minimum force

Problem 511
Find the least value of P required to cause the system of blocks shown in Fig. P-511 to have impending motion to the left. The coefficient of friction under each block is 0.20.
 

Problem 507
The 2225-N block shown in Fig. P-507 is in contact with 45° incline. The coefficient of static friction is 0.25. Compute the value of the horizontal force P necessary to (a) just start the block up the incline or (b) just prevent motion down the incline. (c) If P = 1780 N, what is the amount and direction of the friction force?
 

Problem 506
A 400 lb block is resting on a rough horizontal surface for which the coefficient of friction is 0.40. Determine the force P required to cause motion to impend if applied to the block (a) horizontally or (b) downward at 30° with the horizontal. (c) What minimum force is required to start motion?
 

Problem 325
Determine the amount and direction of the smallest force P required to start the wheel in Fig. P-325 over the block. What is the reaction at the block?
 

Problem 324
A wheel of 10-in radius carries a load of 1000 lb, as shown in Fig. P-324. (a) Determine the horizontal force P applied at the center which is necessary to start the wheel over a 5-in. block. Also find the reaction at the block. (b) If the force P may be inclined at any angle with the horizontal, determine the minimum value of P to start the wheel over the block; the angle P makes with the horizontal; and the reaction at the block.