An automobile engine develops a torque of at 3350 rpm. What is the horsepower of the engine?

The given data can be listed below as:

• The torque developed by an automobile is\(T = 265{\rm{ m}} \cdot {\rm{N}}\).
• The rotation of the engine is \(N = 3350{\rm{ rpm}}\).

The power of the engine is the multiplication of the torque developed by the engine and the angular speed of the engine.The power of the engine can be obtained in the unit of watts. Therefore, convert the power unit from watts to horsepower. One horsepower of the engine is equal to 746 watts.

The power of the engine can be expressed as:

\(\begin{align}P &= T \times \omega \\ &= T \times \frac{{2\pi N}}{{60}}\end{align}\)

Here,\(\omega \)is the angular speed of an engine.

Substitute the values in the above equation.

\(\begin{align}P &= 265{\rm{ m}} \cdot {\rm{N}} \times \frac{{2\pi \times 3350{\rm{ rpm}}}}{{60}}\left( {\frac{{1{\rm{ rps}}}}{{1{\rm{ rpm}}}}} \right)\\ &= 92964.96{\rm{ N}} \cdot {\rm{m/s}}\left( {\frac{{1{\rm{ W}}}}{{1{\rm{ N}} \cdot {\rm{m/s}}}}} \right)\\ &= 92964.96{\rm{ W}}\left( {\frac{{1{\rm{ hp}}}}{{746{\rm{ W}}}}} \right)\\ &= 124.62{\rm{ hp }}\end{align}\)

Thus, the horsepower of the engine is 124.62 hp.