Question

Which of the following best characterizes the work–energy theorem? (A) The work done by any force is proportional only to the magnitude of that force. (B) The total work done on any object is equal to the change in kinetic energy for that object. (C) The work done on an object by any force is proportional to the change in kinetic energy for that object. (D) The work done by an applied force on an object is equal to the change in kinetic energy of that object.

Short answer

Option (B) is correct because the work-energy theorem states that the total work done on an object is equal to the change in kinetic energy for that object.

Step-by-step solution

- Define the Work-Energy Theorem

The work-energy theorem states that the total work done on an object is equal to the change in the object's kinetic energy.

- Identify the Key Concept

The key concept is the relationship between work and kinetic energy, specifically that work done translates to a change in kinetic energy.

- Analyze Each Option

Evaluate each statement for alignment with the work-energy theorem:- (A) The work done by any force is proportional only to the magnitude of that force: Incorrect, because it does not relate to change in kinetic energy.- (B) The total work done on any object is equal to the change in kinetic energy for that object: Correct, as this matches the definition of the work-energy theorem.- (C) The work done on an object by any force is proportional to the change in kinetic energy for that object: Incorrect, since the relationship is not about proportionality but equality.- (D) The work done by an applied force on an object is equal to the change in kinetic energy of that object: Incorrect, the theorem refers to total work done, not just applied force.

- Select the Correct Option

Based on the analysis, the best description is given by option (B).

Key concepts

Kinetic Energy

Kinetic energy is a fundamental concept in physics that plays a pivotal role in understanding motion. It refers to the energy an object possesses due to its motion. The formula for kinetic energy (\text{KE}) is given by $KE=\frac{1}{2}m{v}^2$, where $m$ stands for the mass of the object and $v$ denotes its velocity. This equation shows that kinetic energy depends on both the mass and the square of its velocity. This means that even a small increase in speed will result in a considerably larger increase in kinetic energy.

Total Work

Total work refers to the sum of all the work done by all forces acting on an object. According to the work-energy theorem, this total work (\text{W}) is equal to the change in kinetic energy (\text{∆KE}) of that object: $W=\text{∆KE}$. This means that when work is done on an object, it will result in either an increase or decrease in its kinetic energy, depending on whether the work done is positive or negative.

The equation encompasses all forces acting on the object, not just the applied force, but also frictional forces, gravitational forces, and any other external forces present.

Physics Problem-Solving

Solving physics problems involving the work-energy theorem involves understanding and correctly applying the theorem's principles. Let's break it down into manageable steps:

• Identify the relevant forces acting on the object.
• Calculate the work done by each force. Remember, work (\text{W}) is given by the formula: $W=F\times d\times \text{cos}(\theta )$, where $F$ is the force applied, $d$ is the displacement, and $\theta$ is the angle between the force and the displacement direction.
• Sum up the work done by all forces to find the total work.
• Use the work-energy theorem to determine the change in kinetic energy: $W=\text{∆KE}=K{E}_{final}-K{E}_{initial}$.

By following these steps and understanding the theoretical background, students can effectively apply the work-energy theorem to solve various physics problems.