Question

A dog  races up the stairs in a time of 1.80 seconds.  If the stairs are 12 feet high, how much power in hp is the dog putting out?  The weight of the dog is 48 lbs

Answer 1

The time taken by the dog to climb the stairs, t=1.80 s

The height of the stairs, h= 12 feet=3.66 m

The weight of the dog, m=48 lbs=21.77 kg

The work done by the dog in climbing up the stairs is,

$W=\text{mgh}$

Where g is the acceleration due to gravity.

On substituting the known values,

$W=21.77\times9.8\times3.66=780.85\text{ J}$

The power is given by,

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

On substituting the known values,

$P=\frac{780.85}{1.80}=433.80\text{ J/s}$

1 J/s = 1.34×10³ hp

Therefore,

$433.80\text{ J/s=433.80}\times1.34\times10^3\text{ hp=581.3}\times10^3\text{ hp}$

Therefore the power put out by the dog is 581.3×10³ hp