Mechanical Engineering Principles

134 MECHANICAL ENGINEERING PRINCIPLES

A vector diagram depicting the motion of the crane
and load is shown in Figure 11.5.oarepresents the
velocity of the crane relative to a fixed point on the
Earth’s surface andabrepresents the velocity of the
load relative to the crane. The velocity of the load
relative to the fixed point on the Earth’s surface is
ob. By Pythagoras’ theorem:

ob^2 =oa^2 +ab^2

= 4 + 25 = 29

Hence ob=

√

29 = 5 .385 m/s

Tan θ =^52 = 2 .5 henceθ =tan−^12. 5 = 68. 20 °
i.e. the velocity of the load relative to a fixed point
on the Earth’s surface is5.385 m/s in a direction
68.20°to the motion of the crane.

Now try the following exercise

Exercise 56 Further problems on relative

velocity

1. A ship is sailing due east with a uniform
   speed of 7.5 m/s relative to the sea. If
   the tide has a velocity 2 m/s in a north-
   westerly direction, find the velocity of the
   ship relative to the sea bed.
   [6.248 m/s atE13.08°N]


2. A lorry is moving along a straight road
   at a constant speed of 54 km/h. The tip
   of its windscreen wiper blade has a linear
   velocity, when in a vertical position, of
   4 m/s. Find the velocity of the tip of the
   wiper blade relative to the road when in
   this vertical position.
   [15.52 m/s at 14.93°]


3. A fork-lift truck is moving in a straight
   line at a constant speed of 5 m/s and at
   the same time a pallet is being lowered at
   a constant speed of 2 m/s. Determine the
   velocity of the pallet relative to the earth.
   [5.385 m/s at−21.80°]

Exercise 57 Short answer questions on

linear and angular motion

1. State and define the unit of angular dis-
   placement
   2. Write down the formula connecting an
   angle, arc length and the radius of a
   circle
   3. Define linear velocity and state its unit
   4. Define angular velocity and state its unit
   5. Write down a formula connecting angu-
   lar velocity and revolutions per second
   in coherent units
   6. State the formula connecting linear and
   angular velocity
   7. Define linear acceleration and state
   its unit
   8. Define angular acceleration and state
   its unit
   9. Write down the formula connecting lin-
   ear and angular acceleration


2. Define a scalar quantity and give two
   examples


3. Define a vector quantity and give two
   examples

Exercise 58 Multi-choice questions on lin-

ear and angular motion

(Answers on page 284)

1. Angular displacement is measured in:

(a) degrees (b) radians

(c) rev/s (d) metres

2. An angle of

3 π

4

radians is equivalent to:

(a) 270° (b) 67.5°

(c) 135° (d) 2.356°

3. An angle of 120°is equivalent to:

(a)

2 π

3

rad (b)

π

3

rad

(c)

3 π

4

rad (d)

1

3

rad

4. An angle of 2 rad at the centre of a circle
   subtends an arc length of 40 mm at the
   circumference of the circle. The radius
   of the circle is:
   (a) 40πmm (b) 80 mm
   (c) 20 mm (d) (40/π)mm