Question

Sarah, who has a mass of 55 kg, is riding in a car at 20 m/s. She sees a cat crossing the street and slams on the brakes! Her seatbelt stops her from flying forward, bringing her to rest in 0.5 seconds. How much force did the seatbelt put on Sarah?

plz explain

Answer 1

-2200 N

Explanation:

The change in momentum of Sarah is equal to the impulse, which is the product between the force exerted by the seatbelt on Sarah and the time during which the force is applied:

`\Delta p=I\\m \Delta v = F \Delta t`

where

m is the mass

`\Delta v` is the change in velocity

F is the average force

`\Delta t` is the duration of the collision

In this problem:, we have:

m = 55 kg is Sarah's mass

`\Delta v = 0-20 = -20 m/s` is the change in velocity

`\Delta t = 0.5 s` is the duration of the collision

Solving for F, we find the force exerted by the seatbelt on Sarah:

`F=(m\Delta v)/(\Delta t)=((55)(-20))/(0.5)=-2200 N`

Where the negative sign indicates that the direction of the force is opposite to that of Sarah's initial velocity.