This question has three parts: A set of crash tests consists of running a test c

Question

This question has three parts:

A set of crash tests consists of running a test car moving at a speed of 10.6 m/s (23.7 mi/hr) into a solid wall. Strapped securely in an advanced seat belt system, a 57.0 kg (126 lbs) dummy is found to move a distance of 0.750 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.

Using the direction of motion as the positive direction, calculate the average acceleration of the dummy during that time (in g's, with 1g = 9.81m/s2).

In a different car, the distance the dummy moves while being stopped is reduced from 0.750 m to 0.270 m,
calculate the average force on the dummy as that car stops.

Explanation / Answer

for the first problem you need to set two equations for energy. for the car moving the energy pf the dummy is equal to 1/2mv^2 and for the dummy stopping it is equal to d*f=d*m*a
the only unknown is acceleration.
0.5m*v^2=d*m*a well m=m so they leave the equation...
0.5*v^2=d*a
0.5V^2/d=a
(0.5*(10.6 m/s)^2)/0.75m=74.9 m/s^2 = about 7.64g

0 = v^2 + 2as

0 = 10.6^2 + 2a*.27

a = - 10.6^2/(2*.27)

= - 208.07 m/s^2

F = 57*a

= 11860N

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