Engineering Mechanics - Statics Episode 3 Part 2 pdf

If thesquare-threaded screw has a lead h, radius r, and the coefficient of static friction is μs, determine the horizontal force developed on the board at A and the vertical forces devel

Frictional Forces on Screw: Here

2π d2

The clamp provides pressure from several directions on the edges of the board If the

square-threaded screw has a lead h, radius r, and the coefficient of static friction is μs, determine

the horizontal force developed on the board at A and the vertical forces developed at B and C if a

torque M is applied to the handle to tighten it further The blocks at B and C are pin-connected to

Problem 8-83

The two blocks under the double wedge are brought together using a left and right

square-threaded screw If the mean diameter is d, the lead is r l, and the coefficient of static

friction is μs, determine the torque needed to draw the blocks together The coefficient

of static friction between each block and its surfaces of contact is μ'

s.Units Used:

The two blocks under the double wedge are brought together using a left and right

square-threaded screw If the mean diameter is d, the lead is r l, and the coefficient of static

friction is μs, determine the torque needed to spread the blocks apart The coefficient

of static friction between each block and its surfaces of contact is μ'

s.Units Used:

The cord supporting the cylinder of mass M passes around three pegs, A, B, C, where the

coefficient of friction is μs Determine the range of values for the magnitude of the horizontal

force P for which the cylinder will not move up or down.

The truck, which has mass m t , is to be lowered down the slope by a rope that is wrapped around

a tree If the wheels are free to roll and the man at A can resist a pull P, determine the minimum

number of turns the rope should be wrapped around the tree to lower the truck at a constant

speed The coefficient of kinetic friction between the tree and rope is μk

Problem 8-87

The wheel is subjected to a torque M If

the coefficient of kinetic friction

between the band brake and the rim of

the wheel is μk, determine the smallest

horizontal force P that must be applied

to the lever to stop the wheel

A cylinder A has a mass M Determine the smallest force P applied to the handle of the lever

required for equilibrium The coefficient of static friction between the belt and the wheel is μs

The drum is pin connected at its center, B.

Determine the largest mass of cylinder A that can be supported from the drum if a force P is

applied to the handle of the lever The coefficient of static friction between the belt and the

wheel is μs The drum is pin supported at its center, B.

Given:

P = 20 N

The uniform bar AB is supported by a rope that passes over a frictionless pulley at C and a

fixed peg at D If the coefficient of static friction between the rope and the peg is μD,

determine the smallest distance x from the end of the bar at which a force F may be placed

and not cause the bar to move

Given:

Determine the smallest lever force P needed to prevent the wheel from rotating if it is subjected

to a torque M The coefficient of static friction between the belt and the wheel is μs The wheel

is pin-connected at its center, B.

Determine the torque M that can be resisted by the band brake if a force P is applied to the

handle of the lever The coefficient of static friction between the belt and the wheel is μs The

wheel is pin-connected at its center, B.

ΣM B = 0; − r F r F' + +M = 0

M = F' r−F r M = 177 N m⋅

Problem 8-93

Blocks A and B weigh W A and W B and respectively Using the coefficients of static friction indicated,

determine the greatest weight of block D without causing motion.

Blocks A and B have weight W, and D weighs W D Using the coefficients of static

friction indicated, determine the frictional force between blocks A and B and between

block A and the floor C.

FBD of a section of the belt is shown.

Proceeding in the general manner:

A V-fan-belt (V-angle θ) of an automobile engine passes around the hub H of a generator G

and over the housing F to a fan If the generator locks, and the maximum tension the belt can

sustain is Tmax, determine the maximum possible torque M resisted by the axle as the belt slips

over the hub Assume that slipping of the belt occurs only at H and that the coefficient of

kinetic friction for the hub is μs

M = −T 1 a+T max a M = 23.1 lb ft⋅

Problem 8-97

A cable is attached to the plate B of mass M B , passes over a fixed peg at C, and is attached to

the block at A Using the coefficients of static friction shown, determine the smallest mass of

block A so that it will prevent sliding motion of B down the plane.

The simple band brake is constructed so that the ends of the friction strap are connected to the

pin at A and the lever arm at B If the wheel is subjected to a torque M, determine the smallest

force P applied to the lever that is required to hold the wheel stationary The coefficient of static

friction between the strap and wheel is μs

The uniform beam of weight W 1 is supported by the rope which is attached to the end of the

beam, wraps over the rough peg, and is then connected to the block of weight W 2 If the

coefficient of static friction between the beam and the block, and between the rope and the

peg, is μs , determine the maximum distance that the block can be placed from A and still

remain in equilibrium Assume the block will not tip

The uniform concrete pipe has weight W and is unloaded slowly from the truck bed using the rope

and skids shown If the coefficient of kinetic friction between the rope and pipe is μk ,determine

the force the worker must exert on the rope to lower the pipe at constant speed There is a pulley

at B, and the pipe does not slip on the skids The lower portion of the rope is parallel to the skids.

A cord having a weight density γ and a total length L is suspended over a peg P as shown If the

coefficient of static friction between the peg and cord is μs , determine the longest length h which

one side of the suspended cord can have without causing motion Neglect the size of the peg and

the length of cord draped over it

Granular material, having a density ρ is transported on a conveyor belt that slides over the fixed

surface, having a coefficient of kinetic friction of μk Operation of the belt is provided by a

motor that supplies a torque M to wheel A.The wheel at B is free to turn, and the coefficient of

static friction between the wheel at A and the belt is μΑ If the belt is subjected to a pretension

T when no load is on the belt, determine the greatest volume V of material that is permitted on

the belt at any time without allowing the belt to stop What is the torque M required to drive the

belt when it is subjected to this maximum load?

Blocks A and B have a mass M A and M B, respectively If the coefficient of static friction

between A and B and between B and C is μs and between the ropes and the pegs D and E μ' s,

determine the smallest force F needed to cause motion of block B

Blocks A and B weigh W 1 and W 2, respectively Using the coefficients of static friction

indicated, determine the greatest weight W of block E without causing motion.

Solution: Assume that the wedge slips on the ground, but

the block does not slip on the wedge and theblock does not tip

Block A has mass m A and rests on surface B for which the coefficient of static friction is μ sAB If the

coefficient of static friction between the cord and the fixed peg at C is μsC,determine the greatest

mass m D of the suspended cylinder D without causing motion.

Block A rests on the surface for which the coefficient of friction is μsAB If the mass of the

suspended cylinder is m D , determine the smallest mass m A of block A so that it does not slip or tip The coefficient of static friction between the cord and the fixed peg at C is μsC

The collar bearing uniformly supports an axial force P If the coefficient of static friction is

μs , determine the torque M required to overcome friction.

The collar bearing uniformly supports an axial force P If a torque M is applied to the shaft and

causes it to rotate at constant velocity, determine the coefficient of kinetic friction at the surface

of contact

The double-collar bearing is subjected to an axial force

P Assuming that collar A supports kP and collar B

supports (1 − k)P, both with a uniform distribution of

pressure, determine the maximum frictional moment M

that may be resisted by the bearing

The annular ring bearing is subjected to a thrust P If the coefficient of static friction is μs,

determine the torque M that must be applied to overcome friction.

The floor-polishing machine rotates at a constant angular velocity If it has weight W, determine the

couple forces F the operator must apply to the handles to hold the machine stationary The

coefficient of kinetic friction between the floor and brush is μk Assume the brush exerts a uniformpressure on the floor

Given:

W = 80 lb

μk = 0.3

static friction between the plates A and D is μs Assume the bearing pressure between A and D to be

The shaft of diameter b is held in the hole such that the normal pressure acting around the

shaft varies linearly with its depth as shown Determine the frictional torque that must be

overcome to rotate the shaft

Because of wearing at the edges, the pivot bearing is subjected to a conical pressure distribution at its

surface of contact Determine the torque M required to overcome friction and turn the shaft, which supports an axial force P The coefficient of static friction is μs For the solution, it is necessary to

determine the peak pressure p 0 in terms of P and the bearing radius R.

Problem 8-115

The conical bearing is subjected to a constant

pressure distribution at its surface of contact If the

coefficient of static friction is μs, determine the

torque M required to overcome friction if the shaft

supports an axial force P.

The tractor is used to push the pipe of weight W To do this it must overcome the frictional forces

at the ground, caused by sand Assuming that the sand exerts a pressure on the bottom of the pipe

as shown, and the coefficient of static friction between the pipe and the sand is μs, determine the

force required to push the pipe forward Also, determine the peak pressure p 0

Assuming that the variation of pressure at the bottom of the pivot bearing is defined as p =

p 0 (R2/r), determine the torque M needed to overcome friction if the shaft is subjected to an axial

force P The coefficient of static friction is μs For the solution, it is necessary to determine p 0 in

terms of P and the bearing dimensions R1 and R2

A disk having an outer diameter a fits loosely over a fixed shaft having a diameter b If the

coefficient of static friction between the disk and the shaft is μs, determine the smallest

vertical force P, acting on the rim, which must be applied to the disk to cause it to slip over

the shaft The disk weighs W.

The pulley has a radius r and fits loosely on the shaft of diameter d If the loadings acting on the belt

cause the pulley to rotate with constant angular velocity, determine the frictional force between the

shaft and the pulley and compute the coefficient of kinetic friction The pulley has weight W.

Problem 8-120

The pulley has a radius r and fits loosely on the shaft of diameter d If the loadings acting on the belt

cause the pulley to rotate with constant angular velocity, determine the frictional force between the

shaft and the pulley and compute the coefficient of kinetic friction Neglect the weight of the pulley

A pulley of mass M has radius a and the axle has a diameter D If the coefficient of kinetic

friction between the axle and the pulley is μk determine the vertical force P on the rope required

to lift the block of mass M B at constant velocity

Given:

a = 120 mm

M = 5 kg

D = 40 mm

A pulley of mass M has radius a and the axle has a diameter D If the coefficient of kinetic

friction between the axle and the pulley is μk determine the force P on the rope required to lift

the block of mass M B at constant velocity Apply the force P horizontally to the right (not as

shown in the figure)

A wheel on a freight car carries a load W If the axle of the car has a diameter D, determine the

horizontal force P that must be applied to the axle to rotate the wheel The coefficient of kinetic

The trailer has a total weight W and center of gravity at G which is directly over its axle If the

axle has a diameter D, the radius of the wheel is r, and the coefficient of kinetic friction at the

bearing is μk, determine the horizontal force P needed to pull the trailer.

Problem 8-125

The collar fits loosely around a fixed shaft that has radius r If the coefficient of kinetic

friction between the shaft and the collar is μk , determine the force P on the horizontal segment

of the belt so that the collar rotates counterclockwise with a constant angular velocity Assume

that the belt does not slip on the collar; rather, the collar slips on the shaft Neglect the weight

and thickness of the belt and collar The radius, measured from the center of the collar to the

mean thickness of the belt is R.

The collar fits loosely around a fixed shaft that has radius r If the coefficient of kinetic

friction between the shaft and the collar is μk, determine the force P on the horizontal segment