Question

A mass resting on a horizontal, frictionless surface is attached to one end of a spring; the other end is fixed to a wall. It takes 3.2 J of work to compress the spring by 0.11 m . If the spring is compressed, and the mass is released from rest, it experiences a maximum acceleration of 12 m/s2. Find the value of the spring constant and (b) the mass?

Answer 1

Answer:

a).$K=528.92 \frac{N}{m}$

b).$m=4.84kg$

Explanation:

a).

The work of the spring is find by the formula:

$w_s =\frac{1}{2}*k*x^2$

So knowing the work can find the constant K'

$3.2J =\frac{1}{2}*k*(0.11m)^2$

Solve for K'

$K=\frac{2*W_s}{x^2}=\frac{2*3.2J}{0.11m^2}$

$K=528.92 \frac{N}{m}$

b).

The force of the spring realice a motion so using the force and knowing the accelerations can find the mass

$F=m*a$

$m=\frac{F}{a}=\frac{K*x}{a}$

$m=\frac{528.9*0.11m}{12m/s^2}$

$m=4.84kg$