At the instant in part (a) when the mass has moved downward a distance of 0.04 m, the speed of the mass has decreased to 1.39 m/s. How much work was done on the mass by the spring? Include the appropriate sign. Work done by spring

ΔEP = -1.36 J

Explanation:

Given:

- The complete question is as follows:

" A mass of 0.105 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 5.20 m/s. "

Find:

When the mass has moved downward a distance of 0.04 m, the speed of the mass has decreased to 1.39 m/s.

Solution:

- The initial velocity of the system vi = 5.20 m/s

- The mass m = 0.105 kg

- The final velocity of mass vf = 1.39 m/s

- Change in distance d = 0.04m

Solution:

- When the mass (m) is moved down by (d) the work-done by gravity P.E translates to change in kinetic energy K.E and elastic potential energy of the spring EP . The energy balance can be set as:

                               ΔEP + P.E = ΔK.E  

                                ΔEP + m*g*h = 0.5*m*(vf^2-vi^2)

                               ΔEP = 0.5*m*(vf^2-vi^2) - m*g*h

                               ΔEP = 0.105* (- 9.81*0.04 + 0.5*(1.39^2-5.2^2) )

                               ΔEP = - 1.36 J

- Since, The work done by spring is negative because the displacement is downwards and the force is upwards.

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