A uniform chain of length 8.00 m initially lies stretched out on a horizontal table. (a) Assuming the coefficient of static friction between chain and table is 0.600, show that the chain will begin to slide off the table if at least 3.00 m of it hangs over the edge of the table. (b) Determine the speed of the chain as its last link leaves the table, given that the coefficient of kinetic friction between the chain and the table is 0.400.

μ (a) (b) S A block of mass 1.36kg is on a wedge with a block-wedge static coefficient of friction, µ = 0.204. The wedge's angle of interest is known, where 0 = 28.5° as shown in the above illustration. The wedge is rotated with an angular frequency of oo with the block's center of mass located a distance L = 0.572m up the ramp from the axis of rotation as depicted by the above diagram. (a) What is the largest positive value of oo that is allowed to keep the block at the same location on the wedge? (b) What is the smallest positive value of that is allowed to keep the block at the same location on the wedge? rad/s rad/s Answer part (a) Answer part (b)

Q1. (a) A 15 m long light beam is supported at A and B at two ends. Loads of 60 N and 40 N are applied vertically at distances of 12 m and 6 m from point B respectively as. shown below. Calculate the reactions at A and B. A RA 3 m 60 N 6 m 40 N 35⁰ 6 m B (b) A ball of mass 4 kg is hung by an inelastic string from the ceiling. A horizontal force applied to the ball such that the string deflected with an angle 35° from the vertical. Find the magnitude of the force and the tension in the string. (i) Find the acceleration of the block. (ii) Find the displacement after 8 seconds. RB 4 kg (c) A wooden block of mass 2 kg lying on a horizontal floor is pulled by a horizontal force of 30 N. The coefficient of friction between the block and the floor is 0.3.

A force F = 40N perpendicular to the wall acts on the block in the figure of mass m = 2 kg. What should be the minimum static friction coefficient so that the body does not fall to the ground? (g = 10 m / s2)

On a horizontal plane a block of mass m = 0.30 kg is placed and initially held at rest. To this block a massless string is attached and it initially keeps another block of mass M = 0.50 kg vertically at rest via a fixed pulley as shown in Figure. The coefficient of kinetic friction between the block m and the plane is Pk -0.25, but the friction between the block M and the vertical wall is zero. Calculate the tension T by string in N. (Hint: First calculate the acceleration of m or M. And set up the equation of motion for M to find the tension T.) T m M

A block has a mass of 6kg and rest initially on a plane inclined at 35°. What value of force is required to stop the block from sliding if: (a) the plane is frictionless, (b) the plane has coefficients of fractions static and kinetic equal to 0.20 and 0.18 respectively? What will the value of the force be if the velocity is constant and is directed upward parallel the incline?

Illustrated below is a 14-lb wooden pole tied on a 3-ft long rope at the bottom of a freshwater lake (γ = 62.47 lbs/ft3). The pole is 10 feet long and has a uniform cross-section of 7.5 in2. If the support is 8 feet below the free surface, determine the angle β produced.

In the figure a fastidious worker pushes directly along the handle of a mop with a force F. The handle is at an angle 0-42° with the vertical, and u, -0.68 and p₁,-0.49 are the coefficients of static and kinetic friction between the head of the mop and the floor. Ignore the mass of the handle and assume that all the mop's mass m-0.73 kg is in its head. (a) If the mop head moves along the floor with a constant velocity, then what is F? (b) If @ is less than a certain value 00. then F (still directed along the handle) is unable to move the mop head. Find 0. K (a) Number (b) Number Units Units

At a family picnic you are appointed to push your obnoxious cousin Throckmorton in a swing . His weight is w, the length of the chains is R, and you push Throcky until the chains make an angle u0 with the vertical. To do this, you exert a varying horizontal force F S that starts at zero and gradually increases just enough that Throcky and the swing move very slowly and remain very nearly in equilibrium throughout the process. (a) What is the total work done on Throcky by all forces? (b) What is the work done by the tension T in the chains? (c) What is the work you do by exerting force F ? (Ignore the weight of the chains and seat.)

A student is skateboarding down a ramp that is 5.02 m long and inclined at 23.6° with respect to the horizontal. The initial speed of the skateboarder at the top of the ramp is 2.34 m/s. Neglect friction and find the speed at the bottom of the ramp.