Chapter 9, Problem 28A

A ball is released at the left end of the metal track shown below. Assume it has only enough friction to roll, but not to lessen its speed.

a. Rank from greatest to least the ball’s momentum at each point.

b. Rank from greatest to least the ball’s kinetic energy at each point.

c. Rank from greatest to least the ball’s potential energy at each point.

To determine

To Rank:Ball's momentum from greatest to least.

Answer to Problem 28A

  $\text{C > B = D >A}$

Explanation of Solution

Introduction:

Momentum is mass times velocity. It is a vector quantity.

Momentum is proportional to ball's speed or velocity. If ball's speed is high it will be high and vise versa.

At point A, the ball is at height so its speed is zero. When ball comes to Point B, its potential energy gets converted to kinetic energy. So, it comes to position B with high speed. So, at point B its speed is high. Again, ball goes to point C so its speed increases and then ball speed decreases at point D. The momentum of ball at B and D is same since both are at the same height.

Conclusion:

The rank of ball's momentum from greatest to least is C,B = D,A.

To determine

To Rank: Ball's kinetic energy from greatest to least.

Answer to Problem 28A

  $\text{C > B = D >A}$

Explanation of Solution

Introduction:

When an object is in motion, it possess kinetic energy. This energy is measured in joules.

As velocity of a ball increases, the kinetic energy of the ball increases. At highest point, ball has high potential energy and low kinetic energy. Velocity of ball is high when ball comes to lower position.Here, ball's velocity is highest at point C and it decreases for point B, D and A.

The kinetic energy of ball at B and D is same since both are at same height.

Conclusion:

Ranking of ball's kinetic energy from greatest to least is C, B = D, A.

To determine

To Rank: Ball's potential energy from greatest to least.

Answer to Problem 28A

  $\text{A, B = D, C}$

Explanation of Solution

Introduction:

Potential energy is the energy possessed by the object due to its position. Potential energy is high if object’s position is high and low if object position is low.

Potential energy of ball is proportional to ball's height. Potential energy will be high for high ball's position and low for low position.

Here ball's position is measured from ground and so, will be from highest to lowest will be A, B, = D, C.

The potential energy of ball at B and D is same since both are at same height.

Conclusion:

Ranking of ball's potential energy from greatest to least is A, B = D, C.