A block of mass m, on a rough, horizontal surface is connected to a ball of mass m, by a lightweight cord over a lightweight, frictionless pulley as shown in figure. A force of magnitude F at an angle 0 with the horizontal is applied to the block as shown and the block slides to the right. The coefficient of kinetic friction between the block and surface is Hr Find the magnitude of acceleration of the two objects.

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3. A 5-kg crate is released from rest at Point A of a 20-kg ramp which is inclined at 40 degrees as shown in the figure below. The lengths of the ramp is 2 m. The interface between the ramp and the ground can be assumed to be frictionless. Use Newton's 2nd Law and the definition of the center of mass to determine the horizontal distance that the ramp has moved when the crate reaches Point B. Neglect the size of the crate. Does your answer depend on the frictional force between the crate and the ramp? e S

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5. Three blocks are connected over two frictionless, massless pulleys by two inextensible, massless cords as shown in the figure. There is friction between block m and the horizontal surface of the table. If the block m, 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 m, , and ms, the coefficient of kinetic friction between block my and the table, a. and the acceleration due to gravity, g. Include a force diagram or free-body diagram of the situation.

Problem No. 1 A 200-kg block rests on a horizontal plane. Find the magnitude of the force P required to give the block an acceleration of 1.80 m/s² to the right. The coefficient of kinetic friction between the block and the plane is 0.25. P 30°

Q5. A smooth uniform sphere of mass m and radius r is squeezed between the two massless levers, each of length I, which are inclined at an angle o with the vertical. If a force P is applied between the ends of the levers, as shown, what is the vertical acceleration of the sphere when p=30°? (Problem P3-1 in the text).

A box with mass m is on a frictionless inclined ramp, as shown. The ramp has an angle of θ with respect to the horizontal.  The ramp is firmly attached to the inside of a car. The car is traveling to the right, and is slowing down. The car has a constant acceleration with magnitude a.  You observe that the box doesn’t slide up or down the ramp.     What is the angle of the ramp? Write your answer in variables, using only m, g, and a. This problem should be solved using the “recipe” taught in class. Focus Draw a free body diagram Identify the direction of the acceleration Write Newton's 2nd law (F=ma) Solve for unknowns  Suppose that the driver now presses harder on the brakes. Would the box slide up the ramp, or slide down the ramp? Or would it not slide at all? No calculation required, but very briefly (one or two sentences) justify your answer. Draw a simple diagram if it helps!