Question

Come up with your own scenario (a force and a distance) that would result in \(100 \mathrm{~J}\) of energy expenditure.

Short answer

Answer: In this scenario, a force of 20 Newtons would need to be applied to an object and moved a distance of 5 meters in the same direction as the applied force to result in 100 Joules of energy expenditure.

Step-by-step solution

Choose a force and angle

Let's select a force of 20 Newtons and an angle of 0 degrees, meaning that the force and distance vectors are in the same direction.

Calculate the distance

Now, we will use the formula for calculating work done and solve for the distance, d: Work = Force × Distance × cos(θ) Plugging in the given values: \(100 \mathrm{~J} = 20 \mathrm{~N} \times d \times \cos(0)\) Since cos(0) = 1, the equation simplifies to: \(100 \mathrm{~J} = 20 \mathrm{~N} \times d\) Now, divide both sides by 20 N to get the distance: \(d = \frac{100 \mathrm{~J}}{20 \mathrm{~N}} = 5 \mathrm{~m}\)

State the scenario

The scenario that would result in 100 Joules of energy expenditure is applying a force of 20 Newtons to an object and moving it a distance of 5 meters in the same direction as the applied force.

Key concepts

Physics

Physics is the study of the fundamental principles that govern the universe. It explores concepts like motion, forces, energy, and much more.
In this scenario, we focus on the relationship between work and energy, two core aspects of physics. Work is done when a force moves an object over a distance, closely linking both force and distance in many physical occurrences.
To calculate work, we use the formula:

• Work = Force × Distance × cos(θ)

This formula helps us understand the energy used when force is applied. In our example, we calculated the distance needed to make the energy expenditure equal to 100 Joules when applying a force of 20 Newtons.

Force

Force is a push or pull on an object that can cause it to change its velocity, direction, or shape. It's a vector quantity, meaning it has both magnitude and direction.
Here are key points about force:

• Measured in Newtons (N).
• Can cause acceleration or deceleration.
• Acts at an angle described in the work done equation.

In our exercise, we chose a force of 20 Newtons at an angle of 0 degrees. This means the force is applied in the same direction as the movement, optimizing the work done. When calculating work, angles between the force and direction can change how effective the force is. For angles greater than 0, less force contributes to moving the object in the intended direction.

Distance

Distance in physics refers to the spatial separation between two points, or how much ground an object has covered during its motion. It’s a scalar quantity, meaning it only has magnitude, not direction.
Important aspects include:

• Measured in meters (m).
• In our scenario: 5 meters were needed for the work done to equate to 100 Joules.
• Represents actual length between start and end points of motion.

In this situation, distance directly influences the total energy expenditure. With a constant force of 20 Newtons, the distance determined how far the energy from work was spread. The work energy principle ties the amount of work done directly to changes in kinetic energy, showing how essential distance is to understanding work.