If there is a 23lb. block on a plank and the static friction is .6 and the sliding friction is .35. What angle must the plank be raised to just allow the box to slide?
You don't need the sliding friction coefficeint to answer this; you need the maximum friction force possible without sliding, which is calculated with the static coefficient, Us. You also do not need the weignt (23 lb); it will cancel out.
Let W be the weight and A be the maximum angle without slipping.
W sin A = W cos A Us
Divide both sides by W cos A and you will have an equation for the tangent of the maximum angle A.
So to figure out maximum friction force possible without sliding, that's the product of the 23lb block and the static friction of .6. that will be A?
Then I'm not sure what to do next
You must have not read or understand what I wrote. You don't use the weight AT ALL.
If you do the last step that I suggested, you end up with
tan A = Us = 0.6
Therefore A is the angle with a tangent of 0.6. That is written
A = arctan 0.6
Use a hand calculator or trig table to get A.
Than you for your help
To determine the angle at which the block will start to slide, we need to analyze the forces acting on it. Let's break it down step by step:
1. Identify the forces:
- The weight of the block, which acts vertically downwards. The weight can be calculated as the mass multiplied by the acceleration due to gravity (9.8 m/s^2).
- The normal force, which acts perpendicular to the surface of the plank, balancing the weight of the block.
- The static friction force, which opposes the impending motion of the block.
- The sliding friction force, which opposes the motion of the block once it starts to slide.
2. Set up the equations:
- The force of static friction (Fs) can be calculated as the product of the coefficient of static friction (μs) and the normal force (N).
- The force of sliding friction (Fd) can be calculated as the product of the coefficient of sliding friction (μk) and the normal force (N).
- The component of the weight acting parallel to the plank can be calculated as the weight multiplied by the sine of the angle (θ).
- The component of the weight acting perpendicular to the plank (normal force) remains the same as the weight.
3. Analyze the motion:
- The block will start to slide when the force of static friction reaches its maximum value, which is μs times the normal force.
- At this point, the force of static friction will equal the weight component parallel to the plank (Fs = Weight * sin(θ)).
4. Solve for the angle:
- We know the weight (23 lbs), the coefficient of static friction (μs = 0.6), and the coefficient of sliding friction (μk = 0.35).
- Rearranging the equation, we get: sin(θ) = Fs / Weight = μs * N / Weight.
- From here, we can substitute N with the weight: sin(θ) = μs * Weight / Weight = μs.
5. Calculate the angle:
- To find θ, take the inverse sine (sin^⁻1) on both sides of the equation: θ = sin^⁻1(μs).
- Plug in the value of the coefficient of static friction (μs = 0.6) to calculate θ.
Therefore, the angle at which the plank must be raised to just allow the block to slide is approximately θ = sin^⁻1(0.6), which is about 36.87 degrees.