Chapter 6, Problem 2TC

(a)

To determine

The ranking from most to least in terms of kinetic energy.

Answer to Problem 2TC

The ranking from most to least in terms of kinetic energy is $A=B=C=D$.

Explanation of Solution

The kinetic energy is a mass dependent quantity that varies as the mass or velocity of the object changes.

Write the expression for the kinetic energy.

$KE=\frac{1}{2}m{v}^2$ ......(I)

Here,

$m$ is the mass

$v$ is the velocity

From the figure, it can be seen that the ball starts to move from end of the track to the right. As it has only enough friction to roll, the speed of the ball does not get less. So, the speed of the ball remains small at all the points in metal tracks.

Using equation (I), the kinetic energy of the object varies due to the speed. But, here the speed remains constant at all the points, the kinetic energy also remains same.

Conclusion:

Therefore, the ranking from most to least in terms of kinetic energy is $A=B=C=D$.

(b)

To determine

The ranking from most to least in terms of potential energy.

Answer to Problem 2TC

The ranking from most to least in terms of potential energy is $A>B=D>C$.

Explanation of Solution

Write the expression for potential energy.

$PE=mgh$

Here,

$m$ is the mass

$g$ is the acceleration

$h$ is the height

From the above expression, it can be seen that the potential energy of the object varies as the mass and height changes. As the object gains height, it also gains potential energy.

As point C is the lowest point in the metal track, there the ball will have the least potential energy. In the metal track, point A is the highest point so that the ball will have the greatest potential energy. Since points B and D are at the same height, the potential energy of the ball at these points will be the same.

Conclusion:

Therefore, the ranking from most to least in terms of potential energy is $A>B=D>C$.