A car moving at 10 m/s crashes into a tree and stops in 0.26 s. Calculate the force the seat belt exerts on a passenger in the car to bring him to a halt. The mass of the passenger is 70 kg.
To calculate the force exerted by the seat belt on the passenger, we can use Newton's second law of motion, which states that force is equal to mass times acceleration.
First, we need to determine the acceleration of the car. We can use the formula:
acceleration = (final velocity - initial velocity) / time
Since the car comes to a stop, the final velocity is 0 m/s and the initial velocity is 10 m/s. The time is 0.26 s.
acceleration = (0 m/s - 10 m/s) / 0.26 s
acceleration = -38.46 m/s^2 (note the negative sign indicates deceleration)
Next, we can calculate the force exerted by the seat belt using the formula:
force = mass * acceleration
force = 70 kg * -38.46 m/s^2
Thus, the force exerted by the seat belt on the passenger to bring him to a halt is approximately -2692 N. The negative sign indicates that the force is in the opposite direction to the motion of the car.
To calculate the force exerted by the seat belt on the passenger, we can use Newton's second law of motion, which states that force is equal to mass multiplied by acceleration (F = m*a).
First, let's calculate the acceleration of the car using the formula for acceleration:
acceleration = (final velocity - initial velocity) / time
Given:
Initial velocity (vi) = 10 m/s
Final velocity (vf) = 0 m/s
Time (t) = 0.26 s
Using the formula:
acceleration = (0 - 10) / 0.26
acceleration = -38.46 m/s^2
The negative sign indicates that the car decelerated.
Now, let's substitute the mass of the passenger (m = 70 kg) and the calculated acceleration (a = -38.46 m/s^2) into Newton's second law of motion:
Force (F) = mass (m) * acceleration (a)
Force (F) = 70 kg * -38.46 m/s^2
Therefore, the force exerted by the seat belt on the passenger to bring him to a halt is approximately -2692.2 N (remember to include the negative sign to indicate the direction of the force, opposite to the motion of the car).