Solving Angle Pulling Force w/ Friction & Mass

[dalcde]

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
$$30g-P\sin 20^\circ.$$
The force of friction is
$$(30g-P\sin 20^\circ)0.4,$$
which should be equal to the pulling force,
$$P\cos 20^\circ.$$
Hence
$$(30g-P\sin 20^\circ)0.4=P\cos20^\circ.$$
Taking g as 9.8 and solving the equation yields
$$P=109,$$
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

 

[rock.freak667]

I would say that you are correct. Even putting g = 10 N/kg would not get it to 125 N.

 

[SammyS]

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

20^\circ

$$(30g-P\sin 20^\circ)0.4=P\cos20^\circ$$

 

[Fewmet]

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: cos20^o

 

[rwisz]

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°.