Problem 78 - Algebra and Trigonometry

Question

Determine whether each statement makes sense or does not make sense, and explain your reasoning. The weightlifter does more work in raising 300 kilograms above her head than Atlas, who is supporting the entire world.

Step-by-Step Solution

Answer

The statement makes sense in the context of physics. According to the physics definition of work, the weightlifter does more work because she is moving a weight a certain distance, while Atlas, even though he is exerting a large amount of force, is not doing work as he is not displacing (moving) the world.

Step 1: Review the concept of work

In physics, the concept of work is defined as the effort exerted to move an object a certain distance. The formula for work is given by the equation \( W = F \cdot d \cdot cos(\Theta) \) , where \( F \) is force, \( d \) is distance and \( \Theta \) is the angle (cosine of 0 degree is 1 when the displacement is in the same direction as the force). As such, work is only done when there is movement.

Step 2: Evaluate the work done by the weightlifter

The weightlifter exerts effort to lift 300kg above her head. Here, force is being used to move a weight against gravity, and there is a displacement (movement) involved. As per the definition and formula of work, there is work being done by the weightlifter.

Step 3: Evaluate the work done by Atlas

Atlas, according to mythology, is holding up the world but not moving it in any direction. There's no displacement involved as he is not lifting or lowering the world, just supporting it. Hence, even though a large amount of force is being exerted by Atlas, according to physical definitions of work, there is zero work done by Atlas.

Key Concepts

Understanding Work in Physics

The concept of work in physics differs from our everyday understanding of the term. In physics, work is a specific technical term defined by the equation: \[ W = F \cdot d \cdot \cos(\Theta) \]where:

• W is the work done,
• F is the applied force,
• d is the displacement or distance moved by the object,
• \( \Theta \) is the angle between the force and the direction of displacement.

For work to be accomplished, there must be a displacement of the object upon which the force is acting. This means, even if a considerable force is applied, without movement, no work is done. Therefore, it is important to understand that work requires both a force and a movement in the direction of the force.

Exploring the Concept of Force

Force plays a pivotal role in calculating work. It is the push or pull exerted on an object, causing it to move or change its velocity. Force is a vector quantity, which means it has both magnitude and direction. Here’s what to remember:

• A force can cause a stationary object to move.
• It can also change the speed or direction of a moving object.

The unit of force is the Newton (N), which is equivalent to the force needed to move a mass of one kilogram at a rate of one meter per second squared. In the equation for work, force must always be in the direction of the displacement to contribute to work. If the force is perpendicular to the direction of movement, as in the case of holding a heavy object without moving it, then no work is done in the physical sense.

Understanding Displacement in Work Calculations

Displacement is the measure of the distance moved by an object in a particular direction. It is not to be confused with distance, which is the total path covered. Displacement is a vector quantity and plays a crucial role when calculating work. Here are key points about displacement:

• Displacement involves direction, making it different from just moving over a distance.
• It considers the shortest path between the starting point and the ending point.
• When calculating work, the displacement must be in the direction of the applied force.

For example, if a force lifts an object vertically upwards, and the motion is in the same vertical direction, displacement is taking place. In contrast, if a force is applied but the object does not move, the displacement is zero, and thus, no work is done, regardless of the amount of force applied.