Finding theta on an incline plane

In summary, the angle at which the block begins to move is equal to the arctan of the coefficient of static friction.
  • #1
jorcrobe
12
0

Homework Statement


A block is resting on a wooden plank. On one end of the plank is a hinge so the other end my be lifted to create and angle θ with respect to the horizontal. The plank has a coefficient of static friction of μs.
Using the sum of forces along the plank. Find the angle at which the block begins to move in terms of μs.

Homework Equations


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The Attempt at a Solution



I gathered that in order for the block to move, the force of static friction must be met, so I set the force of friction equal to the weight force pointing down the slope; thinking that these two must be at least equal for movement. So, I have:

Fw_parallelToSlope = mgsin(theta)
Ff_static = mgcos(theta) * μ

Setting equal to:
mgcos(theta) * μ = mgsin(theta)

(rearranged below for theta)
theta = atan(μ)Thoughts? Thanks, and best wishes.
 
Last edited:
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  • #2
Assuming that atan(mu) is arctan(mu), you've got it correct.
 

1. What is theta in an incline plane?

Theta is the angle of inclination of the incline plane, measured from the horizontal surface.

2. How do you find theta on an incline plane?

To find theta on an incline plane, you need to measure the height and length of the incline and use the trigonometric function tan(theta) = height/length.

3. Why is finding theta on an incline plane important?

Finding theta on an incline plane is important because it helps in understanding the forces acting on an object on the incline and calculating its acceleration and velocity.

4. Can theta be negative on an incline plane?

No, theta cannot be negative on an incline plane as it represents the angle of inclination which is always measured as a positive value.

5. How does the value of theta affect the motion of an object on an incline plane?

The value of theta affects the motion of an object on an incline plane by determining the component of its weight that acts along the incline, which in turn affects the object's acceleration and velocity.

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