Question

Two people are applying forces on two opposite sides of a moving cart. The cart still moves with the same speed in the same direction. What do you infer about the magnitudes and direction of the forces applied?
A. Force in the direction opposite to the motion is zero.
B. Force in the direction opposite to the motion is greater
C. Both are pushing with equal and opposite force
D. Force in the direction of motion is greater

Answer 1

Hint: As a first step you could make a rough sketch of the given situation for better understanding. Now recall Newton’s first law of motion, which states that in the absence of external force, the body will continue to be in its state of rest or uniform motion. Using this point you could easily find the true statement.

Complete step by step answer:
In the question, we are given a moving cart. Two people are applying a certain amount of force from each of the opposite sides of this moving cart. Even after the application of these two forces, the cart still continues its motion in the same direction with the same speed as before. We are supposed to find the characteristics of the two forces applied by the two people.

Let v be the velocity with which the cart was moving before the application of force on it by the two people. Now, let us recall Newton’s first law of motion which states that all bodies continue its state of rest and of uniform motion in the absence of an external force. So, the cart moving with the same velocity before and after the application of forces would imply that the net external force on it is zero. So,
${{F}_{1}}+{{F}_{2}}=0$
$\therefore {{F}_{1}}=-{{F}_{2}}$
Therefore, we found that the forces applied by the two people on the cart are equal in magnitude but opposite in direction.

So, the correct answer is “Option C”.

Note: Other than the law used in the above solution, we have two others which stated respectively as:
Second law: The net force acting on a body is equal to the product of its mass and acceleration, that is,
${{F}_{net}}=ma$
Third law: This law states that for every action of a body, there is an equal and opposite reaction by the second body on the first.