A car crashes into a wall at 20 m/s and is brought to rest in 0.1 s. Calculate the average force exerted on a 75 kg test dummy by the seat belt.
Force*time= change in momentum mv
solve for force.
34 n
To solve for the average force exerted on the test dummy by the seat belt, we can use Newton's second law of motion, which states that force equals the rate of change of momentum. The formula can be written as:
Force = (Change in momentum) / (Time)
First, let's find the change in momentum. We know the initial velocity (20 m/s) and the final velocity (0 m/s) of the car when it crashes into the wall. The change in velocity is calculated by subtracting the final velocity from the initial velocity:
Change in velocity = Final velocity - Initial velocity
= 0 m/s - 20 m/s
= -20 m/s
Now, we need to calculate the change in momentum. The formula for momentum is given by:
Momentum = Mass × Velocity
The mass of the test dummy is 75 kg. So, the initial momentum will be:
Initial momentum = Mass × Initial velocity
= 75 kg × 20 m/s
= 1500 kg·m/s
The final momentum will be:
Final momentum = Mass × Final velocity
= 75 kg × 0 m/s
= 0 kg·m/s
Now we can find the change in momentum:
Change in momentum = Final momentum - Initial momentum
= 0 kg·m/s - 1500 kg·m/s
= -1500 kg·m/s
Next, we need to calculate the average force exerted on the test dummy by the seat belt. We know the time taken for the car to be brought to rest is 0.1 s. Plugging the values into the formula:
Force = Change in momentum / Time
= (-1500 kg·m/s) / 0.1 s
= -15000 N
The negative sign indicates that the force is acting in the opposite direction of the car's motion (deceleration).
Therefore, the average force exerted on the 75 kg test dummy by the seat belt is 15000 Newtons (N).