Question

An mm = 3.50 kg block starts from rest and slides down a friction-less incline, dropping a vertical distance of y = 2.60 m, compressing a spring at the bottom of the incline. The spring has a force constant of k = 2.50 ×10⁴ N/m. Find the maximum compression of the spring.

Part 1 +

Give an algebraic expression for finding the maximum compression of the spring in terms of mm, g, y, and k.

x =

Part 2

Find the maximum compression of the spring.

Answer 1

Given that mass, m = 3.50 kg

Vertical distance it has descended, h = 2.60 m

Spring constant of the spring, k = 2.50 x 10^4 N/m

Part 1 -

Suppose maximum compression in the spring = x

So, potential energy lost by the mass, PE = m*g*h

Energy stored in the spring as a form of spring energy, SE = (1/2)*k*x^2

Apply conservation of energy -

PE = SE

=> m*g*h = (1/2)*k*x^2

=> x^2 = (2*m*g*h) / k

=> x = sqrt [(2*m*g*h) / k] (Answer)

Part -2 -

Plug-in the variables in part -1 -

x = sqrt [(2*3.50*9.81*2.60) / (2.50 x 10^4)] = 0.0845 m = 84.5 mm (Answer)