A skier starts at the top of a hill. On which run does her gravitational potential energy change the most (a), (b), (c), or (d), or are they (e) all the same? On which run would her speed at the bottom be the fastest if the runs are icy and we assume no friction or air resistance? Recognizing that there is always some friction, answer the above two questions again. List your four answers now.

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Answer 1

Textbook Question

Chapter 6, Problem 1OQ

A skier starts at the top of a hill. On which run does her gravitational potential energy change the most (a), (b), (c), or (d), or are they (e) all the same? On which run would her speed at the bottom be the fastest if the runs are icy and we assume no friction or air resistance? Recognizing that there is always some friction, answer the above two questions again. List your four answers now.

Chapter 6, Problem 1OQ, A skier starts at the top of a hill. On which run does her gravitational potential energy change the

Expert Solution & Answer

To determine

The path on which the gravitational potential energy changes the most when there is no friction and the skier will have the maximum speed.

Answer to Problem 1OQ

Solution:

All paths undergo the same amount of gravitational potential energy change. Skier will have same speed at the bottom for all the paths.

All paths undergo the same amount of gravitational potential energy change. Skier will have the greatest speed for the shortest path C.

Explanation of Solution

Force of gravity is a conservative force hence, the work done by force of gravity does not depend on the path but on the initial and final position, since in each path initial and final position is same. Hence, each path undergoes the same amount of gravitational potential energy change.

As the skier travels down, the potential energy converts to kinetic energy. Since the change in potential energy is same for each path, the change in kinetic energy is also same for each path. Hence, skier gains the same amount of speed through each path.

Force of gravity is a conservative force hence the work done by force of gravity does not depend on the path but on the initial and final position, since in each path they are same. Hence, each path undergoes the same amount of gravitational potential energy change.

As the skier travels down, the potential energy converts to kinetic energy and work done by frictional force. the change in potential energy is same for each path, but the work done by frictional force depends on the length of the path. Larger the length, larger is the energy lost to friction. So, only a small portion of potential energy converts to kinetic energy. smaller the length, smaller is the energy lost to friction. So, a large portion of potential energy converts to kinetic energy and skier gains larger speed.

Conclusion:

The change in gravitational potential energy for each path comes out to be same.

The speed at the bottom comes out to be same for each path.

The change in gravitational potential energy for each path comes out to be same.

The speed at the bottom comes out to be greatest for the shortest path C.

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06:52

Students have asked these similar questions

Sketch the harmonic on graphing paper.

Exercise 1: (a) Using the explicit formulae derived in the lectures for the (2j+1) × (2j + 1) repre- sentation matrices Dm'm, (J/h), derive the 3 × 3 matrices corresponding to the case j = 1. (b) Verify that they satisfy the so(3) Lie algebra commutation relation: [D(Î₁/ħ), D(Î₂/h)]m'm₁ = iƊm'm² (Ĵ3/h). (c) Prove the identity 3 Dm'm,(Î²) = Σ (D(Î¡)D(Î¡))m'¡m; · i=1

Sketch the harmonic.

Answer 2

Textbook Question

Chapter 6, Problem 1OQ

A skier starts at the top of a hill. On which run does her gravitational potential energy change the most (a), (b), (c), or (d), or are they (e) all the same? On which run would her speed at the bottom be the fastest if the runs are icy and we assume no friction or air resistance? Recognizing that there is always some friction, answer the above two questions again. List your four answers now.

Chapter 6, Problem 1OQ, A skier starts at the top of a hill. On which run does her gravitational potential energy change the

Expert Solution & Answer

To determine

The path on which the gravitational potential energy changes the most when there is no friction and the skier will have the maximum speed.

Answer to Problem 1OQ

Solution:

All paths undergo the same amount of gravitational potential energy change. Skier will have same speed at the bottom for all the paths.

All paths undergo the same amount of gravitational potential energy change. Skier will have the greatest speed for the shortest path C.

Explanation of Solution

Force of gravity is a conservative force hence, the work done by force of gravity does not depend on the path but on the initial and final position, since in each path initial and final position is same. Hence, each path undergoes the same amount of gravitational potential energy change.

As the skier travels down, the potential energy converts to kinetic energy. Since the change in potential energy is same for each path, the change in kinetic energy is also same for each path. Hence, skier gains the same amount of speed through each path.

Force of gravity is a conservative force hence the work done by force of gravity does not depend on the path but on the initial and final position, since in each path they are same. Hence, each path undergoes the same amount of gravitational potential energy change.

As the skier travels down, the potential energy converts to kinetic energy and work done by frictional force. the change in potential energy is same for each path, but the work done by frictional force depends on the length of the path. Larger the length, larger is the energy lost to friction. So, only a small portion of potential energy converts to kinetic energy. smaller the length, smaller is the energy lost to friction. So, a large portion of potential energy converts to kinetic energy and skier gains larger speed.

Conclusion:

The change in gravitational potential energy for each path comes out to be same.

The speed at the bottom comes out to be same for each path.

The change in gravitational potential energy for each path comes out to be same.

The speed at the bottom comes out to be greatest for the shortest path C.

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

06:52

Answer 3

Textbook Question

Chapter 6, Problem 1OQ

A skier starts at the top of a hill. On which run does her gravitational potential energy change the most (a), (b), (c), or (d), or are they (e) all the same? On which run would her speed at the bottom be the fastest if the runs are icy and we assume no friction or air resistance? Recognizing that there is always some friction, answer the above two questions again. List your four answers now.

Chapter 6, Problem 1OQ, A skier starts at the top of a hill. On which run does her gravitational potential energy change the

Expert Solution & Answer

To determine

The path on which the gravitational potential energy changes the most when there is no friction and the skier will have the maximum speed.

Answer to Problem 1OQ

Solution:

All paths undergo the same amount of gravitational potential energy change. Skier will have same speed at the bottom for all the paths.

All paths undergo the same amount of gravitational potential energy change. Skier will have the greatest speed for the shortest path C.

Explanation of Solution

Force of gravity is a conservative force hence, the work done by force of gravity does not depend on the path but on the initial and final position, since in each path initial and final position is same. Hence, each path undergoes the same amount of gravitational potential energy change.

As the skier travels down, the potential energy converts to kinetic energy. Since the change in potential energy is same for each path, the change in kinetic energy is also same for each path. Hence, skier gains the same amount of speed through each path.

Force of gravity is a conservative force hence the work done by force of gravity does not depend on the path but on the initial and final position, since in each path they are same. Hence, each path undergoes the same amount of gravitational potential energy change.

As the skier travels down, the potential energy converts to kinetic energy and work done by frictional force. the change in potential energy is same for each path, but the work done by frictional force depends on the length of the path. Larger the length, larger is the energy lost to friction. So, only a small portion of potential energy converts to kinetic energy. smaller the length, smaller is the energy lost to friction. So, a large portion of potential energy converts to kinetic energy and skier gains larger speed.

Conclusion:

The change in gravitational potential energy for each path comes out to be same.

The speed at the bottom comes out to be same for each path.

The change in gravitational potential energy for each path comes out to be same.

The speed at the bottom comes out to be greatest for the shortest path C.

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

06:52

Answer 4

Textbook Question

Chapter 6, Problem 1OQ

A skier starts at the top of a hill. On which run does her gravitational potential energy change the most (a), (b), (c), or (d), or are they (e) all the same? On which run would her speed at the bottom be the fastest if the runs are icy and we assume no friction or air resistance? Recognizing that there is always some friction, answer the above two questions again. List your four answers now.

Chapter 6, Problem 1OQ, A skier starts at the top of a hill. On which run does her gravitational potential energy change the

Expert Solution & Answer

To determine

The path on which the gravitational potential energy changes the most when there is no friction and the skier will have the maximum speed.

Answer to Problem 1OQ

Solution:

All paths undergo the same amount of gravitational potential energy change. Skier will have same speed at the bottom for all the paths.

All paths undergo the same amount of gravitational potential energy change. Skier will have the greatest speed for the shortest path C.

Explanation of Solution

Force of gravity is a conservative force hence, the work done by force of gravity does not depend on the path but on the initial and final position, since in each path initial and final position is same. Hence, each path undergoes the same amount of gravitational potential energy change.

As the skier travels down, the potential energy converts to kinetic energy. Since the change in potential energy is same for each path, the change in kinetic energy is also same for each path. Hence, skier gains the same amount of speed through each path.

Force of gravity is a conservative force hence the work done by force of gravity does not depend on the path but on the initial and final position, since in each path they are same. Hence, each path undergoes the same amount of gravitational potential energy change.

As the skier travels down, the potential energy converts to kinetic energy and work done by frictional force. the change in potential energy is same for each path, but the work done by frictional force depends on the length of the path. Larger the length, larger is the energy lost to friction. So, only a small portion of potential energy converts to kinetic energy. smaller the length, smaller is the energy lost to friction. So, a large portion of potential energy converts to kinetic energy and skier gains larger speed.

Conclusion:

The change in gravitational potential energy for each path comes out to be same.

The speed at the bottom comes out to be same for each path.

The change in gravitational potential energy for each path comes out to be same.

The speed at the bottom comes out to be greatest for the shortest path C.

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

06:52

Answer 5

Textbook Question

Answer 6

Textbook Question

Answer 7

Expert Solution & Answer

To determine

The path on which the gravitational potential energy changes the most when there is no friction and the skier will have the maximum speed.

Answer to Problem 1OQ

Solution:

All paths undergo the same amount of gravitational potential energy change. Skier will have same speed at the bottom for all the paths.

All paths undergo the same amount of gravitational potential energy change. Skier will have the greatest speed for the shortest path C.

Explanation of Solution

Force of gravity is a conservative force hence, the work done by force of gravity does not depend on the path but on the initial and final position, since in each path initial and final position is same. Hence, each path undergoes the same amount of gravitational potential energy change.

As the skier travels down, the potential energy converts to kinetic energy. Since the change in potential energy is same for each path, the change in kinetic energy is also same for each path. Hence, skier gains the same amount of speed through each path.

Force of gravity is a conservative force hence the work done by force of gravity does not depend on the path but on the initial and final position, since in each path they are same. Hence, each path undergoes the same amount of gravitational potential energy change.

As the skier travels down, the potential energy converts to kinetic energy and work done by frictional force. the change in potential energy is same for each path, but the work done by frictional force depends on the length of the path. Larger the length, larger is the energy lost to friction. So, only a small portion of potential energy converts to kinetic energy. smaller the length, smaller is the energy lost to friction. So, a large portion of potential energy converts to kinetic energy and skier gains larger speed.

Conclusion:

The change in gravitational potential energy for each path comes out to be same.

The speed at the bottom comes out to be same for each path.

The change in gravitational potential energy for each path comes out to be same.

The speed at the bottom comes out to be greatest for the shortest path C.

Answer 8

Expert Solution & Answer

To determine

The path on which the gravitational potential energy changes the most when there is no friction and the skier will have the maximum speed.

Answer to Problem 1OQ

Solution:

All paths undergo the same amount of gravitational potential energy change. Skier will have same speed at the bottom for all the paths.

All paths undergo the same amount of gravitational potential energy change. Skier will have the greatest speed for the shortest path C.

Explanation of Solution

Force of gravity is a conservative force hence, the work done by force of gravity does not depend on the path but on the initial and final position, since in each path initial and final position is same. Hence, each path undergoes the same amount of gravitational potential energy change.

As the skier travels down, the potential energy converts to kinetic energy. Since the change in potential energy is same for each path, the change in kinetic energy is also same for each path. Hence, skier gains the same amount of speed through each path.

Force of gravity is a conservative force hence the work done by force of gravity does not depend on the path but on the initial and final position, since in each path they are same. Hence, each path undergoes the same amount of gravitational potential energy change.

As the skier travels down, the potential energy converts to kinetic energy and work done by frictional force. the change in potential energy is same for each path, but the work done by frictional force depends on the length of the path. Larger the length, larger is the energy lost to friction. So, only a small portion of potential energy converts to kinetic energy. smaller the length, smaller is the energy lost to friction. So, a large portion of potential energy converts to kinetic energy and skier gains larger speed.

Conclusion:

The change in gravitational potential energy for each path comes out to be same.

The speed at the bottom comes out to be same for each path.

The change in gravitational potential energy for each path comes out to be same.

The speed at the bottom comes out to be greatest for the shortest path C.

Answer 9

Expert Solution & Answer

Answer 10

Expert Solution & Answer

Answer 11

To determine

The path on which the gravitational potential energy changes the most when there is no friction and the skier will have the maximum speed.

Answer 12

Answer to Problem 1OQ

Solution:

All paths undergo the same amount of gravitational potential energy change. Skier will have same speed at the bottom for all the paths.

All paths undergo the same amount of gravitational potential energy change. Skier will have the greatest speed for the shortest path C.

Answer 13

Explanation of Solution

Force of gravity is a conservative force hence, the work done by force of gravity does not depend on the path but on the initial and final position, since in each path initial and final position is same. Hence, each path undergoes the same amount of gravitational potential energy change.

As the skier travels down, the potential energy converts to kinetic energy. Since the change in potential energy is same for each path, the change in kinetic energy is also same for each path. Hence, skier gains the same amount of speed through each path.

Force of gravity is a conservative force hence the work done by force of gravity does not depend on the path but on the initial and final position, since in each path they are same. Hence, each path undergoes the same amount of gravitational potential energy change.

As the skier travels down, the potential energy converts to kinetic energy and work done by frictional force. the change in potential energy is same for each path, but the work done by frictional force depends on the length of the path. Larger the length, larger is the energy lost to friction. So, only a small portion of potential energy converts to kinetic energy. smaller the length, smaller is the energy lost to friction. So, a large portion of potential energy converts to kinetic energy and skier gains larger speed.

Conclusion:

The change in gravitational potential energy for each path comes out to be same.

The speed at the bottom comes out to be same for each path.

The change in gravitational potential energy for each path comes out to be same.

The speed at the bottom comes out to be greatest for the shortest path C.