The system below consists of two masses connected by an ideal rope and pulley. A

Question

The system below consists of two masses connected by an ideal rope and pulley. Assume m1=40 kg, m2=15 kg, and the angle of incline is 42 degrees.

Draw a free body diagram for the system

Determine the acceleration of the system and the tension in the rope if m1moves on a frictionless incline.

If the plane is rough and the coefficient of kinetic friction between the block and the ramp is 0.20, what is the acceleration of the sytem?

If the plane is rough, what is the frictional force required to keep the system in equalibrium?

Please show all work, thanks!

Explanation / Answer

a) motive force F = (m2 - m1*sin)*g
F = (15kg - 40kg*sin42º) * 9.8m/s² = -115.3 N
The negative sign means the net force acts downslope instead of upslope as assumed in my equation.

acceleration a = F / m = 115.3N /55kg = 2.1 m/s² downslope

b) Now there is a resistive force of up to
Ff = µ*m1*g*cos = 0.20*40kg*9.8m/s²*cos42º = 58.3 N
This is less than the motive force 115.3 N
and the acceleration is 2.1 m/s²

c) We need 58.3 N = µ * 40kg * 9.8m/s² * cos42º
min µ = 0.2

Hope this helps!

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