Question

A lift cage of mass 826 kg accelerates uniformly upwards from rest to a velocity of 7 ms−1
whilst travelling a distance of 36 m. The frictional resistance to motion is 244 N. Making
use of the principle of conservation of energy, determine:

i) The work done
ii) The tension in the lifting cable
Iii) The average power developed

Answer 1

Answer on Question #74533-Engineering-Mechanical Engineering

A lift cage of mass 826 kg accelerates uniformly upwards from rest to a velocity of 7 ms⁻¹ whilst travelling a distance of 36 m. The frictional resistance to motion is 244 N. Making use of the principle of conservation of energy, determine:

i) The work done

ii) The tension in the lifting cable

iii) The average power developed

Solution

i)

$$W = (mg + F_{fr})h + \frac{m}{2}v^2 = (826(9.8) + 244)36 + \frac{826}{2}7^2 = 320000\,J$$

ii)

$$T = (mg + F_{fr}) + ma$$ $$a = \frac{v^2}{2h}$$ $$T = (mg + F_{fr}) + m\frac{v^2}{2h} = (826(9.8) + 244) + \frac{826}{2(36)}7^2 = 8900\,N$$

iii)

$$P = T\frac{v}{2} = \left((826(9.8) + 244) + \frac{826}{2(36)}7^2\right)\frac{7}{2} = 31000\,W.$$

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