You compress a spring with k = 3000 N/m a distance of 0.2 m with a block of mass

Question

You compress a spring with k = 3000 N/m a distance of 0.2 m with a block of mass 4 kg. You then release the block. It slides along a frictionless surface and then goes up an incline of 35 degrees.

A. What is the velocity of the block after it leaves the spring but before it gets to the incline?

B. How far up the incline (along the hypotenuse of the triangle) does the block travel?

You have the same spring and same mass as #1. You compress the spring 0.3 m and release the block. After being released, the block hits a rough surface with a coefficient of friction of 0.6. How far does the block travel across the rough surface before it comes to a stop?

Explanation / Answer

A) initial spring is compressed so system have spring potential energy.

that completely converted into KE of block.

using energy conservation,

kx^2 /2   = mv^2 /2

3000 (0.2^2) = 4 v^2

v = 5.48 m/s

B) now this KE converts into gravitational PE.

mv^2 /2 = mgh

5.48^2 = 2 x 9.8 x h

h = 1.53 m

h = d sin35

d = 1.53 / sin35 = 2.67 m

--------------------------------

In this case block will until its all spring PE dissipated into work against friction .

friction force = uN = 0.6mg

work done by friction = initial spring PE

f.d = k x^2 /2

0.6mg d = 3000 (0.3^2) /2

0.6 x 4 x 9.8 x d = 135

d = 5.74 m

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