Pulling a block along a surface using a string inclined at an angle

  • #1
Memo
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Homework Statement
A block with a weight of P is being pulled by a string of length l at a constant rate and an angle. The distance between the tip of the block to the surface is h. (see the photo below)
Find the kinetic coefficient of friction (the string is attached to the centre of the block)
Answer hint: k=(F*sqrt(l^2-h^2))/(Pl-Fh)
Relevant Equations
f=k*N
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  • #2
Memo said:
The tension force along the string is equal in magnitude and opposite in direction to the force being applied
I don't understand this. The tension is ##\vec F## and has the same magnitude and direction.
Memo said:
Can I put Fx=sqrt(l^2-h^2) and Fy=h?
No you cannot. It says that a force is equal to a length which is never true.

Try getting two equations, saying that vertical and horizontal components of the net force are zero which is always true when the acceleration is zero.
 
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  • #3
kuruman said:
I don't understand this. The tension is ##\vec F## and has the same magnitude and direction.

No you cannot. It says that a force is equal to a length which is never true.

Try getting two equations, saying that vertical and horizontal components of the net force are zero which is always true when the acceleration is zero.
I watched a somewhat relevant YouTube video and saw there was also the tension force, so I included it. But I've my problems, thank you so much!
 
  • #4
Your solution looks correct. For future reference, please don't edit the original post because it can be confusing to people who have seen it and are trying to respond to it. Corrections or additions to the first post should be posted separately.

Also, you are encouraged to use LaTeX to write equations. It's a useful skill and makes everybody's life much easier. Click on the link "LaTeX Guide" (lower left above "Attach files") to learn how.
 
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FAQ: Pulling a block along a surface using a string inclined at an angle

What is the effect of the angle of the string on the force required to pull the block?

The angle of the string affects the vertical and horizontal components of the pulling force. As the angle increases, the vertical component of the force increases, which reduces the normal force and thus the friction. However, the horizontal component, which is responsible for moving the block, decreases. There is an optimal angle where the required pulling force is minimized.

How does friction affect the motion of the block?

Friction opposes the motion of the block. The force of friction is proportional to the normal force, which is the component of the block's weight perpendicular to the surface. When the string is inclined, the normal force is reduced, thereby reducing the frictional force. If the friction is too high, more force will be required to move the block.

What equations are used to describe the forces involved in pulling the block?

The primary equations used are Newton's second law (F = ma) and the equations for the components of forces. The horizontal component of the pulling force is F*cos(θ), and the vertical component is F*sin(θ). The frictional force is μ*N, where μ is the coefficient of friction and N is the normal force. The normal force is affected by the vertical component of the pulling force and is given by N = mg - F*sin(θ).

How do you calculate the normal force when the string is inclined at an angle?

The normal force (N) is the force perpendicular to the surface that the block exerts due to its weight, adjusted for any vertical component of the pulling force. It is calculated as N = mg - F*sin(θ), where m is the mass of the block, g is the acceleration due to gravity, F is the pulling force, and θ is the angle of the string with the horizontal.

What role does the coefficient of friction play in this scenario?

The coefficient of friction (μ) determines the magnitude of the frictional force opposing the motion of the block. It is a measure of how rough or smooth the surfaces in contact are. A higher coefficient of friction means more force is needed to overcome friction and move the block, while a lower coefficient of friction means less force is required.

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