A mass of 0.072 kg hangs from a vertical spring in the lab room. You pull down o

Question

A mass of 0.072 kg hangs from a vertical spring in the lab room. You pull down on the mass and throw it vertically downward. The speed of the mass just after leaving your hand is 4.60 m/s.

(a) While the mass moves downward a distance of 0.05 m, how much work was done on the mass by the Earth? Include the appropriate sign.
Work done by Earth = ___________J

(b) The speed of the mass has decreased to 3.63 m/s. How much work was done on the mass by the spring? Include the appropriate sign.
Work done by spring = ____________J

Explanation / Answer

W=F*d
(W=work, F=force, d=distance on which the force is applied)

Part 1:
d = 0.04m
F = ma = mg (only taking into consideration the work done by gravity, not the net work)
W = mgd = 0.072*9.81*0.05 = 0.0353 Nm

Part 2:
Let Fs be the force with which the spring is pulling the mass up and Fg the gravitational force acting on the spring(pulling down). Then Fs+Fg=ma (Note:here we consider the net acceleration). It is important to note here the direction of those forces and acceleration. Fs is upwards, Fg downwards and a upwards. For convenience, I will have the downward direction positive.
Fg = mg = 0.942 N
a = (vf^2 - vi^2)/2d = -154.375 m/s^2 , vf=final velocity and vi=initial velocity (note the negative sign means the mass is accelerating upwards)

Fs = ma - Fg = 0.072*(-154.375) - 0.942
Fs = -12.057 N (the negative sign indicates the force acting on the mass is directed upwards)

Ws = Fs*d
Ws = 0.6 Nm

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.