Question

A 2kg block is released 4m from a massless spring with a forceconstant k=100N/m that is fixed along a frictionless plane inclinedat 30degree.

a) Find the maximum compression of the spring
b) If the plane is not frictionless and the coefficient of kineticfriction between it and the block is 0 .2 find the maximumcompression
c) For the rough incline, how far up the incline will the blocktravel after leaving the spring?

Answer 1

The maximum compression of the spring is 1.76 meters.

Step-by-step explanation:

To find the maximum compression of the spring, we can use the concept of potential energy. The potential energy of the block-spring system is given by the equation:

PE = (1/2)kx^2

where PE is the potential energy, k is the force constant of the spring, and x is the compression or extension of the spring. At maximum compression, the potential energy is equal to the gravitational potential energy of the block at the release height:

mgh = (1/2)kx^2

where m is the mass of the block, g is the acceleration due to gravity, and h is the height of the block above the release position.

Using the given values, we can calculate the maximum compression of the spring:

x = sqrt((2mgh)/k)

Substituting the given values, we get:

x = sqrt((2 * 2 * 9.8 * 4) / 100) = 1.76 m

Therefore, the maximum compression of the spring is 1.76 meters.