You work for an automobile manufacturer developing a new...

You work for an automobile manufacturer developing a new plug-in hybrid car. The car's mass is $1200 \mathrm{~kg}$, and it uses a 360 - V battery driving an electric motor that can handle a maximum current of 190 A. You're to specify the greatest slope the car can climb, maintaining $68 \mathrm{~km} / \mathrm{h}$, without its gasoline engine coming on to assist.

Key Concepts

Inclined Plane Mechanics

Inclined plane mechanics deals with analyzing forces on a slope. It includes understanding how the component of gravitational force along the plane acts as a resistive force when climbing. Calculating this component allows one to establish the maximum gradient that an available power output can overcome while maintaining a certain speed.

Unit Conversion

Unit conversion is crucial for ensuring consistency in physical calculations. In this context, converting speed from kilometers per hour to meters per second, or ensuring that mass, acceleration due to gravity, and power are in compatible units, is necessary to correctly apply formulas and arrive at a reliable analysis of the vehicle’s performance on an incline.

Electric Motor Power

This concept involves calculating the power output available from an electric motor using the product of voltage and current. It is essential in determining how much energy per unit time the motor can provide, which directly relates to the vehicle’s ability to perform work against resistive forces, such as gravity when climbing a slope.

Gravitational Potential Energy

Gravitational potential energy is the energy an object possesses due to its position in a gravitational field. When a vehicle climbs an incline, it must work against gravity to raise its altitude, and the rate at which this energy is required is key to assessing whether the available power can maintain motion on a gradient.

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