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Work and energy are central concepts in physics, especially when discussing power calculation problems like the one involving lifting crates. Work is done when a force acts on an object to move it through a distance. The work done, often denoted as \(W\), is calculated by the formula:

• \(W = F \cdot d \cdot \cos(\theta)\)

where:

• \(F\) is the force applied,
• \(d\) is the distance moved,
• \(\theta\) is the angle between the force and the direction of motion.

If the motion is vertical, like lifting crates, the angle \(\theta\) is 0 degrees, making the \(\cos(0) = 1\). Hence, work done is simply the force times the distance. In our problem, the force is the weight of the crate, which is equal to its mass \(m\) times gravitational acceleration \(g\). This gives us the work done per crate:

• \(W = m \times g \times h\).

This formula highlights the link between work and energy, specifically gravitational potential energy, as the work done in lifting the crate is converted to potential energy.

Understanding how to convert horsepower to watts is essential when working with power calculations in physics, particularly dealing with motor or engine power. Horsepower (hp) is a unit of power that originated in the 18th century when horses were the main source of machinery.
To match modern standards, horsepower is often converted to watts. One horsepower is defined as 746 watts. This means:

• 1 hp = 746 W.

In the exercise problem, the power provided by 0.50 horsepower needs to be expressed in watts to calculate the number of crates lifted. Therefore, we multiply 0.50 hp by 746 W/hp to get:

• 0.50 hp \(\times\) 746 \(= 373\) W.

Converting power into common units like watts allows for uniform calculations, ensuring that different forms of power measurements can be compared or used within the same problem effortlessly.

Gravitational potential energy is a type of energy that an object possesses due to its position in a gravitational field, commonly experienced as the Earth's gravity. The potential energy \(U\) for an object of mass \(m\) lifted to a height \(h\) can be calculated using the equation:

• \(U = m \cdot g \cdot h\)

where:

• \(m\) is the mass of the object,
• \(g\) is the acceleration due to gravity (approximately \(9.8 \ \text{m/s}^2\) on Earth),
• \(h\) is the height above the reference point.

In the exercise, lifting a 30 kg crate over a height of 0.90 meters on Earth requires calculating the potential energy (or the work done since energy is transferred) using the given formula. This results in:

• \(U = 30 \times 9.8 \times 0.9 = 264.6 \ \text{J}\)

Understanding how potential energy works in this context helps illustrate why it's necessary to account for the energy involved in lifting objects, whether for moving crates or assessing any lifting task.