Momentum Review: Force & Time for Rhonda's Brakes/Windshield

[andthismeans]

Homework Statement

Rhonda, who has a mass of 60.0 kg, is riding at 25.0 m/s in her sports car when she suddenly slams on the brakes to avoid hitting a dog crossing the road. She is wearing her seat belt, which brings her body to a stop in 0.400s. What average force did the seat belt exert on her body? If she had not been wearing her seat belt, and the windshield had stopped her head in 1.0 X 10^-3s, what average force would the windshield have exerted on her?

Homework Equations

The only ones I know is P_i = P_f
[mv_1i + mv_2i = mv_1f + mv_2f] <---I don't know this as well
P = momentum i = initial f = final 1 = mass of first object 2 = mass of second object

The Attempt at a Solution

I don't know where force and time come in so I don't know how to start/finish it. Do I need another formula. If so, that's all the information I would need.

 

[LowlyPion]

Welcome to PF.

Consider that Force can also be expressed as the change in momentum (p) divided by the time over which it changes.

F = ma = Δp/Δt

 

[thomate1]

I can provide a response to this content by using the concepts of momentum, force, and time.

Firstly, we can use the equation P = mv, where P is momentum, m is mass, and v is velocity. Since Rhonda has a mass of 60.0 kg and is traveling at a velocity of 25.0 m/s, her initial momentum can be calculated as:

P_initial = 60.0 kg x 25.0 m/s = 1500 kg·m/s

When Rhonda slams on the brakes, her velocity decreases to 0 m/s in a time of 0.400s. This means that her final momentum is 0 kg·m/s.

Using the principle of conservation of momentum, we can equate the initial and final momenta:

P_initial = P_final

Thus, we can calculate the average force exerted by the seat belt on Rhonda's body as:

F = (P_initial - P_final)/t = (1500 kg·m/s - 0 kg·m/s)/0.400 s = 3750 N

This means that the seat belt exerted an average force of 3750 N on Rhonda's body to bring her to a stop in 0.400 s.

If Rhonda had not been wearing her seat belt and the windshield had stopped her head in 1.0 x 10^-3 s, we can calculate the average force exerted by the windshield on her head using the same formula:

F = (P_initial - P_final)/t = (1500 kg·m/s - 0 kg·m/s)/(1.0 x 10^-3 s) = 1.5 x 10^6 N

This means that the windshield would have exerted an average force of 1.5 x 10^6 N on Rhonda's head if she had not been wearing her seat belt. This is a much larger force compared to the force exerted by the seat belt, highlighting the importance of wearing a seat belt while driving.