A set of crash tests consists of running a test car moving at a speed of 11.6 m/s (25.52 m/h) into a solid wall. Strapped securely in an advanced seat belt system, a 61 kg (134.2 lbs) dummy is found to move a distance of 0.69 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.
force = change of momentum/change of time
change of momentum = -61 * 11.6 = - 708 kg m/s
time:
moved .69 meters at average speed of 11.6/2
so .69/5.8 = .119 second
so
force = -(708 kg m/s) / .119 s
= 5948 kg m/s^2 or Newtons
To calculate the size of the average force acting on the dummy, you can use Newton's second law of motion, which states that the force (F) acting on an object is equal to the mass (m) of the object multiplied by its acceleration (a). In this case, the acceleration can be determined using the following kinematic equation:
v^2 = u^2 + 2as
Where:
v = final velocity (0 m/s, since the car is stopped)
u = initial velocity (11.6 m/s)
a = acceleration
s = displacement (0.69 m)
Rearranging the equation to solve for the acceleration (a):
a = (v^2 - u^2) / (2s)
Substituting the given values:
a = (0^2 - 11.6^2) / (2 * 0.69)
a ≈ -207.62 m/s²
The negative sign indicates that the acceleration is in the opposite direction to the initial velocity. Now, you can calculate the force (F) using Newton's second law:
F = m * a
Substituting the given mass of the dummy:
F = 61 kg * (-207.62 m/s²)
F ≈ -12,675.82 N
The negative sign indicates that the average force acting on the dummy is directed opposite to the initial motion of the car. However, since force is a vector quantity, you can simply take the magnitude of the force, which is equal to the absolute value:
|F| ≈ 12,675.82 N
Therefore, the size of the average force acting on the dummy during the crash test is approximately 12,675.82 Newtons.