Question

A 0.2 kg plastic cart and a 20 kg lead cart both roll without friction on a horizontal surface. Equal forces are used to push both carts forward for a time of 1 s, starting from rest. Is the momentum of the plastic cart greater than, less than, or equal to the momentum of the lead cart? Explain in complete sentences.

Answer 1

Answer:

Equal

Explanation:

The impulse theorem states that the impulse exerted on each cart is equal to the change in momentum of the cart:

$I=\Delta p=p_f -p_i$

where

I is the impulse

pf is the final momentum

pi is the initial momentum

The impulse is equal to the product between the force applied and the contact time:

$I=F\Delta t$

In this case, the force applied to the two carts (F) is the same, and the contact time ($\Delta t$) is the same as well. Therefore, the impulse exerted on the two carts is the same.

Moreover, the initial momentum of the two carts is also the same (zero, because they start from rest: $p_i=0$). So the formula becomes

$p_f = I$

And since I is the same for the two carts, the final momentum ($p_f$) will also be equal.