Gravitation Always Does Negative Work. Question 12 Options: True False

Gravitation Always Does Negative Work: True or False? A Deep Dive into Gravitational Potential Energy

The statement "Gravitation always does negative work" is true, but understanding why requires a nuanced look at the concepts of work, potential energy, and the nature of gravitational forces. This exploration will delve into the physics behind this statement, examining various scenarios and clarifying common misconceptions.

Understanding Work and Potential Energy

Before diving into the specifics of gravitation, let's establish a firm understanding of work and potential energy. In physics, work is done when a force causes a displacement of an object. The formula for work (W) is:

W = Fd cos θ

where:

• F is the magnitude of the force
• d is the magnitude of the displacement
• θ is the angle between the force and displacement vectors

Crucially, only the component of the force parallel to the displacement contributes to the work done. If the force and displacement are perpendicular (θ = 90°), no work is done.

Potential energy (PE) is stored energy that has the potential to do work. Gravitational potential energy is a specific type of potential energy associated with the gravitational force. It's the energy an object possesses due to its position in a gravitational field. The higher an object is above a reference point, the greater its gravitational potential energy.

The Nature of Gravitational Force

Gravity is an attractive force. This means it always pulls objects towards each other. This seemingly simple fact is key to understanding why gravity always does negative work.

Consider a scenario where you lift a ball. You are applying an upward force to counteract the downward gravitational force. You are doing positive work on the ball, increasing its gravitational potential energy. The gravitational force itself, however, is acting downwards, opposite to the displacement (which is upwards). Therefore, the angle θ between the gravitational force and the displacement is 180°, and cos(180°) = -1. This results in negative work being done by gravity.

Analyzing Different Scenarios

Let's analyze several scenarios to reinforce this concept:

1. Object Falling Freely

When an object falls freely under gravity, the gravitational force is in the same direction as the displacement. The angle θ is 0°, and cos(0°) = 1. While the work done is positive (W = Fd), this positive work represents the work done by gravity, increasing the object's kinetic energy. The gravitational potential energy decreases; this is the source of the kinetic energy increase. The system's total mechanical energy (kinetic + potential) remains constant, ignoring air resistance.

2. Projectile Motion

Consider a projectile launched upwards. While ascending, gravity does negative work, decreasing the projectile's potential energy. During descent, gravity does positive work, increasing the projectile's kinetic energy. However, the net work done by gravity over the entire trajectory (from launch to landing at the same height) is zero. This is because the positive work done during descent exactly cancels out the negative work done during ascent.

3. Orbiting Satellites

Satellites orbiting Earth are constantly experiencing gravitational force. However, their velocity is constantly changing direction, maintaining a circular (or elliptical) path. The gravitational force is always perpendicular to the instantaneous velocity of the satellite (at least at each point along the orbital path, for the idealized case of a purely circular orbit). Thus, the instantaneous work done by gravity is zero at each point, meaning the total work done over a complete orbit is also zero, assuming a perfect, circular orbit.

4. Pushing an Object Uphill

Imagine pushing an object uphill against gravity. You are doing positive work, increasing the object's potential energy. Gravity, acting downwards, is doing negative work, opposing the upward motion.

5. Sliding Down a Frictionless Incline

If an object slides down a frictionless incline, gravity does positive work, converting potential energy into kinetic energy. However, the statement about gravity always doing negative work still holds if we consider the change in potential energy. As the object moves down the incline, its potential energy decreases. This decrease in potential energy is equivalent to the positive work done by gravity.

Misconceptions and Clarifications

It's crucial to address common misunderstandings:

• Work done by gravity vs. change in potential energy: While gravity might do positive work in certain situations (like an object falling), the key is that this positive work reflects a decrease in the object's gravitational potential energy. The negative sign in the work-energy theorem reflects this decrease in potential energy.

• Reference Point: The choice of reference point affects the value of the potential energy, but it doesn't change the fact that gravity does negative work when an object moves to a higher potential energy state.

• Positive vs. Negative Work: Negative work doesn't mean no work is done. It simply means the force is acting in opposition to the displacement.

Conclusion: Gravitation's Persistent Negative Influence

The statement that gravitation always does negative work is a nuanced truth best understood within the framework of work, potential energy, and the vector nature of forces. While gravity can lead to an increase in kinetic energy (positive work in some frames of reference), this always corresponds to a decrease in gravitational potential energy. The negative sign associated with the work done by gravity always reflects this reduction in potential energy, hence the statement being accurate. Understanding this subtlety is vital for grasping fundamental principles of classical mechanics and their applications in various physical scenarios. The careful consideration of vectors and potential energy changes is crucial in accurately analyzing any gravitational interaction.