I have a test soon and I don't understand these types of problems very well...can anyone please explain these?
1) A carton of eggs rests on the seat of a car moving at 22.5 m/s. What is the least distance in which the cart can be uniformly slowed to a stop if the eggs are not to slide? The coefficient of friction between the seat and the carton is 0.24
Answer is 107m
2) Two blocks are connected by string of negligible mass that passes over a frictionless pulley. The mass of the block on the table is 43.1 kg and the mass of the block in the air is 18.9 kg. Assume the table is frictionless. Find the acceleration of the two blocks and the tension in the string
Answers are 2.98 m/s^2 & 129N
3) 2 masses 5 kg and 10 kg are tied to the opposite ends of a massless rope, and the rope is hung over a massless and friictionless pulley. Find the acceleration of the masses
Answer is 3.3 m/s^2
4) Block 1, 8 kg, is moving on a 33 degree incline ( coefficient of kinetic friction is 0.25. This block is connected to block 2, 22 kg, by a cord that passes over a massless and frictionless pulley. Find the acceleration of each block and the tension in the cord
Answers are 5.2 m/s^2 and 101N
22 kg mass:
22 a = (22)(9.8) - T .... (1)
8 kg mass:
Perpendicular to slope: 0 = R - (8)(9.8) cos 33 => R = (8)(9.8) cos 33 .... (2)
Parallel to slope: 8a = T - (8)(9.8) sin 33 - (0.25) R .... (3)
Substitute equation (2) into equation (3) and solve equations (1) and (3) simultaneously for a and T.