Simple pulley problem with weights

In summary, the problem involves two 0.25 kg blocks connected by a thread over a frictionless pulley. When a 0.20 kg block is added to one of the blocks, it disrupts the equilibrium and the 0.20 kg block accelerates. Using Newton's laws and treating it as a standard pulley problem, the acceleration can be calculated by solving the equations T - m1g = m1a and T - m2g = -m2a and combining them to find the acceleration of the 0.20 kg block. Proper subscripts for the masses must be used in the 'ma' terms.
  • #1
djokoman95
7
0

Homework Statement


Two 0.25 kg blocks are connected by a thread that passes over a frictionless pulley. The thread has no mass, and no friction. The two blocks are in balance. If a third block that weighs 0.20 kg is put on one of the blocks, then what is the acceleration of the 0.20 kg block?


Homework Equations





The Attempt at a Solution



I was thinking that since the 0.20 kg block just disrupts the equilibrium of the 0.25 kg blocks, then wouldn't the 0.20kg block just accelerate as if it were just dropped, at 9.8 m/s^2?? That seems like too obvious of an answer though...
 
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  • #2
Something accelerates at 9.8 m/s^2 only if there are no forces on it other than gravity--but that's not the case here, since it's in contact with another block.

How would you figure out the acceleration using Newton's laws?
 
  • #3
Well.. I could try using F=ma, and then solve for acceleration. But if I were to use this equation, how would I figure out what F was?
 
  • #4
Why not treat it as a standard pulley problem? Apply F=ma to both sides, then combine the equations. What forces are acting on each mass?
 
  • #5
Ok, so how about this. If we do T-m1g=ma, and then T-m2g=-ma, then combine both equations and solve for a?
 
  • #6
djokoman95 said:
Ok, so how about this. If we do T-m1g=ma, and then T-m2g=-ma, then combine both equations and solve for a?
Great! But make sure that the masses in the 'ma' terms have the proper subscripts also. For example: T - m1g = m1a.
 
  • #7
Oh yes, that's important. Thanks for your help!
 

1. How do I calculate the mechanical advantage of a simple pulley system?

The mechanical advantage of a simple pulley system can be calculated by dividing the weight being lifted by the force required to lift it. This means that if you have a weight of 10 pounds and you only need to pull with a force of 5 pounds to lift it, the mechanical advantage would be 2 (10/5 = 2).

2. Can a simple pulley system change the direction of the force?

Yes, a simple pulley system can change the direction of the force. This is because the pulley redirects the force being applied to lift the weight in a different direction. For example, if you pull downward on one end of the rope, the weight attached to the other end will be lifted upward.

3. How many pulleys do I need to create a simple pulley system?

You only need one pulley to create a simple pulley system. However, adding more pulleys can increase the mechanical advantage and make it easier to lift heavier weights.

4. What is the difference between a fixed pulley and a movable pulley?

A fixed pulley is attached to a stationary object, such as a ceiling or wall, and does not move. It only changes the direction of the force. A movable pulley is attached to the object being lifted and moves along with it, which can increase the mechanical advantage.

5. Can a simple pulley system be used to lift objects that are heavier than the force being applied?

Yes, a simple pulley system can be used to lift objects that are heavier than the force being applied. The mechanical advantage of the pulley system allows for the weight to be distributed across multiple ropes and pulleys, making it easier to lift heavy objects.

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