1. A 4 kg mass is resting on a ramp inclined at an angle of 30 degrees with resp

Question

1. A 4 kg mass is resting on a ramp inclined at an angle of 30 degrees with respect to the horizontal. A string is attached to the 4 kg mass and passes over a frictionless pulley and is connected to a 5 kg mass hanging over the side. If the coefficient of friction between the ramp and the 4 kg mass if 0.3 find; A) Find the initial energy of both blocks. Hint: you can take the zero of gravitational potential energy of both blocks to be their initial position. B) Find the work done by the force of friction as the 4 kg block moves 2 meters. C) Write down the expression for the final energy of the two blocks after they have moved 2 meters. D) Use the equation that relates work and energy to find the final speed of both blocks.

Explanation / Answer

A) initially blocks are at rest so K.E. = 0

P.E. = 0

So initial energy of both blocks is 0 .

B) friction force f = u.N

N = mgcos30

f = 0.3 x 4 x 9.81 x cos30 = 10.19 N

Work done by friction = Fdcos@ = 10.19 x 2 x cos180 = - 20.39 J

C)

Final P.E. of 4kg block = 4g * 2 sin30 = 8gsin30 = 4g

final P.E. of 5 kg block = - 5g*2 = - 10g

K,E of 4 kg block = 4v^2 /2 = 2v^2

K.E. of 5 kg block = 5v^2 /2 = 2.5v^2

so final energy of 2 block = 4.5v^2 - 6g

d) work done by friction = change in Energy

-20.39 = (4.5v^2 - 6g ) - 0

4.5v^2 = 6*9.81 - 20.39 = 38.47

v = 4.13 m/s

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