Question

The boom of a fire truck raises a fireman (and his equipment – total weight 280 lbs) 60 ft into the air to fight a building fire. (a) Showing all your work and using unity conversion ratios, calculate the work done by the boom on the fireman in units of Btu. (b) If the useful power supplied by the boom to lift the fireman is 3.50 hp, estimate how long it takes to lift the fireman

Answer 1

Explanation:

Given that,

Weight = 280 lbs

Height = 60 ft

Power = 3.50 hp

(a). We need to calculate the work done by the boom on the fireman

Using formula of work done

$Work\ done =Weight\ \times height$

$W'=W\times h$

Put the value into the formula

$W'=280\times60$

$W'= 16800 ftlbf$

$W'=\dfrac{16800}{778.169}$

$W'=21.59\ Btu$

The work done by the boom is 21.59 Btu.

(b). We know that,

1 hp = 550 ft lbf

So, $P = 3.50\times550$

$P=1925\ ft-lbf/s$

We need to calculate the time

Using formula of time

$t = \dfrac{W}{P}$

Put the value into the formula

$t=\dfrac{16800}{1925}$

$t =8.7\ sec$

The time is 8.7 sec.

Hence, This is the required solution.