A 0.45 kg mass sliding on a horizontal frictionless surface is attached to one e
ID: 1331404 • Letter: A
Question
A 0.45 kg mass sliding on a horizontal frictionless surface is attached to one end of a horizontal spring (with k = 575 N/m) whose other end is fixed. The mass has a kinetic energy of 18.0 J as it passes through its equilibrium position (the point at which the spring force is zero). At what rate is the spring doing work on the mass as the mass passes through its equilibrium position? At what rate is the spring doing work on the mass when the spring is compressed 0.125 m and the mass is moving away from the equilibrium position?
Explanation / Answer
At what rate is the spring doing work on the mass as the mass passes through its equilibrium position?
Rate of Workdone = F*dx/dt
= 0 (since Force exerted by spring is zero at equibrium point)
At what rate is the spring doing work on the mass when the spring is compressed 0.125 m and the mass is moving away from the equilibrium position?
Let v is the speed of block at x = 0.125 m
Total Energy = KE + PE
18 = 0.5*m*v^2 + 0.5*k*x^2
18 = 0.5*0.45*v^2 + 0.5*575*0.125^2
18 = 0.225*v^2 + 4.492
V^2 = (18 - 4.492)/0.225
v = sqrt( (18 - 4.492)/0.225 )
= 7.5 m/s
Force exerted by spring, F = k*x
= 575*0.125
= 71.875 N
Rate of workdone, W = F*dx/dt
= F*v
= 71.875*7.5
= 539 W
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