Solved: Determine the force P required to (a) raise and (b) lower the cylinder of weight

It is observed that the two cylinders will remain in slow steady motion as indicated in the drawing. Determine the coefficient of friction \(\mu\) between the cord and the fixed shaft.

Determine the force P required to (a) raise and (b) lower the cylinder of weight W at a slow steady speed. The coefficient of friction between the cord and the fixed shaft is 0.40.

A dockworker adjusts a spring line (rope) which keeps a ship from drifting alongside a wharf. If he exerts a pull of 200 N on the rope, which has \(1 \frac{1}{4}\) turns around the mooring bit, what force T can he support? The coefficient of friction between the rope and the cast-steel mooring bit is 0.30.

The 20-lb block and the 50-lb block are connected by a rope hung over the fixed curved surface. If the system is on the verge of slipping, calculate the coefficient of friction between the rope and the surface.

For a certain coefficient of friction \(\mu\) and a certain angle \(\alpha\), the force P required to raise m is 4 kN, and that required to lower m at a constant slow speed is 1.6 kN. Calculate the mass m.

Determine the value of the force P which will cause motion of the 40 - kg block to impend up the \(25^{\circ}\) incline. The cylinder is fixed to the block and does not rotate. The coefficients of static friction are \(\mu_1\) = 0.40 and \(\mu_2\) = 0.20.

Determine the magnitude of the force P which will cause motion of the block of Prob. 6/102 to impend down the incline. All given information in that problem remains the same.

The tape slides around the two fixed pegs as shown and is under the action of the horizontal tensions \(T_1=40 \mathrm{~N}\) and \(T_2=160 \mathrm{~N}\). Determine the coefficient of friction \(\mu\) between the tape and the pegs.

In western movies, cowboys are frequently observed hitching their horses by casually winding a few turns of the reins around a horizontal pole and letting the end hang free as shown––no knots! If the freely hanging length of rein weighs 2 oz and the number of turns is as shown, what tension T does the horse have to produce in the direction shown in order to gain freedom? The coefficient of friction between the reins and wooden pole is 0.70.

Calculate the horizontal force P required to raise the 100-kg load. The coefficient of friction between the rope and the fixed bars is 0.40.

Mover A exerts a horizontal force P = 180 N on the 50-kg crate. What horizontal tension T must mover B exert in order to move the crate up the rough ramp (\(\mu_k\) = 0.40) at a slow steady speed? There is a fixed horizontal pole C across the rear opening of the truck, for which the coefficient of kinetic friction is \(\mu_k\) = 0.30.

The 180-lb tree surgeon lowers himself with the rope over a horizontal limb of the tree. If the coefficient of friction between the rope and the limb is 0.60, compute the force which the man must exert on the rope to let himself down slowly.

Determine the minimum coefficient of static friction for which the bar can be in static equilibrium in the configuration shown. The bar is uniform and the fixed peg at C is small. Neglect friction at B.

The positions of shafts A and C are fixed, while that of shaft B can be varied via the vertical slot and the locking bolt. If the coefficient of static friction is \(\mu\) at all interfaces, determine the dependence of T on the coordinate y, where T is the tension required to begin to lift the cylinder of mass m. All shafts are fixed against rotation.

Repeat Prob. 6/110, only now the coefficients of static friction are as follows: 0.60 at A and C and 0.20 at B. Plot T/mg as a function of y for 0 \(\leq\) y \(\leq\) 10r, where r is the common radius of all three shafts. What are the limiting values of T/mg for y = 0 and for large values of y?

The uniform drum A with center of mass at midlength is suspended by a rope which passes over the fixed cylindrical surface B. The coefficient of static friction between the rope and the surface over which it passes is \(\mu\). Determine the maximum value which the dimension a may have before the drum tips out of its horizontal position.

The uniform I-beam has a mass of 74 kg per meter of length and is supported by the rope over the fixed 300-mm drum. If the coefficient of friction between the rope and the drum is 0.50, calculate the least value of the force P which will cause the beam to tip from its horizontal position.

The block of weight \(W_1\) has a circular groove to accommodate the light rope. Determine the minimum value of the ratio \(W_2/W_1\) for which the block will be in static equilibrium. The coefficient of static friction between the rope and the groove is 0.35. State any assumptions.

For the design of the band brake shown, find the couple M required to turn the pipe in the V-block against the action of the flexible band. A force P = 25 lb is applied to the lever, which is pivoted about O. The coefficient of friction between the band and the pipe is 0.30, and that between the pipe and the block is 0.40. The weights of the parts are negligible.

Determine the range of mass \(m_2\) for which the system is in equilibrium. The coefficient of static friction between the block and the incline is \(\mu_1=0.25\) and that between the cord and the fixed disk on the block is \(\mu_2=0.15\).

Replace the flat belt and pulley of Fig. 6/11 by a V-belt and matching grooved pulley as indicated by the cross-sectional view accompanying this problem. Derive the relation among the belt tensions, the angle of contact, and the coefficient of friction for the V-belt when slipping impends. A V-belt design with \(\alpha=35^{\circ}\) would be equivalent to increasing the coefficient of friction for a flat belt of the same material by what factor n?

A light cable is connected to the ends of the uniform bar AB and goes over a fixed peg C. Beginning from the horizontal position shown in part a of the figure, a length d = 0.15 m of cable is moved from the right to the left side of the peg as shown in part b of the figure. If the cable first slips on the peg at this position, determine the coefficient of static friction between the peg and the cable. Neglect the effects of the diameter of the peg.