Question

A man of mass 70 kg stands on weighting scale in a lift which is moving 

(a) Upwards with a uniform speed of 10 ms⁻¹. 

(b) Downwards with a uniform acceleration of 5 ms⁻².

(c) Upwards with a uniform acceleration of 5 ms⁻². 

(d) What would be the reading if the lift mechanism failed and it hurtled down freely under gravity? What would be the readings on the scale in each case?

Answer 1

The reading shown by the weighting scale is the normal reaction between the man and the weighing scale.

(a) In this case,

N – mg = 0

⇒ N = mg = 70 × 10 = 700 Newton.

⇒ reading by the scale = 70 kg

(b) In the frame of the lift;

⇒ N + ma = mg

⇒ N = m(g − a)

⇒ N = 70 (10 – 5)

⇒ N = 70 × 5 N

N = 350 Newton

⇒ Reading by the scale = 35 kg

(c)

N = mg + ma

⇒ N = m(a + g)

⇒ N = 70 (10 + 5)

⇒ N = 70 (15)

N = 1050 Newton 

⇒ reading by the scale = 105 kg

(d) Now In this case a = g downward,

∴ from case (b);

⇒ N = m (g – a)

⇒ N = m(g – g)

N = 0

i. e the man is in free fall.

Answer 2

(a) 70 kg, 

(b) 35 kg, 

(c) 105 kg, 

(d) zero