Direction. COPY THE PREMISE ONLY, Indicate the letter of the questions you are answering. Using the concepts that we discussed, explain in your own words the following scenarios. You may use diagrams and equations for your answer.
1. A roller coaster car of mass m starts from rest at the top of a hill of heighth and slides down the hill, reaching a speed of v at the bottom. Assume that there is no
frictional force acting on the car. a. it possible for the roller coaster car to reach the bottom of the hill with
less kinetic energy than it would have if it had been released from rest at the bottom of the hill instead of the top? If so, explain how this could happen. If not, explain why not b. At what point(s) during the roller coaster ride does the car experience a change in gravitational potential energy without a corresponding change in
kinetic energy? How is this possible, and what is the significance of this observation in the context of the conservation of anergy?
2. An object of mass m is lifted to a height in above the ground and held stationary a. At what point(s) during the motion of the lifted object does it have the maximum and minimum potential energy? Describe how the change in
potential energy affects the motion of the object, and how the law of
conservation of energy is applicable in this context. hit the object is released from rest at the top of the height, describe the motion of the object as it fails and explain how the total mechanical energy of the system remains conserved during its free fall. How does the velocity of the object vary with time, and how can you relate this to the conservation
of energy principle? c. How would the answers to parts (a) and (b) change if the object was lifted to a different height, or if the object had a different mass? Explain your
reasoning, including any relevant equations and physical principles d. Finally, consider the scenario where the object is not lifted to a height but is instead given an initial velocity vo in the upward direction. How does the mation of the object differ from that in part (b)7 in particular, how does the maximum height reached by the object depend on its initial velocity, and what is the significance of this in the context of the conservation of energy?
1. A roller coaster car of mass m starts from rest at the top of a hill of heighth and slides down the hill, reaching a speed of v at the bottom. Assume that there is no
frictional force acting on the car. a. it possible for the roller coaster car to reach the bottom of the hill with
less kinetic energy than it would have if it had been released from rest at the bottom of the hill instead of the top? If so, explain how this could happen. If not, explain why not b. At what point(s) during the roller coaster ride does the car experience a change in gravitational potential energy without a corresponding change in
kinetic energy? How is this possible, and what is the significance of this observation in the context of the conservation of anergy?
2. An object of mass m is lifted to a height in above the ground and held stationary a. At what point(s) during the motion of the lifted object does it have the maximum and minimum potential energy? Describe how the change in
potential energy affects the motion of the object, and how the law of
conservation of energy is applicable in this context. hit the object is released from rest at the top of the height, describe the motion of the object as it fails and explain how the total mechanical energy of the system remains conserved during its free fall. How does the velocity of the object vary with time, and how can you relate this to the conservation
of energy principle? c. How would the answers to parts (a) and (b) change if the object was lifted to a different height, or if the object had a different mass? Explain your
reasoning, including any relevant equations and physical principles d. Finally, consider the scenario where the object is not lifted to a height but is instead given an initial velocity vo in the upward direction. How does the mation of the object differ from that in part (b)7 in particular, how does the maximum height reached by the object depend on its initial velocity, and what is the significance of this in the context of the conservation of energy?
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1a. Yes, it is possible for the roller coaster car to reach the bottom of the hill with less kinetic energy than it would have if it had been released from rest at the bottom of the hill instead of the top. This is because the roller coaster car has potential energy due to its height above the ground at the top of the hill, which gets converted into kinetic energy as it slides down the hill. So, if the roller coaster car is released from rest at the bottom of the hill, it will only have kinetic energy. But if it is released from rest at the top of the hill, it will have both potential and kinetic energy. Therefore, the roller coaster car can have the same final kinetic energy at the bottom of the hill, regardless of whether it was released from rest at the top or the bottom of the hill.
1b. The roller coaster car experiences a change in gravitational potential energy without a corresponding change in kinetic energy at the top of the hill and at the bottom of the hill. At the top of the hill, the roller coaster car has maximum potential energy and zero kinetic energy. At the bottom of the hill, the roller coaster car has maximum kinetic energy and zero potential energy. The significance of this observation is that the total mechanical energy (i.e., the sum of kinetic and potential energy) of the roller coaster car is conserved as it moves from one position to another, assuming no external forces are acting on it.
2a. The lifted object has maximum potential energy at the highest point and minimum potential energy at the ground level. When the object is lifted, work is done against gravity to increase its potential energy. When the object is lowered, work is done by gravity to decrease its potential energy. According to the law of conservation of energy, the total mechanical energy of the system (i.e., the object and the Earth) is conserved, so the decrease in potential energy is converted into an increase in kinetic energy.
2b. When the object is released from rest at the top of the height, it falls freely under the influence of gravity and its potential energy is converted into kinetic energy. The total mechanical energy of the system remains conserved during the free fall because there are no external forces acting on the object. The velocity of the object increases as it falls, and the velocity at any time can be calculated using the equation v = gt, where g is the acceleration due to gravity and t is the time. The velocity of the object increases as time increases, and the kinetic energy of the object also increases correspondingly, while the potential energy decreases. The total mechanical energy of the system remains constant.
2c. If the object is lifted to a different height or has a different mass, the maximum potential energy and the maximum height it can reach will change. The maximum potential energy is proportional to the mass and the height of the object, and the maximum height it can reach is determined by the initial potential energy and the kinetic energy at the highest point. The conservation of energy principle still applies to these scenarios.
2d. If the object is given an initial velocity vo in the upward direction, it will move upward, but its velocity will decrease due to the gravitational force until it reaches the highest point. At the highest point, the velocity is zero and the potential energy is maximum. Then, the object falls freely under the influence of gravity and its potential energy is converted into kinetic energy. The maximum height reached by the object depends on its initial velocity and can be calculated using the conservation of energy principle. The significance of this observation is that the total mechanical energy of the system remains conserved throughout the motion of the object.