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.
When you are talking about a no-slipping condition, the static coefficient of friction, 0.23 in this case, is what matters.
There is a gravity weight component of 70.7 sin 21.6 = 26.0 N parallel to the incline. The maximum static friction force than can resist motion, in the same direction, is
70.7 cos 21.6 * 0.23 = 65.73 N
That is more than enough to prevent the block from sliding. No additional force is needed.
F = 0
See, I thought that was right, too. But I plug that into my computer and it says it's not right. So I'm not sure what I'm doing wrong...
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 apply the concepts of friction, equilibrium, and trigonometry. Here are the steps you can follow:
Step 1: Draw a free-body diagram of the block, showing all the forces acting on it. In this case, there are three forces:
- The weight of the block acting vertically downwards (70.7 N) can be resolved into two components: perpendicular (mg * cosθ) to the inclined plane and parallel (mg * sinθ) to the inclined plane.
- The normal force (N) acting perpendicular to the inclined plane.
- The friction force (Ff) acting parallel to the inclined plane.
Step 2: Determine the magnitudes of the perpendicular and parallel components of weight. Use trigonometry to find these components:
- Perpendicular component = weight * cosθ
- Parallel component = weight * sinθ
Step 3: Determine the normal force (N) acting perpendicular to the inclined plane. The normal force is equal in magnitude but opposite in direction to the perpendicular component of weight.
Step 4: Calculate the friction force (Ff) using the formula Ff = μN, where μ is the coefficient of static friction. Here, we are finding the minimum force to prevent slipping, so we use the coefficient of static friction.
Step 5: Set up an equilibrium equation to find the minimum magnitude of force F. Since the block is on the verge of slipping, the friction force Ff must be equal to the force parallel to the plane, F.
- Ff = F
Step 6: Substitute the calculated values into the equilibrium equation and solve for F:
- F = μN
Step 7: Substitute the values of μ and N into the equation to get the final answer.
By following these steps, you will be able to determine the minimum magnitude of the force F that will prevent the block from slipping.