The motor in a 1590 -kg Nissan Leaf electric car supplies...

The motor in a 1590 -kg Nissan Leaf electric car supplies energy to the wheels at the rate of $80.0 \mathrm{~kW}$. (a) What's the maximum speed for the Leaf when it's ascending an $11.8^{\circ}$ slope using only its electric motor? (b) What's the motor's power output in horsepower? Neglect air resistance.

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Key Concepts

Mechanical Power

In mechanics, power is the rate at which work is done or energy is transferred. For vehicles, it quantifies how quickly energy from the engine or motor is converted into motion or to overcome forces such as gravity, especially when climbing a slope.

Gravitational Potential Energy and Its Rate of Change

When a vehicle ascends a slope, it gains height and therefore gravitational potential energy, which is calculated as the product of mass, gravitational acceleration, and height. The rate at which this potential energy is gained (mgh per unit time) must equal the power supplied by the motor, linking energy concepts with motion.

Inclined Plane Mechanics

This concept involves analyzing forces acting on objects on a slope. The gravitational force acting parallel to the incline is found by multiplying the weight of the object by the sine of the incline angle. This component is critical for determining the energy required to move an object upward against gravity.

Unit Conversion (Kilowatts to Horsepower)

This conversion is essential in contexts where different systems of power measurement are used. One horsepower is approximately equal to 746 watts. This conversion allows for the comparison of engine outputs in terms familiar in various industries and regions.

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