Is the work done on the particle positive or negative? Or is there not enough information to tell?
The correct answer and explanation is:
Correct Answer: There is not enough information to tell.
Explanation:
To determine whether the work done on a particle is positive, negative, or zero, one must know the relationship between the direction of the force applied and the displacement of the particle. Work is a scalar quantity defined by the dot product of force and displacement:
Work (W) = F × d × cos(θ)
Where:
- F is the magnitude of the force,
- d is the displacement of the particle,
- θ is the angle between the direction of the force and the direction of the displacement.
If the angle between the force and displacement is less than 90 degrees (i.e., the force has a component in the direction of motion), the work is positive. This means energy is being transferred to the particle, possibly increasing its speed or kinetic energy.
If the angle is greater than 90 degrees (i.e., the force opposes the motion), the work is negative. In this case, energy is being taken from the particle, typically slowing it down or reducing its kinetic energy.
If the angle is exactly 90 degrees (i.e., the force is perpendicular to the direction of motion), the work done is zero because the force does not change the speed of the particle, even if it alters the direction.
Without knowing both the direction and magnitude of the force relative to the displacement of the particle, it is impossible to determine the sign or value of the work done. The question does not specify the angle or directions involved, so the only correct answer is that there is not enough information to tell. Understanding the context of motion and force direction is essential for evaluating work in physics.