Question

In which of the following, the net force acting is not zero?
(A) a retarding train
(B) a ball falling with terminal velocity
(C) a kite held stationary
(D) a truck moving with constant velocity
(E) a book placed on a table

Answer 1

Hint
Use the fact that if there is a net force on an object then it will result in an acceleration, since the force is given by $ F = m.a $ where m is the mass of the object and a is the acceleration.

Complete step by step answer
A retarding train – We know that retarding means decelerating which means the train is undergoing deceleration or negative acceleration.
Since acceleration is a change in velocity with respect to time, $ \left( {a = \dfrac{{dv}}{{dt}}} \right) $ , and the velocity of the train is reducing we can say that the value of acceleration is non-zero. Hence,
 $ \Rightarrow F = m.a \ne 0 $
Therefore, the retarding train is experiencing an external force. This force is acting against the motion of the train to slow it down. Therefore, we can say that the net force acting on – a retarding train is non-zero.

Note
Alternate Method – We can eliminate all the other options and determine that they do not include an object with non-zero acceleration.
(B). A ball falling with terminal velocity – Terminal Velocity is the maximum velocity attainable by an object whilst falling through a fluid e.g. water or air (in this case). Since the ball is falling with terminal velocity, which, by definition is the maximum attainable velocity, it has no change in velocity, therefore, its velocity doesn’t change with time,
 $ \Rightarrow \dfrac{{dv}}{{dt}} = 0 $
Which means that the acceleration of the ball is zero,
 $ \Rightarrow a = \dfrac{{dv}}{{dt}} = 0 $
Which means that the force on the body is also zero,
 $ \Rightarrow F = ma = 0 $
Therefore the ball experiences net force as zero.
(C). A kite held stationary – since the kite is stationary, therefore it has no velocity, hence it has no acceleration, and hence the net force on it is zero. Mathematically this can be represented identically to the previous case.
(D). A truck moving with constant velocity – since the truck is moving with constant velocity, its change in velocity w.r.t. time is equal to zero. Hence, its acceleration is equal to zero and hence the net force acting on the truck is zero. Mathematically this can be represented identically to the previous case.
(E). A book placed on the table, clearly has no motion and is stationary; therefore, the change in velocity is zero w.r.t. time hence, its acceleration is zero and hence the net force acting on it is zero. Mathematically this can be represented identically to the previous case.