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?

Answer 1

-2200 N

Step-by-step explanation:

Here we can use the impulse theorem, which states that the impulse exerted on Sarah (product of force and duration of collision) is equal to Sarah's change in momentum:

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

where

F is the average force

`\Delta t` is the duration of the collision

m is the mass

`\Delta v` is the change in velocity

In this problem:

m = 55 kg

`\Delta v = 0-20 = -20 m/s`

`\Delta t = 0.5 s`

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

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

And the negative sign means the direction is opposite to that of Sarah's initial motion.