Mass and Tension: Comparing Magnitudes

[gummybeargirl]

Homework Statement

In the figure, M2 has more mass than M1 and M1 has more mass than M3. The questions refer to the magnitudes of tensions and weights.

There is friction between the horizontal plane and M2 (μk ≠ 0). M2 is observed to travel at a constant speed. Assume that the pulleys are frictionless and have negligible mass. Select the appropriate statements to complete the following sentences.

Each has the option of True/False/Greater than/Less than/Equal To
1) The magnitude of the net force on M2 is T2 - T3.
2) T1 is ... M1g.
3) T4 is ... M3g
4) T2 is ... T1.
5) M1 accelerates downwards.
6) T3 is ... T2.
2. The attempt at a solution
1) False (friction is playing a role so it has to have a lower magnitude than just T2-T3)
2) Less than (I am making the assumption it will move towards the heavier mass, so it will
have a lower tension to lower the mass)
3) Greater than (it must have a greater tension to raise the mass)
4) Equal to (the tensions will have the same magnitude in opposite directions)
5) There would be no acceleration since it travels at a constant speed)
6) Less than (since it would move towards T2 it would have a greater magnitude for T2 than
T3)
I am not sure where i am going wrong with my thought process.

 

[Nathanael]

2) Less than (I am making the assumption it will move towards the heavier mass, so it will
have a lower tension to lower the mass)

Are there any other forces acting on M_{1} other than M_{1}g and T_{1}? What would happen if T_{1} were less than M_{1}g?

(I am making the assumption it will move towards the heavier mass, so it will have a lower tension to lower the mass)

Are you talking about the tension? The tension should be of uniform magnitude throughout the rope. If there were greater tension towards the heavier mass, the rope would move toward the heavier mass (it would un-taut itself) which is counter-intuitive.

3) Greater than (it must have a greater tension to raise the mass)

Are there any other forces acting on M_{3} other than M_{3}g and T_{4}? What would happen if T_{4} were greater than M_{3}g? Is this consistent with the information that says "the system moves at constant velocity"?

6) Less than (since it would move towards T2 it would have a greater magnitude for T2 than T3)

Because it moves toward T_{2}, T_{2} must equal T_{1} plus the force of friction, which is said to be nonzero. T_{3} is therefore less than T_{2}
(It doesn't really matter that it moves towards T2, since it's not accelerating. It only matters that that movement causes a frictional force.)

 

[tms]

Each has the option of True/False/Greater than/Less than/Equal To
2) T1 is ... M1g.
3) T4 is ... M3g
5) M1 accelerates downwards.

2. The attempt at a solution
2) Less than (I am making the assumption it will move towards the heavier mass, so it will
have a lower tension to lower the mass)
3) Greater than (it must have a greater tension to raise the mass)
5) There would be no acceleration since it travels at a constant speed)

Look at your answer to 5, and compare it to your answers for 2 and 3. In 5 you correctly state that constant speed implies no acceleration. What does an acceleration of 0 say about the net force?

 

[gummybeargirl]

Look at your answer to 5, and compare it to your answers for 2 and 3. In 5 you correctly state that constant speed implies no acceleration. What does an acceleration of 0 say about the net force?

If there is no acceleration then there should be no net force. So that would mean that for both 2 and 3 they would be equal to.
Does that seem correct?

 

[tms]

Yes.

 

[gummybeargirl]

Yes.

Thank you so much for help, i got correct