Question

A spring is compressed by 50 cm from it's equilibrium length by an unattached block of mass 5.0 kg (the spring constant is 400 N/m). The box is released from rest, slides along a friction-less surface for a time, and then ascends a ramp of length 10 m, which is inclined at an angle of 20 degrees above the horizontal. What is the maximum distance that the box travels up the ramp?

Answer 1

L = 2.98 m

Step-by-step explanation:

In this exercise we are told that there is no friction, so we can use energy conservation

Starting point. Compressed spring

Em₀ = Ke = ½ k x²

Final point. At the highest point of the ramp

`Em_(f)` = U = mg h

As there is no friction the energy is conserved

Emo = Em_{f}

½ k x² = mg h

h = ½ k x² / mg

h = ½ 400 0.50² / (5.0 9.8)

h = 1.02 m

This is the height that the body reaches, to calculate the distance traveled on the ramp let's use trigonometry

sin θ = h / L

L = h / sin θ

L = 1.02 / sin 20

L = 2.98 m