Please Read the Question Below !

Question

A block of mass 0.243 kg is placed on top of a light, vertical spring of force constant 4 975 N/m and pushed downward so that the spring is compressed by 0.097 m. After the block is released from rest, it travels upward and then leaves the spring. To what maximum height above the point of release does it rise? (Round your answer to two decimal places.)

______m

Answer 1

What you know:

m = 0.243 kg

k = 4975 N/m

x_i = 0.097 m

v_i = 0 m/s

x_f = 0 m

h_i = 0 m

v_f = 0 m/s

h_f = ?

This a conservation of energy question:

E_i = E_f

PE_gi + PE_si + KE_i = PE_gf + PE_si + KE_f

mgh_i + 0.5kx_i² + 0.5mv_i² = mgh_f + 0.5kx_i² + 0.5mv_f²

0.243(9.8)(0) + 0.5(4975)(0.097)² + 0.5(0.243)(0)^2 = 0.243(9.8)h_f + 0.5(4975)(0)² + 0.5(0.243)(0)^2

23.40 = 2.38h_f

9.83 m = h_f

The height above the point of release is:

9.83 m - 0.097 m = 9.73 m