Answer:
The magnitude of the average force the seat belt exerts on the passenger is 2692.3 N.
It takes 0.26 s to bring the passenger in the car to a halt.
Explanation:
Hi there!
The negative work (W) needed to bring a moving object to stop is equal to its kinetic energy (KE):
W = KE
F · s = 1/2 · m · v²
Where:
F = applied force on the passenger.
s = displacement of the passenger.
m = mass of the passenger.
v = velocity of the passenger.
Solving the equation for F:
F = 1/2 · m · v² / s
Replacing with the data:
F = 1/2 · 70 kg · (10 m/s)² / 1.3 m
F = 2692.3 N
The magnitude of the average force the seat belt exerts on the passenger is 2692.3 N.
According to the second law of Newton:
F = m · a
Where "a" is the acceleration of the passenger.
We also know from kinematics that the velocity of an object can ve calculated as follows:
v = v0 + a · t
Where:
v = velocity of the passenger at time t.
v0 = initial velocity.
t = time.
a = acceleration.
When the passenger stops, its velocity is zero. So replacing a = F/m, let´s solve the equation for the time it takes the passenger to stop:
v = v0 + a · t
0 = 10 m/s + (-2692.3 N/ 70 kg) · t
-10 m/s / (-2692.3 N/ 70 kg) = t
t =0.26 s
It takes 0.26 s to bring the passenger in the car to a halt.
