A set of crash tests consists of running a test car, moving at a speed of 12.80 m/s into a solid wall. Strapped securely in an advanced seat belt system, a 63.00 kg dummy is found to move a distance of 0.690 m from the moment the car touches the wall until the time the car is stopped. Calculate the size of the average force which acts on the dummy during that time.
To calculate the average force acting on the dummy, you can use Newton's second law of motion, which states that force (F) is equal to the mass (m) of an object multiplied by its acceleration (a):
F = m * a
In this case, the dummy is initially moving at a speed of 12.80 m/s and comes to a stop after moving a distance of 0.690 m. To find the acceleration of the dummy, you can use the equation for uniformly accelerated linear motion:
vf^2 = vi^2 + 2aΔx
Where:
- vf is the final velocity (0 m/s, since the car comes to a stop)
- vi is the initial velocity (12.80 m/s)
- a is the acceleration
- Δx is the displacement (0.690 m)
Rearranging the equation to solve for acceleration:
a = (vf^2 - vi^2) / (2Δx)
Substituting the values:
a = (0 - 12.80^2) / (2 * 0.690)
Calculating the acceleration:
a = (-163.84) / (1.38) = -118.84 m/s²
Since the car hits a wall, the acceleration is negative.
Now, substituting the mass of the dummy (63.00 kg) and the calculated acceleration (-118.84 m/s²) into the equation for force (F = m * a):
F = 63.00 kg * -118.84 m/s²
Calculating the force:
F = -7,486.92 N
Therefore, the size of the average force acting on the dummy during the crash test is approximately 7,486.92 N.