Solve Pulley-Mass System: m1=4.00 kg, m2=1.00 kg

[Taniaz]

Homework Statement

The pulleys in the figure (attached) are massless and frictionless, determine the acceleration of eah of m1 and m2, given that m1=4.00 kg, and m2=1.00 kg, and the surface is frictionless and horizontal.

Homework Equations

For mass m1: T1=m1a1 and mass m2: w2-T2=m2a2
For the pulley 2T1=T2

The Attempt at a Solution

I don’t understand how the mass m2, which is hanging, is moving. Why is it moving downwards? If m1 is moving to the right, then shouldn’t the pulley move anticlockwise and pull m2 upwards?
How is it attached?
How is the pulley making it move upwards or downwards if it’s attached to the center of the pulley?
How is the acceleration of a1=2a2?

Thank you

 

[Orodruin]

If m1 is moving to the right, then shouldn’t the pulley move anticlockwise and pull m2 upwards?

No. I suggest that you write down an equation for the total length of the string as the sum of the length of all parts of the string and differentiate it with respect to time. Since the string length is fixed, this time derivative should be zero. Also, you should specify which pulley you are talking about.

How is it attached?

Assuming that you are talking about the lower right pulley, it is not attached to anything. It is hanging by the string.

How is the pulley making it move upwards or downwards if it’s attached to the center of the pulley?

The pulley itself will move up or down and so the mass attached to it will do so as well.

How is the acceleration of a1=2a2?

This should follow after you differentiate the total length of the string (which I told you to write down in the first hint) a second time.

 

[Taniaz]

Got it, thank you!