An electric motor is rated to have a maximum power output of...

An electric motor is rated to have a maximum power output of 0.75 hp. If this motor is being used to lift a crate of mass $200 \mathrm{kg}$, how fast (i.e., at what speed) can it lift the crate? Hint: Assume the only other force on the crate is the force of gravity.

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Key Concepts

Power

Power is the rate at which work is done or energy is transferred over time. It is a fundamental concept in physics used to measure how quickly a system can perform work. In mechanics, power is crucial for understanding the energy output of machines like electric motors and is often expressed in units such as watts or horsepower.

Work and Energy in Gravitational Fields

When lifting an object, the work done against gravity is stored as gravitational potential energy, which depends on the object's mass, gravitational acceleration, and the height it is lifted. This concept links mechanical work to energy transfer and is essential for analyzing problems involving lifting or moving masses within a gravitational field.

Relationship Between Power, Force, and Velocity

Power in mechanical systems can be expressed as the product of force and velocity. For lifting objects against gravity, the force is equivalent to the weight of the object (mass multiplied by gravitational acceleration), and the lifting speed at which the object can be raised is determined by how much power is available. This relationship allows for calculating the maximum velocity given a certain power output.

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