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, parallel to the plane, that will prevent the block from slipping, you can follow these steps:
1. Decompose the weight of the block into its components parallel and perpendicular to the plane.
- The weight of the block (70.7 N) can be decomposed into two components: one parallel to the plane and one perpendicular to the plane.
- The parallel component (F_parallel) can be calculated as the weight of the block multiplied by the sine of the angle of inclination (21.6°).
- The perpendicular component (F_perpendicular) can be calculated as the weight of the block multiplied by the cosine of the angle of inclination (21.6°).
F_parallel = 70.7 N * sin(21.6°)
F_perpendicular = 70.7 N * cos(21.6°)
2. Calculate the maximum static friction force (F_static_max) acting parallel to the plane.
- The maximum static friction force can be found by multiplying the coefficient of static friction (0.23) by the perpendicular component of the weight.
F_static_max = 0.23 * F_perpendicular
3. Compare the maximum static friction force (F_static_max) with the parallel component of the weight (F_parallel).
- If F_static_max is greater than or equal to F_parallel, the block will not slip, and a force F equal to F_parallel is sufficient to prevent slipping.
- If F_static_max is less than F_parallel, the block will start to slip, and you need to consider the kinetic friction force.
4. Calculate the kinetic friction force (F_kinetic) acting parallel to the plane.
- The kinetic friction force can be calculated by multiplying the coefficient of kinetic friction (0.12) by the perpendicular component of the weight.
F_kinetic = 0.12 * F_perpendicular
5. Compare the kinetic friction force (F_kinetic) with the parallel component of the weight (F_parallel).
- If F_kinetic is greater than or equal to F_parallel, then the block will not slip, and a force F equal to F_parallel is sufficient to prevent slipping.
- If F_kinetic is less than F_parallel, then the block will continue slipping, and you need to apply a force greater than F_parallel to prevent slipping.
So, after performing these steps, you will have the information needed to determine whether the block will slip or not and the minimum magnitude of the force F parallel to the plane required to prevent slipping.