Inclined Plane Force w/ Friction

In summary, a mass of 11 kg is placed on an inclined plane with friction. A force of 59 Newtons is applied downward, perpendicular to the plane. The angle of the incline increases from 0 degrees until it reaches 56.7 degrees, at which point the block begins to slide. The coefficient of static friction for this situation is 0.762.
  • #1
yankeekd25
27
0

Homework Statement


A mass of m = 11 kg is placed on incline plane with friction. A force with a magnitude of F = 59 Newtons is applied downward, perpendicular to the plane at all times. As the angle of the incline is increased from zero degrees it remains static until it reaches an angle of x = 56.7 degrees when it begins to slide. What is the coefficient of static friction for this situation?

I'm guessing that I sum up the forces as I would for a non-friction inclined plane problem, and then divide by the 59 N that they give you? Would I be assuming correctly?
 
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  • #2
The normal reaction on the block due to the plane is not 59 N. Draw a complete FBD and you'll see. (Resolve the grav. force on the block into its sine and cosine components)
 
  • #3
sArGe99 said:
The normal reaction on the block due to the plane is not 59 N. Draw a complete FBD and you'll see. (Resolve the grav. force on the block into its sine and cosine components)

I believe the answer is .762. mg sin theta / 118, where 118 is the calculated normal force?
 

1. What is an inclined plane?

An inclined plane is a simple machine that consists of a flat surface that is at an angle, or inclined, to the ground. It is used to reduce the force needed to lift an object to a higher level.

2. How does friction affect the force on an inclined plane?

Friction is a force that opposes motion and acts in the opposite direction of the motion. On an inclined plane, friction acts in the direction opposite to the motion of the object, making it harder to move the object up the plane.

3. How do I calculate the force needed to move an object up an inclined plane with friction?

The force needed to move an object up an inclined plane with friction can be calculated using the formula F = mgsinθ + μmgcosθ, where F is the force, m is the mass of the object, g is the acceleration due to gravity, θ is the angle of the inclined plane, and μ is the coefficient of friction.

4. Is it easier to move an object up an inclined plane with or without friction?

It is easier to move an object up an inclined plane without friction because friction adds an additional force that must be overcome. In the absence of friction, the force required to move the object up the plane is equal to the force of gravity pulling the object down the plane.

5. How does the angle of the inclined plane affect the force needed to move an object?

The force needed to move an object up an inclined plane increases as the angle of the plane increases. This is because a steeper angle increases the force of gravity acting on the object, making it harder to lift. However, the force needed decreases as the angle decreases, as the force of gravity acting on the object decreases.

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