Two masses are connected with a rope and pulley...

Question

Two masses are connected with a rope and pulley as shown:

a. If the mass on the ramp is m1 and the hanging mass is m2 carefully complete the free-body diagram for the system. Be sure that forces include the subscript "1" if they are associated with mass 1 and "2" if they are associated with mass 2. Assume frictionless for now.

b. What forces (or components of forces) must we compare to determine if the box on the ramp goes up or down? Identify these forces below then circle these forces on the free-body diagram.

c. Why must we do part "b" before we label any friction forces?

d. If m1 = 7 kg, m2 = 6 kg, and the angle between the ramp and the floor is 40°, which way does the block on the ramp accelerate? Show any calculations below.

e. If the coefficient of friction between the ramp and the block is μ = 0.1, what is the acceleration of the system?

f. What is the tension in the rope?

Answer 1

Unfortunately this part does not allow diagram or drawing.

Complete Solution can be provided on request.

Brian

 

Assuming the system is static i.e. no motion.





The system Free body diagram
The system is moving up or down depends on the strength of the two forces on a frictionless plane and they are M_1 g sin?θ and M_2 g
If the former is greater than the latter then object M1 is moving down the ramp and vice versa.

If frictional force is present, this force is always against the motion. For example, if the objects move down the ramp then the frictional force is up the ramp. So after solving (b) we know which direction are the objects moving we can then know the direction of the frictional force.

The two forces are: 7g sin 40 = 45 N and 60 N
M1 is moving up the ramp because M_1 g sin??θ<M_2 g?

Frictional force = M_1 gμ cos?θ = 7g*0.1 cos 40 = 5.36 N
The net force equation: M_2 g-M_1 g sin??θ-5.36=7a?
Where a is the acceleration
60 – 45 – 5.36 = 7a
a = 1.38 m/s2

Tension in the rope = M_2 g = 60 N