Question

At a race track, a car of mass 2000kg crashes into a concrete wall at a speed of 77m/s. A. The car crashes into the wall, stopping in .08 seconds. What force is applied to the car? B. To make things safer, the race track installs barrels of sand along the wall. They want to reduce the force on a 2000kg car crashing at 77m/s to 500,000N. By what factor must the barrels increase the time of the crash?

Answer 1

A)

Assume that the car changes its speed from 77 m/s to 0 in 0.08 s. Use these data to find the acceleration of the car:

`\begin{gathered} a=(v_f-v_i)/(\Delta t) \\ =(0(m)/(s)-77(m)/(s))/(0.08s) \\ =(-77(m)/(s))/(0.08s) \\ =-962.5(m)/(s^2) \end{gathered}`

According to the Newton's Second Law of Motion, the net force applied to the car is equal to its mass times its acceleration:

The sign of the force is negative, this means that the force is applied in the direction opposite to the movement of the car. Therefore, the force applied to the car is 1,925,000 N in the direction opposite to the movement of the car.

B)

Use the fact that the force is equal to 500,000N to find the new acceleration of the car. Isolate a from the Newton's Second Law of Motion:

Use the value of the acceleration to find the time needed for a car at a speed of 77 m/s to stop:

`\begin{gathered} a=(v_i)/(\Delta t) \\ \Rightarrow\Delta t=(v_i)/(a) \\ =(77(m)/(s))/(250(m)/(s^2)) \\ =0.308s \end{gathered}`

Divide the new time (0.308s) by the old value of the time (0.08s) to find by what factur the barrels must increase the time of the crash:

`(0.308s)/(0.08s)=3.85`

Therefore, the barrels must increase the time of the crash by a factor of 3.85.