เป็นเครื่องกลอย่างง่ายที่แปลงแรงให้เป็นแรงขนาดใหญ่ขึ้นในแนวตั้งฉาก ลิ่ม เป็นเครื่องกลอย่างง่ายที่แปลงแรงให้เป็นแรงขนาดใหญ่ขึ้นในแนวตั้งฉาก ใช้ขยับวัตถุหนัก Consider the wedge used to lift a block of weight W by applying a force P to the wedge
FBD of the block and the wedge Exclude the weight of the wedge since it is small compared to weight of the block
Frictional forces F1 and F2 must oppose the motion of the wedge Frictional force F3 of the wall on the block must act downward as to oppose the block’s upward motion Location of the resultant forces are not important since neither the block or the wedge will tip Moment equilibrium equations not considered 7 unknowns - 6 normal and frictional force and force P
2 force equilibrium equations (∑Fx = 0, ∑Fy = 0) applied to the wedge and block (4 equations in total) and the frictional equation (F = μN) applied at each surface of the contact (3 equations in total) If the block is lowered, the frictional forces will act in a sense opposite to that shown Applied force P will act to the right if the coefficient of friction is small or the wedge angle θ is large
Otherwise, P may have the reverse sense of direction in order to pull the wedge to remove it If P is not applied or P = 0, and friction forces hold the block in place, then the wedge is referred to as self-locking
Example 8.7 The uniform stone has a mass of 500kg and is held in place in the horizontal position using a wedge at B. if the coefficient of static friction μs = 0.3, at the surfaces of contact, determine the minimum force P needed to remove the wedge. Is the wedge self- locking? Assume that the stone does not slip at A.
Solution Minimum force P requires F = μs NA at the surfaces of contact with the wedge FBD of the stone and the wedge On the wedge, friction force opposes the motion and on the stone at A, FA ≤ μsNA, slipping does not occur
Solution 5 unknowns, 3 equilibrium equations for the stone and 2 for the wedge
Solution Since P is positive, the wedge must be pulled out If P is zero, the wedge would remain in place (self-locking) and the frictional forces developed at B and C would satisfy FB < μsNB FC < μsNC