Find the man's tension pulling the rope

In summary, the task involves determining the amount of tension exerted by a man pulling a rope, which can be calculated by considering the forces at play, including the weight of the objects involved and any additional forces acting on the system. Understanding the principles of physics, such as Newton's laws of motion, is essential for analyzing the situation and deriving the correct tension value.
  • #1
Adam Hanns F A Cong
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Homework Statement
Ignore the mass of the rope and the pulley,frictional force between the man and the board, the board and ground. Now the man is pulling the rope in order to make him and the board move to the right uniformly. Find the man's tension of pulling the rope.
I got a wrong answer.
Could you please explain the pulley's principle in moment of the force or (angular) momentum?
Relevant Equations
The gravity G_1 of the man is 600N,the gravity G_2 of the board is 400N. The coefficient of the kinetic friction μ both between the man and the board,the board and ground is 0.2.
The elastic force of the board,N=G_1+G_2=1000N.
The kinetic friction f=μN=200N.
The tension T=f=200N.
IMG_20240207_220031.jpg
 
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  • #2
You need to show the forces on your diagram.

PS have you heard the term mechanical advantage?
 
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  • #3
You mean like it? Forgive my ignorance,please. I may not know term mechanical advantage. Do you mean the next fig.2? I learnd that it comes from the level principle,and the level seems that it comes from the moment force or (angular) momentum,but I don't know how to find the momentum or radius vector.
IMG_20240208_001356.jpg
view.jpeg
 
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  • #4
Tension is a two-way force in a rope.

A lever is not the only example of mechanical advantage. Sometimes you can use a pulley system!
 
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  • #5
Thank you.😊
I learned pulley system two years ago at junior high,but I am not good analyse it.
All in all, thanks for your help!😸
 

FAQ: Find the man's tension pulling the rope

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What is the formula to find the tension in a rope when a man is pulling it?

The formula to find the tension in a rope when a man is pulling it depends on the specific setup, but generally, it can be given by T = m * g * cos(θ) + m * a, where T is the tension, m is the mass of the object being pulled, g is the acceleration due to gravity, θ is the angle of the rope with the horizontal, and a is the acceleration of the object.

How does the angle of the rope affect the tension?

The angle of the rope affects the tension because the tension has both vertical and horizontal components. As the angle increases, the vertical component of the tension decreases, and the horizontal component increases. This relationship is captured in the formula T = m * g * cos(θ) for the vertical component and T = m * a for the horizontal component.

Does the mass of the man pulling the rope affect the tension?

Yes, the mass of the man can affect the tension in the rope, especially if the man is accelerating or if his weight contributes to the overall force exerted on the rope. If the man is stationary and only pulling horizontally, his mass might not directly affect the tension unless considering friction or other forces.

What role does friction play in calculating the tension in the rope?

Friction can play a significant role in calculating the tension in the rope. If there is friction between the object being pulled and the surface, the tension needs to overcome both the frictional force and the force due to gravity. The frictional force can be calculated using F_friction = μ * N, where μ is the coefficient of friction and N is the normal force.

How can we measure the tension in the rope experimentally?

The tension in the rope can be measured experimentally using a device called a dynamometer, which measures the force exerted on it. Alternatively, one can use force sensors or load cells attached to the rope to directly measure the tension as the man pulls it.

```

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