Chapter 6, Problem 3TC

The roller coaster starts from rest at point A, then proceeds down the incline. Compare the following for points A-E from most to least.

(a) Speed.

(b) KE.

(c) PE.

To determine

The ranking from most to least in terms of speed at different points.

Answer to Problem 3TC

The ranking from most to least in terms of speed at different points is $D>B>C>E>A$.

Explanation of Solution

The roller coaster will have maximum speed when it reaches the lowest point in the track. It is so because the potential energy of the roller coaster converts to kinetic energy. The points in the track are at different heights, so the speed of the coaster changes according to the law of conservation of energy. As the height of the roller coaster decreases, the potential energy gets converted into kinetic energy. In the case given, point A is highest in the track, so the coaster will have minimum speed. Whereas, point D is lowest in the track, so the coaster will have maximum speed.

Conclusion:

Therefore, the ranking from most to least in terms of speed at different points is $D>B>C>E>A$.

To determine

The ranking from most to least in terms of KE at different points.

Answer to Problem 3TC

The ranking from most to least in terms of KE at different point is $D>B>C>E>A$.

Explanation of Solution

The energy that is possessed by a body when it is in motion is known as kinetic energy. The variation in this energy takes place due to the change in velocity or mass of the object.

Write the expression for the kinetic energy of the body.

$KE=\frac{1}{2}m{v}^2$

Here,

$m$ is the mass

$v$ is the velocity

From the expression, it can be seen that the kinetic energy of the body varies directly to the square of the velocity of the object. So, greater the velocity of the body, greater will be the kinetic energy. Since the roller coaster has a maximum speed at point D, thus kinetic energy will also be greater than point D. On the other hand, the speed of the roller coaster minimum at point A, so the roller coaster will have least kinetic energy at point A.

Conclusion:

Therefore, the ranking from most to least in terms of KE at different points is $D>B>C>E>A$.

To determine

The ranking from most to least in terms of PE at different points.

Answer to Problem 3TC

The ranking from most to least in terms of PE at different points is $A>E>C>B>D$.

Explanation of Solution

The type of energy generated in a system, as it gains the height, is termed as potential energy.

Write the expression for the potential energy.

$PE=mgh$

Here,

$m$ is the mass

$g$ is the acceleration gravitational

$h$ is the height

From the expression, it can be seen that the potential energy of the object is depended upon the height. As the height of the object increases, the potential energy of the object also increases. The height of the roller coaster is maximum at the point A in the track, so the roller coaster will have maximum potential energy at this point. Further, the lowest point in the track is point D, so the roller coaster will have minimum potential energy at this point.

Conclusion:

Therefore, the ranking from most to least in terms of PE at different points is $A>E>C>B>D$.