Find the speed of the descending block

In summary: Yes, I also has to find the acceleration , which is the easier part. But I can't figure out if the acceleration on the ring in x direction should be the same as......the acceleration of the block.
  • #1
NoahCygnus
96
2

Homework Statement


19059384_748454021995385_4693005147032055119_n.jpg

So, we have a ring 'A' having mass 'm' that can slide on the horizontal rod. It is attached to a massless string, whose other end is attached to a block of mass 'M = 2m'. 'B' is a massless and frictionless pulley.
The problem states that at an instant, the string between ring and the pulley makes an angle 'θ' with the horizontal rod. If the speed of the ring at that instant is 'v', what will be the speed with which the block C descends.

Homework Equations


Σ Fx = max
∑ Fy = may
∑ Fz = maz

The Attempt at a Solution


I have drawn the free body diagrams listing all the forces.
The forces acting on the ring 'C' are:
Σ Fx = Tcosθ = ma
∑ Fy = N - mg - Tsinθ = 0

Forces acting on the block are:
∑ Fy = T - Mg = Ma' .

That's all I did.

What I don't understand is, will the acceleration due to the X component of tension force, Tcosθ be the same in magnitude as the acceleration a' of the descending block?
 
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  • #2
NoahCygnus said:

Homework Statement


View attachment 205162
So, we have a ring 'A' having mass 'm' that can slide on the horizontal rod. It is attached to a massless string, whose other end is attached to a block of mass 'M = 2m'. 'B' is a massless and frictionless pulley.
The problem states that at an instant, the string between ring and the pulley makes an angle 'θ' with the horizontal rod. If the speed of the ring at that instant is 'v', what will be the speed with which the block C descends.

Homework Equations


Σ Fx = max
∑ Fy = may
∑ Fz = maz

The Attempt at a Solution


I have drawn the free body diagrams listing all the forces.
The forces acting on the ring 'C' are:
Σ Fx = Tcosθ = ma
∑ Fy = N - mg - Tsinθ = 0

Forces acting on the block are:
∑ Fy = T - Mg = Ma' .

That's all I did.

What I don't understand is, will the acceleration due to the X component of tension force, Tcosθ be the same in magnitude as the acceleration a' of the descending block?
I don't think you need to use forces for this problem (but I could be wrong). They give you the speed of the ring horizontally, and as long as the string stays taut, that will just translate into a change in the length of the string between the pulley and M. Can you try approaching the problem that way?
 
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  • #3
berkeman said:
I don't think you need to use forces for this problem
Quite so.
@NoahCygnus , these kinematics problems can be confusing. The best way is to think in terms of the component of relative velocity in the direction of the string (or bar, in some questions). How fast is the ring moving towards the pulley?
 
  • #4
berkeman said:
I don't think you need to use forces for this problem (but I could be wrong). They give you the speed of the ring horizontally, and as long as the string stays taut, that will just translate into a change in the length of the string between the pulley and M. Can you try approaching the problem that way?
I'll try to approach it the way you mentioned. Though I face only one problem , does the acceleration of the ring in x direction have the same magnitude as the acceleration of the block ? Or is it more?
 
  • #5
NoahCygnus said:
I'll try to approach it the way you mentioned. Though I face only one problem , does the acceleration of the ring in x direction have the same magnitude as the acceleration of the block ? Or is it more?
That's for you to figure out, but I checked my answer by thinking about it intuitively. Say θ is small, so the top part of the string is almost parallel with the bar. What is the speed of the string in relation to the ring at that small angle? And what happens as the ring gets close to directly over M, so the string is vertical and θ = 90 degrees? What is the vertical speed of the string at that point? Does this function remind you of any trig functions...? :smile:
 
  • #6
NoahCygnus said:
does the acceleration of the ring in x direction have the same magnitude as the acceleration of the block ?
The question as posted involves speeds, not accelerations. But maybe there are more parts to the question?
 
  • #7
haruspex said:
The question as posted involves speeds, not accelerations. But maybe there are more parts to the question?
Yes, I also has to find the acceleration , which is the easier part. But I can't figure out if the acceleration on the ring in x direction should be the same as that of the block in y direction .
 
  • #8
NoahCygnus said:
I can't figure out if the acceleration on the ring in x direction should be the same as that of the block in y direction .
Did you try the approach I recommended in post #3? Did you understand it?
 

Related to Find the speed of the descending block

1. How can I calculate the speed of a descending block?

The speed of a descending block can be calculated by dividing the distance the block travels by the time it takes to travel that distance. This is known as average speed and is typically measured in meters per second (m/s).

2. What information do I need to find the speed of a descending block?

To find the speed of a descending block, you will need to know the distance the block travels and the time it takes to travel that distance. This information can be obtained through measurements or by using equations if other variables are known.

3. Is there a specific formula for finding the speed of a descending block?

Yes, the formula for finding the speed of a descending block is: speed = distance / time. This formula is commonly known as the average speed formula and can be used for any object in motion, including a descending block.

4. How can I measure the time it takes for a block to descend?

The time it takes for a block to descend can be measured using a stopwatch or timer. Start the timer when the block begins to descend and stop it when it reaches its final position. This will give you the total time the block took to descend.

5. Can the speed of a descending block change?

Yes, the speed of a descending block can change depending on various factors such as the angle of descent, air resistance, and the surface the block is descending on. These factors can affect the distance and time, and thus the speed, of the descending block.

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