2.9 A block of mass of 2 kg slides on an inclined plane that makes an angle of 30 with the horizontal. The coefficient of friction between the block and the

surface is 3/2.

(a) What force should be applied to the block so that it moves down without any acceleration?

(b) What force should be applied to the block so that it moves up without any acceleration?

2.10 A block is placed on a ramp of parabolic shape given by the equation y = x2/20, If s = 0.5, what is the maximum height above the ground at which the block can be placed without slipping?

2.11 A block slides with constant velocity down an inclined plane that has slope angle = 30.

(a) Find the coefficient of kinetic friction between the block and the plane.

(b) If the block is projected up the same plane with initial speed v0 = 2.5 m/s, how far up the plane will it move before coming to rest? Whatfraction of the initial kinetic energy is transformed into potential energy?

What happens to the remaining energy?

(c) After the block comes to rest, will it slide down the plane again? Justify

your answer.

2.12 Consider a fixed inclined plane at angle . Two blocks of mass M1 and M2 are attached by a string passing over a pulley of radius r and moment of inertia I1

(a) Find the net torque acting on the system comprising the two masses, pulley and the string.

(b) Find the total angular momentum of the system about the centre of the

pulley when the blocks are moving with speed v.

(b) Calculate the acceleration of the blocks.

2.13 A box of mass 1 kg rests on a frictionless inclined plane which is at an angle of 30 to the horizontal plane. Find the constant force that needs to be applied

parallel to the incline to move the box

(a) up the incline with an acceleration of 1 m/s2

(b) down the incline with an acceleration of 1 m/s2

2.14 A wedge of mass M is placed on a horizontal floor. Another mass m is placed on the incline of the wedge. Assume that all surfaces are frictionless, and the incline makes an angle with the horizontal. The mass m is released from rest on mass M, which is also initially at rest. Find the accelerations of M and m

2.15 Two smooth inclined planes of angles 45 and hinged together back to back. Two masses m and 3m connected by a fine string passing over a light pulley move on the planes. Show that the acceleration of their centre of mass is 5/8 g at an angle tan1 to the horizon

2.16 Two blocks of masses m1 and m2 are connected by a string of negligible mass which passes over a pulley of mass M and radius r mounted on a frictionless axle. The blocks move with an acceleration of magnitude a and direction as shown in the diagram. The string does not slip on the pulley, so the tensions T1 and T2 are different. You can assume that the surfaces of the inclines are frictionless. The moment of inertia of the pulley is given by I = Mr 2:

(a) Draw free body diagrams for the two blocks and the pulley.

(b) Write down the equations for the translational motion of the two blocks

and the rotational motion of the pulley.

(c) Show that the magnitude of the acceleration of the blocks is given by

a = g(

3m2 m1)

M + 2(m2 + m1)

2.17 Two masses in an Atwood machine are 1.9 and 2.1 kg, the vertical distance of

the heavier body being 20 cm above the lighter one. After what time would the

lighter body be above the heavier one by the same vertical distance? Neglect

the mass of the pulley and the cord