Question
1.
A girl whose
mass is 55 kg stands on a spring weighing machine inside a lift. When the lift
starts to ascend, its acceleration is 2 ms^{2}. What will be the
reading on the machine? (take g = 10 ms^{2})
Solution:
Note: Two
forces are acting in opposite direction on the girl. These are the force due to
her weight (acting downwards), which equals
mg = 55 x 10 = 550
Newtons
and the
upwards force, the reaction, R, of the surface of the weighing machine on her.
When the lift starts to move upward, the net force (Rmg) equals ma.
From the
formula for force, R  mg = ma
R = ma
+ mg
R = m
(a + g)
= 55 (2 + 10)
= 660 Newtons
The force of
Reaction, which is read by the machine is equal to 660 Newtons.
In terms of
mass, the reading on the machine will be
^{660}/_{10}
= 66 kg
Question
2.
A spring
balance, which is suspended from the roof of a lift, carries a mass of 1 kg at
its free end. If the lift accelerates upwards at 2.5ms^{2}, determine
the reading on the spring balance if acceleration due to gravity (g) is 10m/s^{2}.
Solution:
Note: There
are two different forces acting on the mass of 1 kg in opposite direction  the
force due to its weight as a result of the force of gravity, mg, and the upward
force on it from the spring balance (F).
The net
value of these two forces causes the lift to accelerate upward.
Therefore,
using the formula of force,
F  mg
= ma
F = ma
+ mg
F =
m(a + g)
=
(2.5 + 10)
F =
12.5N
The reading
on the spring balance is equal to 12.5 Newtons
Question
3.
An elevator
of mass 4800 kg is supported by a cable which can safely withstand a maximum
tension of 60 000 N. The maximum upward acceleration the elevator can have,
taking acceleration due to gravity as 10 ms^{2}, is?
Solution:
Two forces
are acting on the elevator: 1. the weight of the elevator, given by the force
formula,
W = mg
W =
4800 x 10
= 48000 Newtons
 The
tension (T) in the cable acting upwards and given as 60 000N when the elevator
starts to move upward, the net force equals the difference in the two forces.
Using the formula of force,
T  mg = ma
60 000  48 000 = 4800a
12 000 = 48 00a
a = 12 000/4800 = 2.5
The maximum upward acceleration the elevator can have is 2.5
m/s^{2}
Question
4.
A body of
mass 2 kg is suspended from the ceiling of a lift with a light insensible
string. If the lift moves upwards with acceleration of 2 ms^{2},
calculate the magnitude of the tension in the string. (g = 10 ms^{2}).
Solution:
There are
two forces acting on the body: vertical upward force, which is same as the
tension (T) in the string, and downward force, which is due to its weight (mg).
Since the
lift is moving upwards, the net force acting on the body is given by the
equation:
T  mg
= ma
Given: mass
of the body m = 2 kg, acceleration a = 2 ms^{2}, acceleration due to
gravity g = 10 ms^{2}, tension in the string T = ?
Therefore,
T = ma
+ mg
T = m
(a + g)
= 2
(2 + 10)
= 2 x
12
=
24 N
The tension
in the string is 24 Newtons.
Question
5.
A 1000 kg
elevator is descending vertically with an acceleration of 1.0 ms^{2}.
If the acceleration due to gravity is 10.0 ms^{2}, the tension in the
suspending cable is?
Solution:
Two forces
act on the elevator: the vertical upward force (it actually acts downwards in
this case), which is also the tension (T), and the weight of the elevator, mg.
Since the
elevator is moving downwards, the same direction as its weight due to the force
of gravity acting on it, the net force acting on it is
T + mg
= ma
T +
1000 x 10 = 1000 x 1
T +
10000 = 1000
T =  9000 N
(the negative sign shows that the tension in the cable is acting downwards)
Therefore, the tension in the cable is 9000 Newtons.
See more calculations of force based on apparent weight.
