10/10/2010

1

Chapter 7(Cont’n)Belt Friction

ROPES AND FLAT BELTS

peg

Weight W is held in static equilibrium by a

rope that passes over a peg.

If peg is frictionless: P = W to maintain static

equilibrium

W

50N

•

•

•

•

B

A

D

C

Determine the weight W

to maintain equilibrium if

pulleys are frictionless:

W = 400N

ROPES AND FLAT BELTS

peg

Weight W is held in static equilibrium by a

rope that passes over a peg.

If peg is frictionless: P = W

If the contact surface between the peg and

the rope has friction : P W to maintain

equilibrium. There is a possibility that P < W

and still maintain equilibrium

Thin, flat belt

Analysis of Belt Friction

s

When motion is impending:

seTT 12

Where:

T1= tension in the slack side

T2= tension in the tight side

T2 > T1

S= coefficient of static friction

= angle of wrap

= radians

( radians = 180 deg.)

The 30N weight is attached to a rope that runs over a fixed

cylinder. The coefficient of static friction between the rope and the

cylinder is 0.3. Determine the range of the force P for which the

system will be at rest.

7.64

seTT 12

3030 .ePCW motion: NP 77

CCW motion: 3030 .Pe N.P 711

System is at rest if:

11.7N P 77N

s

10/10/2010

2

The rope is wrapped 1 and ½ times

around a circular peg. What is ?

3

)(. 251

)(n 2

or:

n = no. of turns

2 radians = 1 revolution

= 360 deg. Capstan – a device for fastening a ship to the dock.

How many turns of rope around the capstan are needed for the 60-

N force to resist the 9000-N pull of a docked ship? The coefficient

of friction between the capstan and the rope is 0.2.

7.59

Other Applications of Belt Friction:

Capstan – a device for fastening a ship to the dock.

Belt Drives – the friction between the belt and the pulleys

enables power to be transmitted between rotating shafts.

Band Brakes – use friction between a band (belt) and a

cylindrical drum to reduce the speed of a rotating

machinery.

7.59

seTT 12

20609000 .e

radians.0525

)(n 2

4 turns are required to hold the ship.

s=0.2

Solving:

)(n. 20525

turnsor.n 4983

The rope running over two fixed cylinders carries the 4-kg mass at

one end. Determine the force P that must be applied to the other

end to initiate motion. The coefficient of friction between the rope

and the cylinders is 0.15.

Problem

s=0.15s=0.15

T• •

40o

A B

s=0.15

s=0.15

T

T

4(9.81)

Cylinder A:

seTT 12

A.e).(T

1508194 B.TeP

150

•A

•B

Cylinder B:

seTT 12

10/10/2010

3

Determination of :

1.

• ••

•

2.

•

3.

o

o

180180

o

o

18090

2

90o

o

o

18090

•

o180

T

T

4(9.81)

Determination of A and B

•

•

40o

40o40o

90o

40o

o

ooA

1804090

o

oB

18040

oA180

130

oB180

40

7.62 s=0.15

s=0.15

T

T

4(9.81)

Cylinder A:

seTT 12

A.e).(T

1508194 B.TeP

150

•A

•B

180

130150

8194.

e).(T

seTT 12

Cylinder B:

180

40150

1555.

e.P

N.T 1555 N.P 2461

FIN.