elevator begins, the scale reading will go down. That is the direction of velocity and acceleration. The 1.5 acceleration becomes negative. Force points to the weight in this case. 7b. ∑f=ma N-w=ma N=ma+mg; 50(-1.5)+50(9.8)=415 N 8a. The forces are equal. The reading on the scale will remain 50 kg because it is at rest. The weight will be 490 N. 8b. V and A go up, and ∑f go up as well. The normal force is greater than weight. N=590. 8c. As the elevator travels up at constant speed, the reading on the scale will remain the same because all forces are equal. Normal is equal to weight. 9. In the first picture the elevator is at rest/constant velocity. The scale is going to read 113 lb because that is home much the person weighs. The forces are equal because acceleration is 0. In the second picture the elevator is in free fall. The reading on the scale is 0 because there is no force keeping him down, the only force is gravity and there is nothing to balance that out. In the third picture the elevator is accelerating upward. The reading on the scale is going to be greater because when you are accelerating upward that force is greater so it is going to make your weight seem heavier. 10. Our roller coaster is meant for those 13 and up. We have a steep first drop which is thrilling and provides a change in direction. This fall down will make the person riding it feel lighter. Immediately, there is a vertical loop which provides thrill. You want a good amount of acceleration (changes in direction) to create thrill and screams. Loops, twists, turns, and flips create this thrill. Dangers would be a free fall because someone can die.
 * Physics To Go**
 * **Motion of the Elevator** || **Acceleration (up, down, zero)** ||  || **Relative Scale Reading (greater, less or equal to weight)** ||
 * At rest, bottom floor || 0 ||  || N=W ||
 * Starting at Rest, Increasing Up || up ||  || N>W ||
 * Continuing to move, Constant Up || 0 ||  || N=W ||
 * Slowing down to top floor, Decreasing Up || down ||  || NW ||

4/6/11 Your weight on a roller coaster does not changed. Your apparent weight changes. You feel like your weight is changing but it really isn't. On a roller coaster at different points, your weight would change. When you are going up a hill, you feel heavier then when you are at the bottom of a hill, and you weight on a scale at the top of the hill would be heavier. This is because you are exerting more normal force that weight at the top compared to the bottom.
 * What Do You Think Now?**

Chapter 4- Section 7
The people going around the curve are about to fall off. The speed is increasing and wants to go straight. Need a force that will make you go in a circle.
 * What Do You See? **

You don't fall out of the cart when it goes upside down during a loop because gravity is keeping you in place in the seat. Acceleration and force are pointing toward the center of the loop.
 * What Do You Think? **

4/7/11 **Summary**: The force toward the center is the normal force of the track on the wheels. The force is perpendicular to the track. Centripetal force is the force that keeps the object moving in a circle. Center seeking, the force is always directed toward the center. Mass, velocity (squared) and radius are components of the equation. If there is a net force, an object must be accelerating. Because the force is towards the center, the acceleration is directed toward the center. Safety on a roller coaster is required to be less than 4 gs. Acceleration is 9.8 m/s^2. Changes in small accelerations may make a better ride than one big thrill from a large acceleration.
 * Physics Talk **

1. Centripetal acceleration allows an object to stay in the motion of a circle. 2. If traveling in a circular motion and constant speed, you are centripetal acceleration. 3. The forces at the top of the loop are the gravitational force and normal force. 4. Normal force is responsible for apparent weight. 5. As mass increases, Fc increases. As velocity increases, Fc increases (direct-square relationship) and as radius increases, Fc decreases.
 * Checking Up Questions: **

4/11/11 1a. The path is a circle
 * PTG **

1b. If the string breaks, the car would travel on a tangent to the circular path. 2a. Friction of the tires replaces the string of the car. 2b. If hitting a patch of ice, you will go tangent to the circular path. 6a. The speed did not change. Velocity has changed. 6b. The velocity changed because it changed direction. 6c. delta V=Vf-Vi 20^2 + 20^2 = c^2 c = 28.2 m/s tan-1 = 20/20 theta = 45 degrees 7. Ac=v^2/r =20^2/200 = 2 m/s^2 10a. Fast Moving 10b. Slow Moving 13a. C- heavier 13b. D- uncertain 13c. E- heavier 13d. F- heavier 13e. Lift hill- normal 14a. C- up 14b. D- down 14c. E- up 14d. F- up 14e. Lift hill (going up at constant speed)- zero 14f. Horizontal loop- towards the center of the loop (sideways) 14g. Back curve- towards the center of the loop (sideways)
 * || Required Fc (N) || Required Weight (N) || Normal Force (N) ||
 * top of the loop || 4000 || 500 || 3500 ||
 * bottom of the loop || 6000 || 500 || 6500 ||
 * || Required Fc (N) || Required Weight (N) || Normal Force (N) ||
 * top of the loop || 800 || 500 || 300 ||
 * bottom of loop || 2800 || 500 || 3300 ||

4/11/11 1a. As mass increases, the net force increases. They share a direct relationship. 1b. Velocity and the net force share a direct-square relationship. When the velocity is doubled for example, the Fnet is 4 times as great. 2. Fc=mv^2/r. If velocity is doubled, the force needs to be 4 times as strong because of the direct square relationship. 3.The Fnet decreases because the radius increases. 4. The larger radius for the curve, the LESS the force required to keep the car moving along a curve. If the curve is tight, than a GREATER force is required. 5.The more string that was let out, the less force was needed. 6a. Ac=v^2/r =12^2/20 =7.2 m/s^2 6b. Fc=mv^2/r = (300)(12^2)/20 =2160 N
 * Physics Plus**

4/12/11
 * What Do You Think Now?**

You do not fall out when you go upside down in a roller coaster car. Centripetal force (Fc) keeps the passenger in a circular motion large enough to keep you in your seat during a loop, while maintaining safety. The loop has a smaller radius at the top of the clothoid loop which decreases velocity. The radius is bigger at the bottom which increases the velocity. The normal force from the track pushes down on the cart with a certain amount of force. At the top of a loop, the normal force and the weight are both facing down, which means that net force is also facing down.

Chapter 4- Section 8
Towards the left, the carts are climbing up the big hill about to reach the top. When at the top, they are very nervous approaching a big drop with a lot of speed. When going down, it is very steep because you can see the hats that flew off.
 * What Do You See?**

No, it does not require more work to pull up a cart up a steep incline than a gentle incline. Work=force times distance. As long as the distance is the same, the force should be the same. Therefore, there isn't a difference. It is more difficult to go up a steep incline because the legs are using more force to climb up.
 * What Do You Think?**

4/12/11 **Summary**: W=F*d and displacement is parallel to the force. When an incline is steeper, you need more force, but the distance along the incline is shorter. The product of the force and distance along an incline is always the same. Work is converted into GPE on a roller coaster going up an incline. To stop a roller coaster, brakes or large springs can be used to stop a roller coaster. The kinetic energy is transferred into Spring potential energy to stop the cart. Power is the work divided by the time. P=W/delta t. It is basically the speed from which the work is transferred into energy. Power is measured in watts (J/s). Roller coasters usually use electrical energy, which is measured in voltage, to get up an incline. KE and GPE of a roller coaster are transferred to heat and sound energy as well.
 * Physics Talk**

1. The energy at the top is transferred into GPE. 2. The coaster gets its GPE from the work that the cart has while getting up the hill. 3. Truckers use a ramp because they need less force for a longer distance. 4. The roller coaster's kinetic energy is transferred into work because of the friction. 5. J/s, also known as watts.
 * Checking Up Questions **

4/16/11 1a. At the top, there is full GPE. The second one has less. 1b. Work is the change in the GPE. 1c. It is equal to the amount of work which equals the GPE. 1d. SPE=1/2kx^2 1e. The total amount of energy is kinetic and some GPE because its not all the way down. 1f. When it first hits the spring, it decelerates. 2a. The work is zero because the force and distance are perpendicular. 2b. W=F*d =(60)(.5) =30 J  2c. W=F*d =(75)(40) =3,000 J  2d. W=F*d =(500)(.7) = 350 J  3. Decrease energy consumption, don't waste energy. Don't use it when it isn't useful. 4. Mass would increase, which would require more force which would mean more work which would mean more GPE. 5a. W=F*d =(10,000)(20) =200,000 J  5b. P=W/t =20,000/150 =1,333.33 W  6. GPE increases and work is done. At the top, all is GPE. Going down, you change from GPE to KE. At the bottom of the first hill, you have mostly KE. At the top a vertical loop, you have GPE and KE. At the bottom of the loop, you have KE. At the back curve, you have KE and some GPE depending on height. Then in horizontal loop, you have KE. At the breaking ramp, work is done to stop you due to friction.
 * PTG**

4/16/11 It takes more energy to pull the roller coaster up a steep incline than a gentle incline. The height is a greater distance. Work is equal to GPE according to the LCE. The equation of GPE is mass times gravity times height. Mass is a factor. It is less difficult to walk up a gentle incline because more force is needed to get up a shorter distance. It takes less force to get us up a longer distance. Force and distance share an inverse relationship in this instance.
 * What Do You Think Now?**

Chapter 4- Section 9
The person thinking about energy on the test is having an easy time getting answers on the test. The person thinking about force is struggling and has nothing written on his paper. They are working on a roller coaster. One uses energy and the other uses force. It is easier to measure energy than to measure forces.
 * What Do You See? **

The most thrilling parts of the ride are the changes in the direction (the turns). This relates to acceleration. It will still be fun because when reaching the turns, thrills will occur.
 * What Do You Think? **

4/24/11 **Summary**: A quantity with both a number and direction is called a vector. A quantity with magnitude and no direction is a scalar. Displacement is taken into account with vectors. Vectors need to make a triangle and do Pythagorean theorem to get the hypotenuse because vectors need direction along with size. Energy is a scalar. The total mechanical energy (KE plus GPE) is equal at all points of the roller coaster ignoring friction. Force on the other hand is a vector quantity. Force of gravity is always down. The normal force is always perpendicular to the track. The changes in acceleration in size and direction create the bouncy feelings. Force and energy are related. Weight does work on the roller coaster and increases its KE. *Force in the direction of motion creates work energy and any work done creates changes in energy (Newton's Second Law).* In order to have a net force, you need an acceleration and visa versa (Law of Conservation Energy).
 * Physics Talk**

1. The pythagorean theorem is used to add vector quantities. 2. Energy is a scalar quantity. Force is a vector quantity. 3. GPE and KE are equal at all points of the coaster, GPE only depends on the height (m and g remain the same), if two points have the same heights than its moving at the same speed at those points. 4. Energy considerations are path independent. Energy will remain the same throughout the coaster. It doesn't matter what happens between the places of interest. 5. To provide a change in energy, work must be present. Work is a force applied over distance.
 * Checking Up Questions **

4/27/11 1a. a^2+b^2=c^2 c=7.07 m/s inverse tan (5/5)=45 degrees NW 1b. a^2+b^2=c^2 5^2+5^2=c^2 c= 7.07 m/s NW 2. This is because they are dropped from the same and all the GPE is at the top. Therefore you have the same KE and the same velocity. 3a. scalar 3b. vector 3c. scalar 3d. vector 3e. vector 3f. vector 3g. scalar 3h. scalar 3i. scalar 4a. scalar (no direction) 4b. vector (direction) 4c. scalar (energy) 4d. vector 5. As an energy ride, it is easier when you are trying to find speeds, know the heights. It isn't useful when trying to find accelerations for energy. 6a. 6b. 6c. The forces are the same everywhere. There is an x-component of weight. It is constant and the same at all four points. 7a. 7b. The total energies at these three points are equal. 7c. The KE at these points are the same because velocity is practically the same. 7d. You can ignore other points on the roller coaster because at all points, the GPE plus the KE are equal.
 * PTG**

4/28/11 When the snake switches direction, thrill will be created. With constant sharp left and right turns, there are changes in direction. Also, if there are corkscrews and loops, those will create screams. Any time there is a change in direction there is a change in velocity. Thrills are caused from points of acceleration. The sharp turns, loops, corkscrews, and sudden increases in speed will create thrills.
 * What Do You Think Now?**

Chapter 4- Section 10
In this picture, there is a very large roller coaster with many turns, loops, and large heights. It looks very dangerous as you can see many people falling off of the track, and could easily die. This ride could be too dangerous to ride because there are too many spots that can cause serious injury.
 * What Do You See?**

Knowing that a person can die or get seriously injured creates tremendous negative thrill, to the point where it will not attract people to the ride. If I knew that a certain ride had a caution sign of death, I would not go on it because it is not worth it.
 * What Do You Think?**

4/28/11 **Summary**: The max amount of g's in an acceleration that are considered safe in a roller coaster ride is 4. Centripetal acceleration equals velocity squared over the radius of the loop/circle. You can increase the radius, decrease the speed, decrease the initial hill height, and increase the height of the curve. Decreasing the speed around the loop will decrease the acceleration. Increasing the radius also decreases the acceleration. To find the amount of g's, you take the acceleration of the point and divide it by 9.8. The largest centripetal acceleration requires the larges centripetal force. The sum of the normal force from the track and the weight must equal the required net force. Fnet=mv^2/r. Another safety feature is that the cart needs enough speed to complete the loop.Normal is 5gs at the bottom of the curve and 3 g's at the top of the curve. Acceleration has to be greater than 9.8 m/s^2 at the top of a loop.
 * Physics Talk**

1. The maximum safe acceleration on a roller coaster is 4 g's. 2. Two ways too keep the acceleration low are to make the radii larger and lower the velocity. Also, if you make the height smaller, the GPE becomes smaller, which decreases the KE. 3. The end/bottom of the loop is the greatest acceleration. 4. The bottom of the loop is the greatest normal force.
 * Checking Up Questions **

4/30/11 1. To ensure that the roller coaster is safe, I will check the acceleration and make sure it is less that 4g's. I will also make sure that if there is a loop, the cart will have enough acceleration to go around it and not fall. 2a.GPE=KE mgh=1/2mv^2 (9.8)(h)=1/2(20)^2 h=20 m 2b. a=v^2/r =20^2/12 =33.3 m/s^2 2c. 33.3 m/s^2 / 9.8=3.4 g's. This is safe because the maximum amount of g's considered safe is 4. 2d. 9.8*4=39.2 m/s^2 39.2=v^2/12 v=21.7m/s. At this speed, there will be safety concerns. 2e. 39.2=v^2/7 v=16.57m/s. At this speed, there will be safety concerns. 3a. Ac=v^2/r =25^2/10 =62.5 m/s^2 3b. a/9.8 62.5/9.8 =6.4 g's. This isn't safe because it exceeds 4 which is the maximum. 4a.GPE=KE mgh=1/2mv^2 (9.8)(50)=1/2(V^2) v=31.3m/s. The speed will be this at the bottom. 4b. a=v^2/r a=31.3^2/10 a= 96m/s^2 at the top. 4c. Ac=v^2/r 96=v^2/10 v=24m/s 4d. 58m/s 4e. The acceleration is safe at the top and the bottom of the loop. 5a.mgh=1/2mv^2 9.8(16)=1/2v^2 v=8.9m/s 5b.GPE=KE mgh=1/2mv^2 9.8h=1/2(8.9^2) h=20m 6a. Ac=v^2/r =12^2/18 =8m/s^2 6b. Fc=mv^2/r =(900)(12)^2/18 =7,200 N  6c. The centripetal is the weight and the normal force from the track. 7a. Ac=v^2/r =20^2/15 =26.7 m/s^2 7b. Fc=mv^2/r =(900)(20)^2/15 =24,000 N  7c. Yes, the roller coaster is safe. If it can hold 25,000 newtons, the centripetal force is 24,000 newtons, which is less than the maximum. 8a. No, it will not change because mass is not a factor of centripetal acceleration. 8b. It is the same speed because only mass is being added. 8c. Yes it will require a stronger material because the normal force from the track will need to be greater because weight is increasing.
 * PTG**

5/3/11
 * Physics Plus**

5/2/11 Knowing that a person can die or get seriously injured creates tremendous negative thrill, to the point where it will not attract people to the ride. If I knew that a certain ride had a caution sign of death, I would not go on it because it is not worth it. People must know the cautions of rides before they go on them. With some new knowledge of physics, the maximum amount of g's is 4, which means the greatest acceleration that a coaster can reach safely is 39.2 m/s^2. Accelerations through loops and sudden turns are able to create thrill with safety. To ensure the ride is safe, one must be sure that the person is strapped in at all times, and when there are very sharp turns, the cart stays on the track. Also, when going around a loop vertically, the coaster must have enough speed to complete the loop, or the passengers will fall and die.
 * What Do You Think Now?**