Work Done By A Waiter Carrying A Tray A Physics Problem Explained

Introduction

In the realm of physics, the concept of work carries a precise and often counterintuitive meaning. It's not merely about exerting effort or feeling tired; rather, work is defined as the energy transferred when a force causes displacement. This article delves into a classic physics problem involving a waiter carrying a tray at a constant velocity to illustrate this concept, providing a detailed explanation of how to calculate work done in specific scenarios.

The question at hand is: A waiter is carrying a tray above his head and walking at a constant velocity. If he applies a force of 5.0 newtons on the tray and covers a distance of 10.0 meters, how much work is being done? The options provided are A. 0 joules, B. 2 joules, C. -2 joules, D. 50 joules, and E. -50 joules. To accurately answer this question, we must first grasp the fundamental definition of work and how it relates to force and displacement.

Defining Work in Physics

In physics, work is defined as the product of the force applied to an object and the distance the object moves in the direction of the force. Mathematically, it is expressed as:

${ W = F \cdot d \cdot cos(\theta) }$

Where:

• ${ W }$ represents work (measured in joules).
• ${ F }$ is the magnitude of the force (measured in newtons).
• ${ d }$ is the magnitude of the displacement (measured in meters).
• ${ \theta }$ (theta) is the angle between the force vector and the displacement vector.

The presence of the cosine function is crucial. It signifies that only the component of the force acting in the direction of displacement contributes to the work done. If the force and displacement are perpendicular (${ \theta = 90^\circ }$), then ${ cos(90^\circ) = 0 }$, and no work is done, regardless of the magnitudes of the force and displacement.

Analyzing the Waiter Problem

Now, let's apply this understanding of work to the scenario of the waiter carrying a tray. The waiter applies a force of 5.0 newtons to hold the tray above his head, counteracting the force of gravity. This is necessary to prevent the tray from falling. However, the critical point is the direction of this force relative to the waiter's displacement.

The waiter is walking horizontally, meaning his displacement is in the horizontal direction. The force he applies to the tray to support it is vertical, acting upwards against gravity. Therefore, the angle between the force and the displacement is 90 degrees.

Using the work equation:

${ W = F \cdot d \cdot cos(\theta) }$

We plug in the values:

• ${ F = 5.0 \text{ N} }$
• ${ d = 10.0 \text{ m} }$
• ${ \theta = 90^\circ }$

So, the equation becomes:

${ W = 5.0 \text{ N} \cdot 10.0 \text{ m} \cdot cos(90^\circ) }$

Since ${ cos(90^\circ) = 0 }$, the work done is:

${ W = 5.0 \text{ N} \cdot 10.0 \text{ m} \cdot 0 = 0 \text{ joules} }$

This result might seem counterintuitive at first. The waiter is undoubtedly exerting effort to carry the tray, and we might intuitively feel that work is being done. However, in the physics definition, no work is done because the force applied is perpendicular to the direction of motion. The waiter's muscles are indeed working to counteract gravity, but this work does not contribute to displacement in the direction of the applied force.

Why the Answer is 0 Joules

The correct answer is A. 0 joules. This is because the force applied by the waiter is vertical, and the displacement is horizontal. The angle between these two vectors is 90 degrees, and the cosine of 90 degrees is zero. As a result, the work done, calculated using the formula ${ W = F \cdot d \cdot cos(\theta) }$, is zero.

This scenario underscores a crucial distinction in physics: work is only done when a force causes displacement in the direction of the force. The waiter's effort to hold the tray steady does not translate to work in the physics sense because it does not contribute to the horizontal movement.

Common Misconceptions

One common misconception is equating physical exertion with work in the physics sense. While the waiter might feel tired from carrying the tray, this sensation doesn't automatically mean work is being done in the physics context. The key factor is the direction of the force relative to the displacement. If there is no displacement in the direction of the force, no work is done, regardless of how much effort is exerted.

Another misconception is overlooking the angle between force and displacement. The ${ cos(\theta) }$ term in the work equation is critical. It emphasizes that only the component of the force in the direction of displacement matters. If this angle is 90 degrees, as in the waiter example, the work done is zero, irrespective of the force and displacement magnitudes.

Real-World Examples and Applications

This concept of work being zero when the force and displacement are perpendicular has numerous real-world implications:

1. A satellite in orbit: A satellite orbiting the Earth experiences a gravitational force towards the Earth's center. However, its displacement is tangential to its orbit. Since the gravitational force is perpendicular to the displacement, the Earth's gravity does no work on the satellite, which is why it can maintain a stable orbit without needing fuel to counteract gravity.
2. Walking on a level surface: When you walk on a level surface, the upward force exerted by your legs to counteract gravity does no work because your displacement is horizontal. The work done in walking primarily comes from the forces your muscles exert to move you forward, which do have a component in the direction of displacement.
3. Holding a heavy object stationary: If you hold a heavy object stationary, you are exerting a force to counteract gravity. However, since there is no displacement, no work is done on the object in the physics sense.

Further Exploration of Work and Energy

The concept of work is closely linked to the concept of energy. The work-energy theorem states that the net work done on an object is equal to the change in its kinetic energy. Understanding work is crucial for comprehending various forms of energy and their transformations.

For example, when work is done on an object, it can increase the object's kinetic energy (energy of motion), potential energy (energy of position), or both. In the waiter example, no work is done on the tray in the horizontal direction, so its kinetic energy in that direction remains constant (assuming constant velocity). However, the waiter's muscles are expending energy, which is being converted to heat and other forms of energy due to the internal processes required to maintain the force.

Conclusion

The waiter problem illustrates a fundamental principle in physics: work is done only when a force causes displacement in the direction of the force. In this scenario, the force applied by the waiter to support the tray is perpendicular to the displacement, resulting in zero work done. This concept is essential for a deeper understanding of work, energy, and their applications in various physical systems.

By grasping the precise definition of work and its dependence on the angle between force and displacement, we can avoid common misconceptions and accurately analyze a wide range of physical phenomena. The next time you see someone exerting effort, remember that in the world of physics, work has a very specific meaning that goes beyond mere exertion.