How do you calculate the energy transferred by a force?

You calculate the energy transferred by a force using the formula: Energy = Force × Distance × cos(θ).

To understand this better, let's break it down. The energy transferred by a force is often referred to as work done. The formula for work done is:

\[ \text{Work Done (Energy)} = \text{Force} \times \text{Distance} \times \cos(\theta) \]

Here, 'Force' is the magnitude of the force applied, measured in newtons (N). 'Distance' is how far the object moves in the direction of the force, measured in metres (m). The angle θ (theta) is the angle between the direction of the force and the direction of the movement. The cosine function (cos) is used to account for this angle.

For example, if you push a box with a force of 10 N for a distance of 5 m in the same direction as the force, and the angle θ is 0 degrees (cos(0) = 1), the energy transferred (work done) would be:

\[ \text{Energy} = 10 \, \text{N} \times 5 \, \text{m} \times \cos(0) \]
\[ \text{Energy} = 10 \times 5 \times 1 \]
\[ \text{Energy} = 50 \, \text{J} \]

So, 50 joules (J) of energy is transferred to the box.

If the force is applied at an angle, say 30 degrees, you would use the cosine of 30 degrees (cos(30) ≈ 0.866):

\[ \text{Energy} = 10 \, \text{N} \times 5 \, \text{m} \times \cos(30) \]
\[ \text{Energy} = 10 \times 5 \times 0.866 \]
\[ \text{Energy} \approx 43.3 \, \text{J} \]

This means less energy is transferred when the force is applied at an angle compared to when it is applied directly in the direction of movement. Understanding this concept is crucial in physics as it helps explain how forces cause objects to move and how much energy is involved in these processes.