Force and Work Relationships Quick Check A car applies a force of 36.8 Newtons for a 668-meter loop; what was the work done? (1 point) 18.2J 24,600J 0J 705J
The Correct Answer And Explanation is:
To calculate the work done, we use the formula:
$$
\text{Work} = \text{Force} \times \text{Distance} \times \cos(\theta)
$$
Where:
- Force is the applied force (in Newtons)
- Distance is the distance over which the force is applied (in meters)
- θ (theta) is the angle between the direction of the force and the direction of motion
- Work is measured in joules (J)
Given:
- Force = 36.8 N
- Distance = 668 m
- It’s a loop — the key word here is “loop”, which indicates that the car starts and ends at the same place.
- θ = 90° or undefined depending on direction because if it’s a complete loop, the net displacement is zero.
Step-by-step Explanation:
- Work is only done when there is displacement in the direction of the force.
- If the object travels in a complete loop and ends up where it started, the net displacement is zero.
- Since displacement is vector-based, movement in a loop cancels itself out.
- Therefore, even though a force is applied and a distance is traveled, if there’s no net displacement in the direction of the force, then:
$$
\text{Work} = \text{Force} \times \text{Displacement} = 36.8 \, \text{N} \times 0 \, \text{m} = 0 \, \text{J}
$$
This is because the direction of displacement is crucial in determining work. A closed path (like a loop) has zero net displacement, so no net work is done against displacement even though energy is used in a real-world context (e.g., friction or acceleration).
✅ Correct Answer:
0 J
This is a common conceptual mistake in physics — people often confuse distance with displacement. In the context of work, only displacement in the direction of the force matters.