# Spring / ramp energy problem

• jwxie
In summary, the problem involves a 200-g block pressed against a spring of force constant 1.40 kN/m, compressing the spring by 10.0 cm. The spring is located at the bottom of a ramp inclined at 60.0deg to the horizontal. Using energy considerations, the task is to determine the distance the block travels up the incline before stopping, with and without friction. When there is no friction, the initial potential energy of the block at the highest point is equal to the final kinetic energy of the compressed spring. The assumption is made that the initial kinetic energy of the block is zero. When there is friction, the energy stored in the spring is converted into potential and kinetic energy, and the

## Homework Statement

A 200-g block is pressed against a spring of force constant 1.40 kN/m until the block compresses the spring 10.0 cm. The spring rests at the bottom of the ramp inclined at 60.0deg to the horizontal.

Using energy considerations, determine how far up the incline the block moves before it stops (a) if there is no friction between the block and the ramp and (b) if the coefficient of kinetic friction is 0.400.

## Homework Equations

Delta KE = Delta PE

## The Attempt at a Solution

Okay, since the system is conservered with no fricition, I can assume that
initial energy = final energy, and we can rewrite it as
PE initial (of the block at the highest point) = KE final (of the spring as it gets compressed for 0.01 meter)

PE initial = KE final
X is the length the block travels from its original position
(mg*sin60 * X) = 1/2 * k * (0.01m^2)

And then I was wondering why do we assume that the initial KE of the block is zero? The problem did not state that there was no initial velocity for the block.

Energy store in the spring is
E = 1/2*k*x^2.
When the block detaches from the spring, stored energy in the spring in converted into PE and KE. The PE is m*g*x*sinθ, where x is the compression of the spring.
Now you get the initial velocity. final velocity is zero. Find the distance traveled by the block along the ramp.

hi, thanks. i was so dump did not consider its reverse condition.
thanks!