Question

A block of ice of mass 3.90 kg is placed against a horizontal spring that has force constant k = 230 N/m and is compressed a distance 2.40×10−2 m . The spring is released and accelerates the block along a horizontal surface. You can ignore friction and the mass of the spring.

A. Calculate the work done on the block by the spring during the motion of the block from its initial position to where the spring has returned to its uncompressed length.

B. What is the speed of the block after it leaves the spring?

Answer 1

0.184 m/s

Step-by-step explanation:

Suppose the spring is compressed by a distance of
`x = 2.4*10^(-2)m` or 0.024 m. Then the work done by the spring when it go from initial position to the uncompressed position is

`W = kx^2/2 = 230*0.024^2/2 = 0.06624 J`

According to the law of energy conservation, this work done by the spring would be converted to kinetic energy of the block when it leaves the spring

`E_k = mv^2/2 = 0.06624`

`v^2 = 2*0.066624 / 3.9 = 0.034`

`v = √(0.034) = 0.184 m/s`