Work done by Gravitation force is always negative. True False Which of the following statements regarding the workdone by a force is correct? A) Work done by frictional force can never be positive. B) Work done by spring force can never be positive. C) Work done by gravitational force can never be positive. D) Work done by friction force could be positive under certain special circumstances.
The Correct Answer and Explanation is :
Answer:
The correct answer is A) Work done by frictional force can never be positive.
Explanation:
In physics, work is defined as the transfer of energy through the application of force over a displacement. Mathematically, work (W) is expressed as:
[ W = F \times d \times \cos(\theta) ]
where:
- ( F ) is the magnitude of the force applied,
- ( d ) is the displacement of the object,
- ( \theta ) is the angle between the force vector and the displacement vector.
The sign of the work depends on the angle ( \theta ):
- Positive Work: Occurs when the force and displacement are in the same direction (( 0^\circ \leq \theta < 90^\circ )).
- Negative Work: Occurs when the force and displacement are in opposite directions (( 90^\circ < \theta \leq 180^\circ )).
- Zero Work: Occurs when the force is perpendicular to the displacement (( \theta = 90^\circ )).
Analysis of the Statements:
- A) Work done by frictional force can never be positive. This statement is true. Frictional forces always act opposite to the direction of motion. Since the angle between the frictional force and displacement is ( 180^\circ ), the cosine of ( 180^\circ ) is -1, resulting in negative work. Therefore, frictional forces cannot do positive work.
- B) Work done by spring force can never be positive. This statement is false. A spring force can do positive work when it is compressed and then released, causing an object to move in the direction of the force. The work done by a spring depends on the direction of displacement relative to the force applied.
- C) Work done by gravitational force can never be positive. This statement is false. Gravitational force can do positive work when an object moves downward under gravity, as the force and displacement are in the same direction. Conversely, it does negative work when an object moves upward against gravity.
- D) Work done by friction force could be positive under certain special circumstances. This statement is false. As established, frictional forces always oppose the direction of motion, resulting in negative work. There are no circumstances under which friction can do positive work.
Conclusion:
Understanding the direction of the applied force relative to the displacement is crucial in determining the sign of the work done. Frictional forces always oppose motion, leading to negative work, while other forces like gravity and spring forces can do both positive and negative work depending on the direction of displacement.