A $0.2kg$plastic cart and a $20kg$lead cart can both roll without friction on a horizontal surface. Equal forces are used to push both carts forward for a distance of $1m$, starting from rest. After traveling $1m$, is the momentum of the plastic cart greater than, less than, or equal to the momentum of the lead cart? Explain.

We have given that A $0.2kg$plastic cart and a $20kg$lead cart can both roll without friction on a horizontal surface. Equal forces are used to push both carts forward for a distance of $1m$

We need to find that the momentum of the plastic cart greater than, less than, or equal to the momentum of the lead cart.

Forces, time, and momenta imply the application of the impulse-momentum theorem.

The impulse-momentum theorem describes that to change the momentum of an object, we will exert a net external force on it over a time interval.

$∆\overrightarrow{p}={\overrightarrow{F}}_{avg}∆t$.

Applying Newton's second law, $F=ma$

(having constant force means $a$and $m$are inversely proportional),

The same force applied to the two carts results in

a large acceleration for less massive plastic cart,

enabling it to travel the $1m$distance in a shorter time.

The plastic cart then will have a smaller change in momentum than the lead cart.

Since both had zero initial momentum, the final momentum of each cart is equal to their change in momentum.

The final momentum of the plastic cart is less than that of the lead cart.