Mechanical Engineering Principles

FRICTION 177

Now try the following exercise

Exercise 76 Further problems on friction

on an inclined plane

Where necessary, takeg= 9 .81 m/s^2

1. A mass of 40 kg rests on a flat horizon-
   tal surface as shown in Figure 15.13. If
   the coefficient of frictionμ= 0 .2, deter-
   mine the minimum value of a horizontal
   forcePwhich will just cause it to move.
   [78.48 N]

Motion

mg

P

Figure 15.13

2. If the mass of Problem 1 were equal to
   50 kg, what will be the value ofP?
   [98.1 N]


3. An experiment is required to obtain the
   static value ofμ; this is achieved by
   increasing the value ofθuntil the mass
   just moves down the plane, as shown
   in Figure 15.14. If the experimentally
   obtained value forθ were 22.5°,what
   is the value ofμ?[μ= 0 .414]

q

mg

N

Motion F

Figure 15.14

4. If in Problem 3,μwere 0.6, what would
   be the experimental value ofθ?
   [θ= 30. 96 °]
   5. For a mass of 50 kg just moving up an
   inclined plane, as shown in Figure 15.5,
   what would be the value ofP, given that
   θ= 20 °andμ= 0 .4? [P= 352 .1N]
   6. For a mass of 50 kg, just moving
   down an inclined plane, as shown in
   Figure 15.7, what would be the value of
   P, given thatθ= 20 °andμ= 0 .4?
   [P= 16 .6N]
   7. If in Problem 5,θ = 10 °andμ= 0 .5,
   what would be the value ofP?
   [P= 326 .7N]
   8. If in Problem 6,θ = 10 °andμ= 0 .5,
   what would be the value ofP?
   [P= 156 .3N]
   9. Determine P for Problem 5, if it
   were acting in the direction shown in
   Figure 15.8. [P= 438 .6N]


5. Determine P for Problem 6, if it
   were acting in the direction shown in
   Figure 15.10. [P= 20 .69 N]


6. Determine the value forθwhich will just
   cause motion down the plane, whenP=
   250 N and acts in the direction shown in
   Figure 15.12. It should be noted that in
   this problem, motion is down the plane.
   [θ= 19. 85 °]


7. If in Problem 11,θ= 30 °, determine the
   value ofμ.[μ= 0 .052]

15.8 The efficiency of a screw jack

Screw jacks (see Section 18.4, page 202) are often

used to lift weights; one of their most common uses

are to raise cars, so that their wheels can be changed.

The theory described in Section 15.7 can be used to

analyse screw jacks.

Consider the thread of the square-threaded screw

jack shown in Figure 15.15.

Letpbe the pitch of the thread, i.e. the axial

distance that the weightWis lifted or lowered when

the screw is turned through one complete revolution.

From Figure 15.15, the motion of the screw in lifting

the weight can be regarded as pulling the weight by

a horizontal forceP,upaninclineθ,where

tanθ=

p

πd

,