Solving Angle Pulling Force w/ Friction & Mass

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In summary, The tension in the rope, P, needed to pull a 30kg box at a constant speed along rough horizontal ground at an angle of 20 degrees with the ground can be calculated using the equation (30g-P\sin 20^\circ)0.4=P\cos20^\circ. After solving for P using g = 9.8, the tension is found to be 109 N. However, the correct answer given is 125 N. It is unclear what mistake was made in the solution, and the use of only 2 significant figures for g is not justified. Degrees can be written using the x2 button and a lower case o as a superscript.
  • #1
dalcde
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Homework Statement


A box of mass 30kg is being pulled along rough horizontal ground at a constant speed using a rope. The rope makes an angle of 20 degrees with the ground. The coefficient of friction between the box and the ground is 0.4. The box is modeled as a particle and the rope as a light, inextensible string. The tension in the rope is P Newtons.

Homework Equations



The Attempt at a Solution



The normal force is
[tex]30g-P\sin 20^\circ.[/tex]
The force of friction is
[tex](30g-P\sin 20^\circ)0.4,[/tex]
which should be equal to the pulling force,
[tex]P\cos 20^\circ.[/tex]
Hence
[tex](30g-P\sin 20^\circ)0.4=P\cos20^\circ.[/tex]
Taking g as 9.8 and solving the equation yields
[tex]P=109,[/tex]
corrected to 3 significant figures.

However, the answer says that it should be 125 instead of 109. What did I do wrong? Also, the book seems to prefer to have 3 significant figures but 9.8, the numerical value of g, only has 2, which seems weird to me. Any justifications for it?

(Sorry, I don't know how to type the degree sign in LaTeX. Can anyone teach me how to?

EDIT: added the degree signs
 
Last edited:
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  • #2
I would say that you are correct. Even putting g = 10 N/kg would not get it to 125 N.
 
  • #3
dalcde said:
...
(Sorry, I don't know how to type the degree sign in LaTeX. Can anyone teach me how to?
20^\circ

[tex](30g-P\sin 20^\circ)0.4=P\cos20^\circ[/tex]
 
  • #4
rock.freak667 said:
I would say that you are correct. Even putting g = 10 N/kg would not get it to 125 N.

I am also getting 190 N.

You can also do degrees by making a lower case o into a superscript with the x2 button at the top of the message composing window: cos20o
 
  • #5
using LaTeX)



Your approach to solving this problem is correct. However, there are a few possible reasons why your answer may differ from the given answer of 125.

First, it is possible that the given answer of 125 is rounded or has a margin of error. In scientific calculations, it is common to round to a certain number of significant figures, which may explain why the given answer has 3 significant figures even though g only has 2.

Another reason could be a difference in the value of g used in the calculation. You have used a value of 9.8, but the actual value of g may vary slightly depending on the location and altitude. This could result in a small difference in the final answer.

Finally, it is possible that there is a mistake in the given answer or in the calculations leading to it. It is always important to double check your work and make sure all the equations and units are correct to avoid errors.

As for typing the degree sign in LaTeX, you can use the command \degree or \circ to get the degree symbol. For example, 20\degree or 20\circ will both give you 20°.
 

Related to Solving Angle Pulling Force w/ Friction & Mass

1. What is angle pulling force with friction and mass?

Angle pulling force with friction and mass is a concept in physics that involves the measurement and calculation of the force needed to move an object at a specific angle, taking into account the effects of friction and the mass of the object.

2. How is angle pulling force with friction and mass calculated?

The formula for calculating the angle pulling force with friction and mass is F = μmgcosθ, where F is the pulling force, μ is the coefficient of friction, m is the mass of the object, g is the acceleration due to gravity, and θ is the angle of the pulling force.

3. What is the role of friction in angle pulling force with friction and mass?

Friction is a force that opposes motion and is caused by the contact between two surfaces. In the context of angle pulling force with friction and mass, friction affects the amount of force needed to move an object at a specific angle by increasing the required force due to its opposing nature.

4. How does the mass of an object affect the angle pulling force with friction and mass?

The mass of an object affects the angle pulling force with friction and mass by increasing the amount of force needed to move the object at a specific angle. The greater the mass, the greater the force needed to overcome its inertia and move it.

5. What are some real-world applications of angle pulling force with friction and mass?

Angle pulling force with friction and mass has many real-world applications, such as in engineering and construction to determine the force needed to move objects at different angles, in sports to calculate the force needed to pull or push objects, and in physics experiments to study the effects of friction on different objects and surfaces.

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