Find Coefficient of Friction only given angle at which object slides on ramp.

In summary, the discussion revolved around finding the coefficient of friction for a block of wood on an inclined plane with an angle of 30 degrees to the horizontal. The solution involved drawing a free body diagram and using equations such as Fnet = Fd + Ff and uFn = Ff. The resulting calculation gave a negative value for the coefficient, indicating that the initial choice of direction for the frictional force was incorrect. The correct answer was confirmed to be correct by another user.
  • #1
avsj
26
0

Homework Statement



A block of wood is sitting on an inclined plane. One end of the plane is rised until the wood block slides down. The wood block slides down when the plane has an angle of 30 degrees to the horizontal. What is the coefficient of friction?

Homework Equations



uFn=Ff

Fnet = Fd + Ff

In this case, Fnet =0 because the wood block wasnt moving until 30 degrees.


The Attempt at a Solution



What I tried was drawing the free body diagram.
sin30=Fd/9.8m
cos30=Fn/9.8m

letting m=m, i get (Fd/sin30)=(Fn/cos30)

Substitute 0-Ff for Fd, and Ff/u for Fn.

this simplifies to -ucos30=sin30, giving u= -.577 or .577

Does this seem correct? I don't know what the right answer is but its odd that I got a negative answer and would love some confirmation that this is indeed correct ... or wrong :P

Thanks
 
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  • #2
note that when you say

Fnet = Fd + f

you do not include the sign for f the frictional force that is acting upwards in the opposite direction to the downwards component. When we add forces that work inline we take their direction into account. This means that you should actually say

0 = Fd - f

this implies that you chose downwards along the incline as the positive direction.

Some similar problems would require one to solve for an unknown force. If you were to get a negative value for its value it just means that your initial choice for its direction was wrong, it actually acts in the opposite direction.

Your value for the coefficient is correct.
 
  • #3
Thanks andrevdh :D
 
  • #4
Its a pleasure.
 

1. What is the coefficient of friction?

The coefficient of friction is a dimensionless value that represents the amount of resistance between two surfaces when one object slides or attempts to slide over another.

2. How is the coefficient of friction measured?

The coefficient of friction is typically measured by conducting experiments where one object is placed on top of another and gradually tilted until the object begins to slide. The angle at which the object slides is used to calculate the coefficient of friction.

3. What is the relationship between the angle of sliding and the coefficient of friction?

The coefficient of friction is directly related to the angle at which an object slides. As the angle of sliding increases, the coefficient of friction also increases.

4. Can the coefficient of friction change for the same two surfaces?

Yes, the coefficient of friction can change for the same two surfaces depending on various factors such as the smoothness of the surfaces, the presence of lubricants, and the applied force between the two surfaces.

5. Why is it important to know the coefficient of friction?

The coefficient of friction is important in many scientific and engineering applications as it helps determine the amount of force needed to move an object and the amount of heat generated during the sliding process. It also plays a crucial role in designing structures and machines, as well as predicting and preventing accidents caused by slippery surfaces.

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