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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

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