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?
To find the average force exerted by the seat belt on Jennifer, we can use the equation:
Force = (mass * final velocity - mass * initial velocity) / time
1. Rearranging the equation, we have:
Force = mass * (final velocity - initial velocity) / time
2. Plugging in the given values:
mass = 50.0 kg
initial velocity = 35.0 m/s (since she slams on the brakes, her initial velocity is her speed before braking)
final velocity = 0 m/s (since she comes to a stop)
time = 0.500 s
3. Substituting in the values, we have:
Force = 50.0 kg * (0 m/s - 35.0 m/s) / 0.500 s
4. Evaluating the expression, we find:
Force = -50.0 kg * (-35.0 m/s) / 0.500 s
= 50.0 kg * 35.0 m/s / 0.500 s
= 3500 N
Therefore, the average force exerted by the seat belt on Jennifer is 3500 N.
To find the average force exerted by the windshield on Jennifer if she had not been wearing her seat belt, we can use the same equation:
Force = (mass * final velocity - mass * initial velocity) / time
1. Rearranging the equation, we have:
Force = mass * (final velocity - initial velocity) / time
2. Plugging in the given values:
mass = 50.0 kg (same as before)
initial velocity = 35.0 m/s (same as before)
final velocity = 0 m/s (same as before)
time = 0.002 s
3. Substituting in the values, we have:
Force = 50.0 kg * (0 m/s - 35.0 m/s) / 0.002 s
4. Evaluating the expression, we find:
Force = -50.0 kg * (-35.0 m/s) / 0.002 s
= 50.0 kg * 35.0 m/s / 0.002 s
= 875000 N
Therefore, the average force exerted by the windshield on Jennifer if she had not been wearing her seat belt would be 875000 N.
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):
F = m * a
In this case, the acceleration can be calculated using the equation for average acceleration:
a = (final velocity - initial velocity) / time
Since Jennifer's final velocity is 0 m/s (she comes to a stop), her initial velocity is 35.0 m/s, and the time it takes for her to come to a stop is 0.500 s, we can substitute these values into the equation:
a = (0 - 35.0) / 0.500 = -70.0 m/s²
Now we can calculate the force exerted by the seat belt by multiplying Jennifer's mass by the acceleration:
F = 50.0 kg * (-70.0 m/s²) = -3500 N
The negative sign indicates that the force is directed opposite to the motion, which makes sense since the seat belt is decelerating Jennifer.
If Jennifer hadn't been wearing her seat belt and not had an airbag, her head would have hit the windshield. To find the average force exerted on Jennifer by the windshield, we can use the same formula:
F = m * a
This time, the acceleration can be calculated using the equation for average acceleration:
a = (final velocity - initial velocity) / time
Since Jennifer's final velocity is 0 m/s (she comes to a stop), her initial velocity is 35.0 m/s, and the time it takes for her head to come to a stop is 0.002 s, we can substitute these values into the equation:
a = (0 - 35.0) / 0.002 = -17500 m/s²
Now we can calculate the force exerted on Jennifer's head by multiplying her mass by the acceleration:
F = 50.0 kg * (-17500 m/s²) = -875000 N
Again, the negative sign indicates that the force is directed opposite to the motion, which in this case is toward the windshield.
a = 35/.5 = 70 m/s^2
F = m a = 50*70 = 3500 Newtons
a = 35/.002 = 17500
F = m a = 50 * 17500 = 875,000 Newtons (not good for head)