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.

what type of charge does it have? negative

this is poiselle's equation from fluid mechanic in physics. mech eng