Rope Sag and Force on a Block Being Pulled

In summary: You should be able to calculate the magnitude of the tension force.In summary, a block of mass M is pulled horizontally on a frictionless surface by a rope of mass m. A horizontal force P is applied to one end of the rope. The rope must sag, even if only by an imperceptible amount, due to the weight of the rope. Assuming the sag is negligible, the acceleration of the rope and block, the force that the rope exerts on the block, and the tension in the rope at its midpoint can be calculated using Newton's second law and equilibrium equations. The sag in the rope can be shown through equilibrium equations in the vertical direction, where the downward weight is offset by the vertical upward component of the wire tension
  • #1
Univarn
9
0

Homework Statement


A block of mass M is pulled along a horizontal frictionless surface by a
rope of mass m, as shown. A horizontal force P is applied to one end of
the rope. (a) Show that the rope must sag, even if only by an imperceptible
amount. Then, assuming that the sag is negligible, find (b) the acceleration
of the rope and block, (c) the force that the rope exerts on the block, and (d) the tension in
the rope at its midpoint.


Homework Equations


sumofF=ma


The Attempt at a Solution


To be honest I don't have a clue on where to start any segment of this problem... Especially part a and part d. Any help you guys can offer would be greatly appreciated. If you need to see the image I'm sure I could upload it somewhere (basically it's just a block M being pulled by a rope m in the right horizontal direction by some force P).
 
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  • #2
Univarn said:

Homework Statement


A block of mass M is pulled along a horizontal frictionless surface by a
rope of mass m, as shown. A horizontal force P is applied to one end of
the rope. (a) Show that the rope must sag, even if only by an imperceptible
amount. Then, assuming that the sag is negligible, find (b) the acceleration
of the rope and block, (c) the force that the rope exerts on the block, and (d) the tension in
the rope at its midpoint.


Homework Equations


sumofF=ma


The Attempt at a Solution


To be honest I don't have a clue on where to start any segment of this problem... Especially part a and part d. Any help you guys can offer would be greatly appreciated. If you need to see the image I'm sure I could upload it somewhere (basically it's just a block M being pulled by a rope m in the right horizontal direction by some force P).
A rope of mass m supported at two points not directly above each other will take the shape of a catenary curve and thus sag (the curved shape approximates a parabola for small sags). This can be shown by equilibrium equations in the vertical direction, where the downward weight must be offset by the vertical upward component of the wire tension (if the wire didn't sag, there would be no upward tension component). The acceleration of the rope and block can be determined from Newton 2 applied to the system; then to find the rope force at certain sections of the rope, take a free body of the rope at at those sections and apply Newton 2 again.
 
  • #3
Thanks for your help, I'm still kind of stuck on the rope sag though. Maybe if I could get some help on a free body diagram for the rope with mass? I have going to the right the Fpull, down Fgravity, and up a Fnormal. Not sure where on the free body diagram for the rope I would put Ftension though. Sorry if I'm being a bother, Physics is not my strong point at all.
 
  • #4
Analyze a section of rope in the middle. What forces act on it? If there was no sag, what direction would the tension forces (from the rest of the rope) act? What's the sum of the vertical forces?
 

Related to Rope Sag and Force on a Block Being Pulled

1. What is rope sag and how does it affect the force on a block being pulled?

Rope sag refers to the amount of slack or droop in a rope when it is stretched between two points. It can affect the force on a block being pulled because it creates an extra downward force on the block due to the weight of the sagging rope.

2. How does the angle of the rope affect the force on a block being pulled?

The angle of the rope can affect the force on a block being pulled because it changes the direction of the force being applied to the block. As the angle of the rope increases, the force pulling the block horizontally decreases, while the force pulling the block vertically increases.

3. Why does the force on a block being pulled increase as the rope sags more?

This is because as the rope sags more, the weight of the sagging rope adds an additional downward force on the block. This increases the total force needed to pull the block in the desired direction.

4. How does the weight of the block being pulled affect the rope sag and force?

The weight of the block being pulled has a direct impact on the amount of sag in the rope. The heavier the block, the more the rope will sag, resulting in a greater force needed to pull the block. The weight of the block also affects the angle of the rope, which in turn affects the force needed to pull it.

5. Can the force on a block being pulled be reduced by decreasing the rope sag?

Yes, the force on a block being pulled can be reduced by decreasing the rope sag. This can be achieved by increasing the tension in the rope or by shortening the length of the rope. By decreasing the amount of sag, the downward force from the weight of the rope is reduced, resulting in a lower total force needed to pull the block.

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