Question

A 30.0 kg block is released at the top of a 20° frictionless incline. The block slides down the incline and compresses a spring (k=800 N/m) by 0.75 meters. What is the total distance the block traveled?

It should be 1.5m

Answer 1

Here,

let the total distance traveled is x

Now, distance moved down the incline is (x - 0.75)

Using conservation of energy

increase in spring

0.50 * k * x^2 = m * g * (x)* sin(20 degree)

0.50 * 800 * 0.75^2 = 30 * 9.8 * (x) * sin(20 degree)

solving for x

x = 2.25 m

the total distance traveled is 2.25 m