Question

A man of mass 70 kg stands on a weighing scale in a lift which is moving
a) upwards with a uniform speed of 10 m s^–1,
b) downwards with a uniform acceleration of 5 m s^–2,
c) upwards with a uniform acceleration of 5 m s^–2. What would be the readings on the scale in each case?
d) What would be the reading if the lift mechanism failed and it hurtled down freely under gravity?

Answer 1

Mass of the man, m = 70 kg
Acceleration, a = 0
Using Newton’s second law of motion, we can write the equation of motion as:
R – mg = ma
Where, ma is the net force acting on the man.
As the lift is moving at a uniform speed, acceleration a = 0
R = mg
= 70 × 10 = 700 N

Reading on the weighing scale=700/g=700/10=70kg

Mass of the man, m = 70 kg
Acceleration, a = 5 m/s² downward
Using Newton’s second law of motion, we can write the equation of motion as:

R + mg = ma
R = m(g – a)
= 70 (10 – 5) = 70 × 5
= 350 N

Reading on the weighing scale =350/g=350/10=35kg

Mass of the man, m = 70 kg
Acceleration, a = 5 m/s² upward
Using Newton’s second law of motion, we can write the equation of motion as:

R – mg = ma
R = m(g + a)
= 70 (10 + 5) = 70 × 15
= 1050 N

Reading on the weighing scale =1050/g=1050/10=105kg

When the lift moves freely under gravity, acceleration a = g
Using Newton’s second law of motion, we can write the equation of motion as:

R + mg = ma
R = m(g – a)
= m(g – g) = 0
Reading on the weighing scale=0/g=0 kg

The man will be in a state of weightlessness.