Chapter 8, Problem 49A

If a fully loaded shopping cart and an empty one traveling at the same speed have a head-on collision, which cart will experience the greater force of impact? The greater impulse? The greater change in momentum? The greater acceleration?

To determine

The cart which would experience greater force of impact, greater impulse, greater change in momentum and greater acceleration.

Explanation of Solution

Introduction:

According to Newton’s second law of motion, if external force is zero then the linear momentum is conserved.

Action and reaction have equal magnitude but act in opposite direction according to the Newton’s third law of motion.

The impulse is defined as the product of the force acting on the object 1 from object 2 and time of contact between the objects.

Each cart experiences equal magnitude of force according to the third law of motion but both have same change in momentum due to conservation of linear momentum.

The impulse is product of force and time. As the time of contact and force is same for both the carts. Thus, the impulse force is same for both loaded and empty cart.

Change in the momentum is defined as impulse. Since the impulse is same for both the carts thus, change in momentum will also be same for both the carts.

The fully loaded shopping cart has smaller acceleration because the acceleration inversely varies with the mass. The empty cart has the greater acceleration as compared to the loaded cart.

Conclusion:

The force, impulse and change in momentum will be same for both the carts but, the empty shopping cart has greater acceleration than that of the loaded cart.