Question

A motor of \[100\,{\text{H}}{\text{.P}}{\text{.}}\] is moving with a constant velocity of \[72\,{\text{km/hour}}\]. The forward force exerted by the engine on the car is
A. \[{\text{3}}{\text{.73}} \times {\text{1}}{{\text{0}}^3}\,{\text{N}}\]
B. \[{\text{3}}{\text{.73}} \times {\text{1}}{{\text{0}}^2}\,{\text{N}}\]
C. \[{\text{3}}{\text{.73}} \times {\text{1}}{{\text{0}}^1}\,{\text{N}}\]
D. None of the above

Answer 1

Hint:Use the expression relating between the power, force and velocity. Convert the final answer for the forward force exerted by the engine on the car in the power of 10.

Formula used:
The relation between the power, force and velocity is
\[P = Fv\] …… (1)
Here, \[P\] is the power, \[F\] is the force and \[v\] is the velocity.

Complete step by step answer:
The power \[P\] of the motor of the engine is \[100\,{\text{H}}{\text{.P}}{\text{.}}\] and the velocity \[v\] of the motor is \[72\,{\text{km/hour}}\].
\[P = 100\,{\text{H}}{\text{.P}}{\text{.}}\]
\[v = 72\,{\text{km/hour}}\]
Convert the unit of the power of the motor from horsepower to watt.
\[P = \left( {100\,{\text{H}}{\text{.P}}{\text{.}}} \right)\left( {\dfrac{{745.7\,{\text{W}}}}{{1\,{\text{H}}{\text{.P}}{\text{.}}}}} \right)\]
\[ \Rightarrow P = 74570\,{\text{W}}\]
Convert the unit of the velocity of the car from kilometer per hour to meter per second.
\[v = \left( {72\,\dfrac{{{\text{km}}}}{{{\text{hour}}}}} \right)\left( {\dfrac{{{{10}^3}\,{\text{m}}}}{{1\,{\text{km}}}}} \right)\left( {\dfrac{{1\,{\text{hour}}}}{{3600\,{\text{s}}}}} \right)\]
\[ \Rightarrow v = 20\,{\text{m/s}}\]
Rearrange equation (1) for the forward force exerted by the engine on the car.
\[F = \dfrac{P}{v}\]
Substitute \[74570\,{\text{W}}\] for \[P\] and \[20\,{\text{m/s}}\] for \[v\] in the above equation.
\[F = \dfrac{{74570\,{\text{W}}}}{{20\,{\text{m/s}}}}\]
\[ \Rightarrow F = 3728.5\,{\text{W}} \cdot {{\text{m}}^{ - 1}} \cdot {\text{s}}\]
\[ \Rightarrow F = 3728.5\,{\text{N}}\]
\[ \Rightarrow F \approx 3.73 \times {10^3}\,{\text{N}}\]
Hence, the forward force exerted by the engine on the car is \[3.73 \times {10^3}\,{\text{N}}\].
Hence, the correct option is A.


Note: Use proper conversion factors to convert the units of the power and the velocity. The units of all the physical quantities substituted in the formula for the force must be in the SI system of units.Also remember that from Newton’s second law of motion,the force is directly proportional to the rate of change of momentum of a body.