Question

A crane is lifting a 500 lb car. If the power output of the crane is 1.82 hp, find the velocity of the car.Write the answer with unit.

Answer 1

EXPLANATION.

mass of car (m) = 500 LB

power = 1.82 HP

To find velocity of the car.

according to the question,

as we know that,

1 LB = 0.454 kg

500 LB = 0.454 X 500

500 LB = 227 kg

as we know that,

$1hp \: = 745.7 \: j {s}^{ - 1}$

1.82 hp = 745.7 X 1.82

1.82 hp = 1357.174

Initial velocity = 0 m/s

Acceleration due to gravity = g

as we know that,

$power \: = \frac{work \: done}{time}$

$1357.174 = \frac{f \: \times \: s}{t}$

$1357.174 = \frac{m \: \times a \: \times \frac{ {v}^{2} - {u}^{2} }{2a} }{ \frac{v \: - \: u}{a} }$

$1357.174 = \frac{m \: \times \: a \: \times ( {v}^{2} - {u}^{2}) }{2(v \: - \: u)}$

$1357.174 = \frac{m \: \times \: g \: \times \: {v}^{2} }{2v}$

$1357.174 = \frac{m \: \times \: g \: \times \: v}{2}$

$1357.174 = 1135v$

$v \: = \frac{1357.174}{1135}$

$v \: = \: 1.195 \: ms$

Therefore,

velocity of car = 1.195 m/s