Chapter 7, Problem 39A

Consider two carts, one twice as massive as the other, that fly apart when the compressed spring squeezed between them is released. How fast does the heavier cart roll compared with the lighter cart?

To determine

How fast does the heavier cart roll compared with the lighter cart.

Answer to Problem 39A

The acceleration of the cart of mass $m$ will be twice of the acceleration of the cart of mass $2m$ . Hence, the cart of mass $m$ will move with twice the velocity of the cart of mass $2m$ .

Explanation of Solution

Introduction:

According to Newton’s second law of motion, if the net force $F$ is applied to the mass $m$ , then the acceleration produced is given by,

  $a=\frac{F}{m}$

Now, when given cart system is squeezed, then the force on both the cart will be same. Considering the Newton’s second law of motion, if the force on both the carts is same, then the acceleration of both the carts will be inversely proportional to the masses of the cart.

Conclusion:

Hence, the acceleration and thereby the velocity of the cart of mass $m$ will be twice of that of the cart of mass $2m$ .