A mass sitting on a horizontal, frictionless surface is attached to one end of a spring; the other end is fixed to a wall. 3.0 J of work is required to compress the spring by 0.12 m. If the mass is released from rest with the spring compressed, the mass experiences a maximum acceleration of 15 m/s2 Find the value of (a) the spring stiffness constant and (b) the mass.

Given Information:  

Work done = W = 3.0 J

compressed length = x = 0.12 m

acceleration = α = 15 m/s²

Required Information:  

(a) spring constant = k = ?

(b) mass = m = ?  

(a) spring constant = 416.67

(b) mass = 3.33 kg

Explanation:  

(a)

We are given a mass spring system,

We know that work done is given by

W = ½kx²

Where W is the work done, k is the spring constant and x is the compressed length of the spring.

Re-arranging the equation for spring constant k yields,

k = 2W/x²

k = 2*3/0.12²

k = 416.67

We know that force is given by

F = kx

We also know from the Newton's second law that

F = mα

equating both equations yields,

mα = kx

m = kx/α

m = (416.67*0.12)/15

m = 3.33 kg

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