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.

he kicked it 10 feet straight up into the air? i think this works.

air exerts forces on falling objects near earth’s surface.

explanation:

the term 'free falls' refer to object that are falling towards the earth, in a situation in which gravity is the only force acting on the object.

for an object in free fall, the acceleration is constant (g, the gravitational acceleration), and so the velocity of the object constantly increases.

for objects near earth's surface, there is always another force acting on the object: the resistance due to the air. this force is opposed to the direction of fall of the object, and it is proportional to the velocity of the object, so as the object falls down, this force increases up to a point when it balances the force of gravity, and the object continues its motion at constant velocity (called terminal velocity). since in this case gravity is not the only force acting on the object, we are not in a situation of free fall.