Coefficient of kinetic friction on wooden plane question

In summary, the given problem involves a block on a rough wooden plane that slides down at a constant speed when the plane is tilted 30° to the horizontal. The correct answer, 0.577, can be obtained using the equation tanΘ. A helpful strategy is to draw a free body diagram and consider the forces acting on the block, including friction. A good way to check the answer is to see what happens as the plane's tilt approaches 90°.
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Homework Statement


This is what I was given:
A block is placed on a rough wooden plane it is found that when the plane is tilted 30° to the horizontal, the block will slide down at a constant speed.

Homework Equations


I'm not sure which equations to use other than sinΘmg but I'm not getting the correct answer which is 0.577.

The Attempt at a Solution


I then tried tanΘ and got the correct answer but I'm not sure why it's correct.
Thank you for any help provided.
 
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  • #2
Drawing a FBD is a MUST. This must show all the forces acting on the block.
 
  • #3
Try a sanity check: What happens as the plane's tilt approaches 90°? Once you do that, try calculating the friction force.
 

1. What is the coefficient of kinetic friction on a wooden plane?

The coefficient of kinetic friction on a wooden plane is a measure of the amount of resistance or friction between the wooden plane and another surface when it is in motion. It is represented by the symbol μk.

2. How is the coefficient of kinetic friction on a wooden plane calculated?

The coefficient of kinetic friction on a wooden plane can be calculated by dividing the force required to keep the wooden plane in motion by the weight of the wooden plane. This can be represented by the equation μk = F/W, where F is the applied force and W is the weight of the wooden plane.

3. What factors affect the coefficient of kinetic friction on a wooden plane?

The coefficient of kinetic friction on a wooden plane can be affected by several factors such as the smoothness of the surface, the weight of the wooden plane, and the type of material the wooden plane is in contact with. Additionally, the coefficient of kinetic friction may also vary with the speed of the wooden plane and the presence of any lubricants.

4. How does the coefficient of kinetic friction on a wooden plane affect its motion?

The coefficient of kinetic friction on a wooden plane plays a significant role in determining the motion of the wooden plane. A higher coefficient of kinetic friction means there is more resistance between the wooden plane and the surface, making it harder for the wooden plane to move. On the other hand, a lower coefficient of kinetic friction means less resistance and the wooden plane can move more easily.

5. Can the coefficient of kinetic friction on a wooden plane be reduced?

Yes, the coefficient of kinetic friction on a wooden plane can be reduced by using lubricants or by using a smoother surface. Additionally, reducing the weight of the wooden plane can also help decrease the coefficient of kinetic friction. However, it is important to note that the coefficient of kinetic friction can never be completely eliminated as there will always be some resistance between the wooden plane and the surface it is in contact with.

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