# Problem with box and string

by GingerKhan
Tags: string
 P: 14 1. The problem statement, all variables and given/known data 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. 2. Relevant equations F = kx W = FΔd Ee = 1/2 k x^2 Ek = 1/2 m v^2 3. 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.
 P: 950 [QUOTE=GingerKhan;3613702] ... 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)? ... Note that the force doing the work is varying and so an AVERAGE value of the force must be taken.
PF Gold
P: 960
 Quote by GingerKhan b) How much work is done to compress the spring to 12 cm? W = 27 x 0.12 = 3.24 J
This is not correct. You can only use "work equals force times distance" on the whole distance if both are constant. If they are not you must integrate the work up from the instantaneous force as a function of distance, e.g. W = ∫F(s)*ds, where s is distance.

In the context of this problem you may also solve b) by using conservation of energy. The original kinetic energy from the block must all be stored in the spring since there is no friction and nothing else moves, hence the block does the amount of work on the spring equal to its kinetic energy, which again is equal to the potential energy right after compression.

Emeritus