Accelerating motion with a pulley

• House
In summary, the conversation discusses the motion of two bodies, A and B, connected by a rope and a pulley. The usual approach to solving this problem involves assuming that the rope is inextensible, the pulley is massless, and the rope is massless. However, these assumptions are not entirely true. The conversation also discusses the relationship between the motion of the two bodies and the forces acting on them. The tension in the rope is equal to the weight of B, but this does not necessarily mean that the accelerations are the same. Drawing free body diagrams for each object can help clarify the situation.
House
Let's suppose we have a body A with mass M that can move on a horizontal frictionless ground. Now we connect that with another body B, mass m, with the help of a rope. The body B can move vertically and the rope is curved with a pulley. Now we set the body B free to move.
What's the relationship of the motion of the two bodies? Is there a same force (tensionA = weightB or a same acceleration?

The usual approach to this sort of problem involves three assumptions:
1) the rope is inextensible (it does not stretch)
2) the pulley is massless
3) the rope is massless
None of these is ever strictly true, but they significantly simplify the problem. Are you willing to live with these assumptions, or if not, what do you wish to assume instead about these two matter?

House said:
tensionA = weightB
If the tension would be equal to the weight of B, then B wouldn't start falling.

Dr.D said:
The usual approach to this sort of problem involves three assumptions:
1) the rope is inextensible (it does not stretch)
2) the pulley is massless
3) the rope is massless
None of these is ever strictly true, but they significantly simplify the problem. Are you willing to live with these assumptions, or if not, what do you wish to assume instead about these two matter?

Absolutely, I just forgot to mention them.

You need to draw FBDs for each body, and do not assume that T = Wb. Also, look at the kinematic constraint imposed by the inextensible cord.

Okay, so a professor of mine told me that the rope carries the same force from B to A. But same force means different acceleretion if the masses are different. If this is true how can different parts of the rope have different acceleretions if the rope is inextensible?

House said:
Okay, so a professor of mine told me that the rope carries the same force from B to A. But same force means different acceleretion if the masses are different. If this is true how can different parts of the rope have different acceleretions if the rope is inextensible?
The same net force means the same acceleration. What forces act on object A? What forces act on object B?

I repeat, you need to draw the FBDs for the two blocks. When you do, if done correctly, it will all become clear to you.

Dale
@House I agree completely with @Dr.D on this. Draw the free body diagram

So, according to the FBDs we have a force for each object, but again I can't decide if the tension is the same as the weight or the accelerations are the same. I'm completely stuck here.

Update: Problem solved. Thanks a lot for your time, much appreciated.

1. What is a pulley?

A pulley is a simple machine that consists of a wheel with a groove around its circumference, a rope or belt, and a load. The rope or belt is threaded through the groove of the wheel, and when the rope or belt is pulled, the wheel rotates, allowing the load to be lifted or lowered.

2. How does a pulley accelerate motion?

A pulley can accelerate motion by reducing the amount of force needed to lift a load. By using multiple pulleys, the load is distributed over a larger area, resulting in less force needed to lift the load. This allows for faster and easier movement of the load.

3. Can a pulley be used to change the direction of motion?

Yes, a pulley can change the direction of motion. The direction of the force applied to the rope or belt can be changed by using multiple pulleys and changing the direction of the rope or belt. This is useful in situations where the load needs to be lifted or moved in a different direction.

4. What are the advantages of using a pulley for accelerating motion?

Using a pulley can have several advantages, such as reducing the amount of force needed to lift a load, making it easier and faster to move heavy objects. Pulleys also allow for greater control and precision in the movement of the load, making it useful in various industries and applications.

5. Are there any limitations to using a pulley for accelerating motion?

One limitation of using a pulley for accelerating motion is that the load being lifted can only move in a vertical direction. Another limitation is that the more pulleys that are used, the more friction is created, which can decrease the efficiency of the system. Additionally, the weight of the pulleys themselves can also add to the load being lifted.

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