A spring with a force constant of 225 N/m is resting on a friction-less surface and mounted against a wall horizontally. A 1.5 kg box is pushed against the spring and compresses it 12 cm (0.12m) from equilibrium. When released the spring pushes the box across the surface.
F = kx
W = FΔd
Ee = 1/2 k x^2
Ek = 1/2 m v^2
The Attempt at a Solution
a) How much force needs to be applied to the spring to compress it to 12 cm (0.12m)?
F = 225 x 0.12 = 27 N
b) How much work is done to compress the spring to 12 cm?
W = 27 x 0.12 = 3.24 J
c) How much elastic energy is stored in the spring when compressed?
Ee = 1/2 x 225 x 0.12^2 = 1.62 J
Question: Is it normal that Ee is less than the work energy applied to the system in b)?
d) What maximum speed will the box attain once released?
1.62 = 1/2 x 1.5 x v^2
1.62/0.75 = v^2
v = 1.47 m/s
** not sure about this because I might be using a wrong Ek obtained in c) **
Thanks in advance.