A block weighing 70.7 N rests on a plane inclined at 21.6° to the horizontal. The coefficient of the static and kinetic frictions are 0.23 and 0.12 respectively. What is the minimum magnitude of the force F, parallel to the plane, that will prevent the block from slipping?
Can someone please tell me what steps to do? I don't understand this one.
To find the minimum magnitude of the force F that will prevent the block from slipping, you need to consider the forces acting on the block and then apply the conditions for equilibrium. Here are the steps you can follow:
1. Draw a free-body diagram to represent the forces acting on the block.
- There will be three forces: the weight of the block (mg), the normal force (N), and the force parallel to the plane (F).
- The weight acts vertically downward, the normal force acts perpendicular to the plane (upward), and the force (F) acts parallel to the plane.
2. Resolve the weight of the block into components.
- The weight (mg) can be resolved into two components: one parallel to the plane (mg*sinθ, where θ is the angle of inclination) and one perpendicular to the plane (mg*cosθ).
3. Calculate the perpendicular component of the weight.
- The perpendicular component of the weight (mg*cosθ) provides the normal force (N) required to counteract it.
4. Determine the force of friction.
- The force of friction (f) is given by the coefficient of static friction (µ_s) multiplied by the normal force (N), which is f = µ_s * N.
5. Apply the conditions for equilibrium in the direction parallel to the plane.
- The sum of the forces in the horizontal direction (parallel to the plane) must be zero to prevent the block from slipping.
- The forces acting parallel to the plane are the force (F) and the force of friction (f).
- So, F - f = 0.
6. Substitute the known values into the equation and solve for F.
- Substitute the value of the force of friction (f = µ_s * N).
- Rearrange the equation to solve for F: F = f = µ_s * N.
7. Substitute the value of the normal force (N) using the perpendicular component of the weight (mg*cosθ).
- N = mg * cosθ.
8. Substitute the known values of the weight (m * g), the coefficient of static friction (µ_s), and the angle of inclination (θ), and solve for F.
- F = µ_s * (m * g * cosθ).
By following these steps, you should be able to find the minimum magnitude of the force F that will prevent the block from slipping.