Question

A) A set of crash tests consists of running a test car moving at a speed of 11.8 m/s (26.0 m/h) into a solid wall. Strapped securely in an advanced seat belt system, a 57.0 kg (125.4 lbs) dummy is found to move a distance of 0.840 m from the moment the car touches the wall to the time the car is stopped. Calculate the size of the average force which acts on the dummy during that time.

B) Using the direction of motion as positive direction, calculate the average acceleration of the dummy during that time (in g's) (use 1g=9.8 m/s²).

C) In a different car, the distance the dummy moves while being stopped is reduced from 0.840 m to 0.270 m calculate the average force on the dummy as that car stops.

Answer 1

a) W = delta KE = 1/2 m (v₂² - v₁²)

= 1/2 * 57 * (0 - 11.8²) = -3968 J

F = W / d = -3968 / 0.840

average force = -4724 N = -4.72 * 10³ N

b) a = F / m = -4724 / 57

= -82.88 g / 9.8

average acceleration = - 8.46 g

c) F = W / d = -3968 / 0.270

= -1.46 * 10⁴ N