A crane is lifting a 1500 lb car. If the power output of the crane is 4 hp, find the velocity of the car.
Answers
Explanation:
➡ The velocity of the car is 0.88 ms-¹.
Given :-
A crane is lifting a 1500 lb car .
The power output of the crane is 4 hp.
To Find :-
The velocity of the car.
Calculation :-
According to the question,
A crane is lifting a 1500 lb car .
1500 lb =?
we know, 1lb = 0.454 kg
➡ 1500 lb = 1500 × 0.454
➡ 1500 lb = 681 kg
The power output of the crane is 4 hp.
4 hp = ?
➡ 1 hp = 754.7 Js-¹
➡ 4 hp = 4 × 754.7 Js-¹
➡ 4 hp = 2982.8 Js-¹
Initial velocity (u) = 0 m/s
Acceleration due to gravity = g
Using, Formulae of power,
✨ Power = work done / time
2982.8 Js-¹ = f × s / t
2982.8 Js-¹ = m × a × v²-u²/t / v-u/a
2982.8 Js-¹ = m × a × (v²-u²) / 2(v-u)
2982.8 Js-¹ = m × g × v² / 2v
2982.8 Js-¹ = 681 × 10 × v / 2
2982.8 Js-¹ = 3405 × v
v = 2982.8 / 3405
v = 0.88 ms-¹
The velocity of the car is 0.88 ms-¹.