2.- A 2inx4inx8ft is leaning against the wall, draw afree-body diagram of forces on it. Give an expression throughdetailed steps using the diagram what would be the minimum angle ofthe wooden bar with the floor so it won’t slide.
To determine the minimum angle at which the wooden bar will not slide, we need to consider the forces acting on it. Let's start by drawing a free-body diagram of the forces acting on the wooden bar leaning against the wall.
1. Start by drawing a rectangular shape to represent the wooden bar. Label it as the bar.
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2. Add an arrow pointing upward from the bottom left corner of the bar. Label it as the normal force (N), which represents the force exerted by the floor on the bar to support its weight.
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-------> N (upward)
3. Add an arrow pointing right from the bottom right corner of the bar. Label it as the static friction force (Ff), which opposes the tendency of the bar to slide downwards. The direction is parallel to the floor.
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Ff <------
4. Add an arrow pointing left from the top right corner of the bar. Label it as the weight (W), which acts vertically downward due to the force of gravity.
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W <-----| |
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Now that we have the free-body diagram, we can determine the minimum angle of the wooden bar with the floor so that it won't slide. At this minimum angle, the static friction force (Ff) will be at its maximum value, preventing sliding.
Using trigonometry, the equation for the maximum static friction force is:
Ff = N * μs
where μs is the coefficient of static friction between the bar and the floor.
Since the bar is not sliding, we can equate the vertical component of the weight (W) to the normal force (N):
W = N
Applying trigonometry to the free-body diagram, we can express W in terms of the angle θ between the bar and the floor:
W = mg = m * g * cos(θ)
where m is the mass of the bar and g is the acceleration due to gravity (9.8 m/s^2).
Setting W equal to N, we have:
m * g * cos(θ) = N
Finally, substituting N in the equation for Ff and rearranging, we get:
Ff = m * g * μs * cos(θ)
The minimum angle (θ) can be calculated by rearranging this equation as:
θ = arccos(Ff / (m * g * μs))
So, with the given dimensions and known values of mass and coefficient of static friction, you can substitute them into the equation to calculate the minimum angle at which the wooden bar will not slide.