Question

An automobile having a mass of 1,000 kg is driven into a brick wall in a safety test. The bumper behaves like a spring with constant 5.75 ✕ 10^6 N/m and is compressed 3.12 cm as the car is brought to rest. What was the speed of the car before impact, assuming no energy is lost in the collision with the wall?

Answer 1

To solve this problem it is necessary to apply the concepts related to the conservation of energy, specifically the potential elastic energy against the kinetic energy of the body.

By definition this could be described as

$PE = KE$

$\frac{1}{2}kx^2 = \frac{1}{2}mv^2$

Where

k = Spring constant

x = Displacement

m = mass

v = Velocity

This point is basically telling us that all the energy in charge of compressing the spring is transformed into the energy that allows the 'impulse' seen in terms of body speed.

If we rearrange the equation to find v we have

$v = \sqrt{\frac{kx^2}{m}}$

Our values are given as

$m = 1000kg$

$k = 5.75*10^6N/m$

$x = 3.12*10^{-2}m$

Replacing at our equation we have then,

$v = \sqrt{\frac{kx^2}{m}}$

$v = \sqrt{\frac{(5.75*10^6)(3.12*10^{-2})^2}{1000}}$

$v = 2.3658m/s$

Therefore he speed of the car before impact, assuming no energy is lost in the collision with the wall is 2.37m/s