A microwave oven of mass 13.0 kg is pushed a distance 8.80 m up the sloping surf

Question

A microwave oven of mass 13.0 kg is pushed a distance 8.80 m up the sloping surface of a loading ramp inclined at an angle of 37.5 above the horizontal, by a constant force F with a magnitude 155 N and acting parallel to the ramp. The coefficient of kinetic friction between the oven and the ramp is 0.230.

A-What is the work done on the oven by the force F ?

Take the free fall acceleration to be 9.80 m/s2 .

B-

What is the work done on the oven by the friction force?

Take the free fall acceleration to be 9.80 m/s2

C-Compute the increase in potential energy for the oven.

Take the free fall acceleration to be 9.80 m/s2 .

D-Use your answers to parts (A), (B), and (C) to calculate the increase in the oven's kinetic energy.

Take the free fall acceleration to be 9.80 m/s2 . Express your answer using two significant figures.

E-Use

F =ma  to calculate the acceleration of the oven.

Take the free fall acceleration to be 9.80 m/s2 . Express your answer using two significant figures.

F-Assuming that the oven is initially at rest, use the acceleration to calculate the oven's speed after traveling a distance 8.80

m .

Take the free fall acceleration to be 9.80 m/s2 . Express your answer using two significant figures.

G-From this, compute the increase in the oven's kinetic energy.

Take the free fall acceleration to be 9.80 m/s2 . Express your answer using two significant figures.

Explanation / Answer

a) Work done by the oven is

W = F. d = (155)(8.8) =1364 J

b) Work done by friction force

W = - f .d = - u mg cos theta . d = -(0.23) (13)(9.8) cos 37.5 (8.8) = -204.6 J

c) Increase in potential energy

U = m g h = m g d sin theta = (13)(9.8) sin 37.5 (8.8) =682.5 J

d) The kinetic energy is equal to the change in work done by the applied minus the frictional force and gravitational PE

KE = 1364 J -204.6 J - 682.5 J

KE = 476.9 J

e) The net force is

F (net) = F - u mg cos theta - mg sin theta

F(net) = 155 - (0.23)(13)(9.8) cos 37.5 - (13) (9.8) sin 37.5

F = 54.2 N

acceleration a = F (net) / m = 54.2 /13 = 4.17m/s^2

f) the speed of the oven starting from rest is

V = sqrt [ 2 a L ] = sqrt [ 2 (4.17)(8.8)] = 8.6m/s

g) the increase in KE

KE = (1/2) (13)(8.6)^2 = 476.9 J

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