Jennifer, who has a mass of 50.0 kg, is riding at 35.0 m/s in her red sports car when she must suddenly slam on the brakes to avoid hitting a deer crossing the road. She strikes the air bag that brings her body to a stop in 0.500 s. What average force does the seat belt exert on her? If Jennifer had not been wearing her seat belt and not had an air bag, then the windshield would have stopped her head in 0.002 s. What average force would the windshield have exerted on her?

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To find the average force exerted on Jennifer by the seat belt, we can use Newton's second law of motion, which states that force (F) is equal to mass (m) multiplied by acceleration (a). In this case, the acceleration is the change in velocity (Δv) divided by the time it takes to stop (Δt).

First, let's find the change in velocity (Δv) for Jennifer when she comes to a stop. Her initial velocity (vi) is 35.0 m/s, and her final velocity (vf) is 0 m/s because she comes to a stop.

Δv = vf - vi
Δv = 0 m/s - 35.0 m/s
Δv = -35.0 m/s

Next, we can find the acceleration (a) using the formula:

a = Δv / Δt
a = -35.0 m/s / 0.500 s
a = -70.0 m/s²

Since the acceleration is negative, it means that Jennifer experiences deceleration (opposite direction to her initial motion).

Now, we can calculate the force (F) exerted by the seat belt using the formula:

F = m * a
F = 50.0 kg * -70.0 m/s²
F = -3500 N

The negative sign indicates that the force is in the opposite direction to Jennifer's motion. However, since force is a vector quantity, we can ignore the negative sign and say that the average force exerted by the seat belt on Jennifer is approximately 3500 Newtons.

If Jennifer had not been wearing her seat belt and her head hit the windshield, we can use the same formulas to find the average force exerted by the windshield on her.

Δv = vf - vi
Δv = 0 m/s - 35.0 m/s
Δv = -35.0 m/s

a = Δv / Δt
a = -35.0 m/s / 0.002 s
a = -17500 m/s²

F = m * a
F = 50.0 kg * -17500 m/s²
F = -875000 N

Again, the negative sign indicates that the force is in the opposite direction to Jennifer's motion. Ignoring the negative sign, the average force exerted by the windshield on Jennifer would be approximately 875000 Newtons.