An 8 kg box is on an incline at 40 degrees from the horizontal. It is attached to a 10 kg box via a rope over a pulley that is on another incline of 50 degrees from the horizontal. Both inclines are frictionless. What is the acceleration of the system and what is the tension in the rope connecting the boxes. (Think of a triangle with one box on one side and the other box on the other side connected by a single rope over a pulley).

Two crates of fruit  are released from the top of a ramp inclined at 30 degrees from the horizontal and 4.5 meter long. The two crates consist of  an apple crate of mass 20 kg that is placed in front of a watermelon crate of mass 80 kg.  The apple crate has a coefficient of friction of 0.20 while the watermelon crate has a coefficient of friction of 0.15. How long does it take the apple crate to reach the bottom of the incline if it needs to travel a distance of 4.5 meters?

A 10 m long board that has a mass of 20 kg is held up by two vertical ropes. The left rope is 2 m from the left end of the board, and the other rope is 2 m from the right end of the board. A 40 kg box sits 2 m from the right end. Find the tension in the rope on the left.

A box, initially at rest, is pushed up a ramp that makes an angle of 15◦ with the horizontal as shown in the diagram. The magnitude of the pushing force is 8m newtons, where m is the mass of the box in kilograms. The force is in a direction parallel to and up the ramp. The coefficient of sliding friction between the box and the ramp is 0.25. Model the box as a particle and take the magnitude of the acceleration due to gravity to be g = 9.8 m s−2 . Express the four forces in component form in terms of unknown magnitudes where appropriate and find an expression for the resultant force acting on the box. Hence find the magnitude of the acceleration of the box, in m s−2

Joe, a carpenter with a weight of 600 N, is working on a scaffold. His young son Jack is helping him. Jack has a weight of 450 N.   The scaffold is held up by two ropes. One rope has an upward tension of 750 N. The weight of the scaffold is 400 N. What is the upward tension in the other rope?   Which below is correct? 700 N 850 N 1000 N 750 N

Block A in the figure has mass mA = 4.20 kg, and block B has mass mg = 2.00 kg. The coefficient of kinetic friction between block B and the horizontal plane is k = 0.500. The inclined plane is frictionless and at angle = 30.0°. The pulley serves only to change the direction of the cord connecting the blocks. The cord has negligible mass. Find (a) the tension in the cord and (b) the magnitude of the acceleration of the blocks. Frictionless, massless pulley MA mp B

Three blocks are connected over two frictionless, massless pulleys by two inextensible, massless cords as shown in the figure. There is friction between block m2 and the horizontal surface of the table. If the block m₁ moves downward after being released from rest, then what is the magnitude of the acceleration of the blocks and the magnitude of the tension in the cords in terms of the masses of the blocks m₁, m2, and m3, the coefficient of kinetic friction between block m₂ and the table, uk, and the acceleration due to gravity, g. Include a force diagram or free-body diagram of the situation. m1 mq m3