Question

A runaway railroad car with mass 3.0 ✕ 105 kg coasts across a level track at 2.0 m/s when it collides elastically with a spring-loaded bumper at the end of the track. If the spring constant of the bumper is 2.0 ✕ 106 N/m, what is the maximum compression of the spring during the collision?

Answer 1

Answer:

Maximum compression = 77.5cm

Explanation:

We are given that;

mass; m = 3 x 10^(5) m/s

Speed; v = 2 m/s

Spring Constant; k = 2 x10^(6) N/m

From conservation of energy. Kinetic energy is transformed into potential energy of spring

Kinetic energy = (½)mv ²

Elastic potential energy of spring = (½)kΔx²

Thus,

(½)mv² = (½)kΔx²

1/2 will cancel out and we have;

mv² = kΔx²

Now we are looking for maximum compression which is Δx, so let's make Δx the subject of the formula;

Δx² = mv²/k

Δx = √(mv²/k)

Plugging in relevant values;

Δx = √((3 x 10^(5) x 2²)/2 x10^(6))

Δx = √(0.6) = 0.775 m ≈ 77.5 cm