Page 74 - Mechanical Engineer's Data Handbook

APPLIED MECHANICS 63

2. I. I7 Machines maximum range is achieved if the projection angle is
45". The effect of air resistance is to reduce both range
Load and height.
Mechanical advantage MA (or force ratio)=-
Effort Assuming no air resistance:
Velocity ratio VR (or movement ratio)
Distance moved by effort
-
-
Distance moved by load
Useful work out MA
--
Efficiency 1 = -
Work put in VR Time of flight for 8=45";
2.1.18 Levers Projection up a slope (of angle 8):
u2 2sin(O-#l)cos8
The lever is a simple machine consisting of a pivoted Range R = -
beam. An effort E lifts a load W. Referring to the figure, g cos28 '
and assuming no friction:
R =-
,X
g (l+sin#l)
I V
Firstorder Wr

Second-order lever
& $ E 2. I .20 Rockets

For a rocket travelling vertically against gravity, the
mass of fuel is continually decreasing as the fuel is
burnt, i.e. the total mass being lifted decreases uni-
Third-order lever formly with time.
The following formulae give the velocity and height
at any time up to burn-out, and the velocity, height
and time expired at bum-out.
Let:
Y=jet velocity (assumed constant)
U =rocket velocity
M, = mass of fuel at blast off
2. I. I9 Projectiles M,=mass of rocket with no fuel
m = mass flow rate of fuel
When a projectile is fired at an angle to a horizontal t = time after blast-off
plane under gravity, the trajectory is a parabola if air g=acceleration due to gravity (assumed to be
resistance is neglected. It can be shown that the constant)