Acceleration in a Pulley System

AI Thread Summary
In a frictionless pulley system with masses m1 at 10 kg and m2 at 5 kg, the acceleration of m1 is influenced by the relationship between the accelerations of both masses. The tension in the system is derived from the equations T = m1a and T - m2g = m2a, leading to the conclusion that m1's acceleration is not equal to m2's. The hint suggests that the distance m1 moves affects how far m2 descends, indicating that a1 does not equal a2. Visualizing the rope dynamics is crucial, as the ratio of distances moved by the masses directly correlates to their acceleration ratio. Understanding these relationships is key to solving for the acceleration in this system.
grouchy
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For the system in the figure mass m1 is 10 kg and mass m2 is 5 kg. What is acceleration of m1 if the horizontal surface is frictionless? Hint: How does a1 compare to a2?


http://geocities.com/grouchy187/untitled.bmp

My attemp:
T = m1a T - m2g = m2a
m1a = m2g + m2a
a= m2g / m1-m2
 
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What tension force acts on m2? (Consider the pulley as part of m2.)

What about that hint?
 
for m2, would the weight W, be equal to 2T?

also I think a1 = a2
 
grouchy said:
for m2, would the weight W, be equal to 2T?
No. But those are the forces acting on m2. (They would only be equal if m2 were not accelerating.)

also I think a1 = a2
No. Try to think this through. (Using a piece of string to work it out may help--I'm not kidding.) If m1 moves 1 m to the right, how far down does m2 move?
 
i dunno, I'm thinking about it and I just don't get this one
 
If m2 moves down by 1 meter, how much extra rope will hang down off the table? That extra amount of rope is the distance that m2 moves (since m2 is tied directly to the rope). Once you have that, the ratio of distances in this case is the same as the ratio of accelerations.

If you're having trouble visualizing the amount of extra rope, just start with your orginal diagram. Now draw in the new position of m2 and the lower pulley 1 meter below where they were. Note that you have to extend the lines for the ropes on each side of the pulley. How much extra rope do these new lines represent?
 
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