SOLUTION: A block of mass 4.62 kg is drawn at constant speed a distance of 1.78 m along a horizontal floor by a rope exerting a constant force of magnitude 1.24 N and making an angle of 11.0

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: A block of mass 4.62 kg is drawn at constant speed a distance of 1.78 m along a horizontal floor by a rope exerting a constant force of magnitude 1.24 N and making an angle of 11.0      Log On


   

Question 1056853: A block of mass 4.62 kg is drawn at constant speed a distance of 1.78 m along a horizontal floor by a rope exerting a constant force of magnitude 1.24 N and making an angle of 11.0 degrees above the horizontal. Compute the coefficient of friction between the block and the floor.
Answer by ikleyn(52812) About Me  (Show Source):
You can put this solution on YOUR website!
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A block of mass 4.62 kg is drawn at constant speed a distance of 1.78 m along a horizontal floor by a rope exerting a constant force
of magnitude 1.24 N and making an angle of 11.0 degrees above the horizontal.
Compute the coefficient of friction between the block and the floor.
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Decompose the given force  F  into the horizontal and vertical components.
The horizontal component is equal to  |F|*cos(11°),  the vertical component is  |F|*sin(11°).       
The reaction force  N  acts from the floor vertically up to the box.  Together with
the vertical component  Fy  it balances the weight:  |W| = F%5By%5D + |N|.  So,  |N| = |W| - F%5By%5D.

The friction coefficient is the ratio of the shear force F%5Bx%5D to the reaction force  |N|:

k= F%5Bx%5D%2FN = F%5Bx%5D%2F%28W+-+F%5By%5D%29 = %28F%2Acos%2811%5Eo%29%29%2F%28W+-+F%2Asin%2811%5Eo%29%29.

Complete these calculations. Surely, W = mg = 4.62*9.81 Newtons.


Figure.  The body on the horizontal floor

Similar problem was solved in my lesson
    - Using vectors to solve problems in Mechanics: Force
in this site.

I simply copied and pasted the solution (the text and the Figure) from there and replaced the input data.