Question
For the following 3 scenarios, explain why work is or is not done:
A woman preparing for a trip lifts her suitcase from the floor to the bed so that she may pack more easily.
A man spends 5 minutes thinking about the most efficient way to decorate his roof with Christmas lights.
A student carries his book bag down the hallway.
A woman preparing for a trip lifts her suitcase from the floor to the bed so that she may pack more easily.
A man spends 5 minutes thinking about the most efficient way to decorate his roof with Christmas lights.
A student carries his book bag down the hallway.
Answers
GPT-4o mini
To determine whether work is done in each scenario, we can refer to the physics definition of work. In physics, work is defined as the process of transferring energy to an object via a force causing the object to move through a distance. Mathematically, work (\(W\)) is calculated as the product of the force (\(F\)) applied to the object and the distance (\(d\)) over which that force is applied, in the direction of the force. If there is no displacement, no work is done, regardless of the amount of force applied.
Let’s analyze each scenario:
1. **A woman preparing for a trip lifts her suitcase from the floor to the bed so that she may pack more easily.**
- **Work is done.** In this scenario, the woman exerts an upward force on the suitcase while lifting it from the floor to the bed. Because there is a displacement (the suitcase moves upward) in the direction of the force exerted, work is performed. Specifically, the force she exerts must overcome the weight of the suitcase, and since it results in vertical displacement, this action constitutes work.
2. **A man spends 5 minutes thinking about the most efficient way to decorate his roof with Christmas lights.**
- **No work is done.** In this case, the man is engaging in mental activity, which does not involve any physical displacement or force being applied to any object in the context of the physics definition of work. Although he may be exercising his mind, he is not moving any object over a distance, so he does not do work as defined in physics.
3. **A student carries his book bag down the hallway.**
- **Work is done, but not in the vertical lifting sense.** When the student carries the book bag, he exerts an upward force to hold the bag against gravity. If we assume that the book bag does not move vertically (just being held at a constant height while walking), then no work is done vertically in that sense since the vertical displacement is zero. However, if we consider movement down the hallway as horizontal displacement, one might argue that work is done to an extent (depending on the forces involved, such as friction), but strictly speaking regarding gravitational work, the movement along the horizontal path at a constant height implies no vertical work was done on the bag itself.
In summary:
- Scenario 1: Work is done (lifting the suitcase).
- Scenario 2: No work is done (thinking).
- Scenario 3: Work is done in a limited context depending on horizontal movement and the role of gravity in carrying the bag.
Let’s analyze each scenario:
1. **A woman preparing for a trip lifts her suitcase from the floor to the bed so that she may pack more easily.**
- **Work is done.** In this scenario, the woman exerts an upward force on the suitcase while lifting it from the floor to the bed. Because there is a displacement (the suitcase moves upward) in the direction of the force exerted, work is performed. Specifically, the force she exerts must overcome the weight of the suitcase, and since it results in vertical displacement, this action constitutes work.
2. **A man spends 5 minutes thinking about the most efficient way to decorate his roof with Christmas lights.**
- **No work is done.** In this case, the man is engaging in mental activity, which does not involve any physical displacement or force being applied to any object in the context of the physics definition of work. Although he may be exercising his mind, he is not moving any object over a distance, so he does not do work as defined in physics.
3. **A student carries his book bag down the hallway.**
- **Work is done, but not in the vertical lifting sense.** When the student carries the book bag, he exerts an upward force to hold the bag against gravity. If we assume that the book bag does not move vertically (just being held at a constant height while walking), then no work is done vertically in that sense since the vertical displacement is zero. However, if we consider movement down the hallway as horizontal displacement, one might argue that work is done to an extent (depending on the forces involved, such as friction), but strictly speaking regarding gravitational work, the movement along the horizontal path at a constant height implies no vertical work was done on the bag itself.
In summary:
- Scenario 1: Work is done (lifting the suitcase).
- Scenario 2: No work is done (thinking).
- Scenario 3: Work is done in a limited context depending on horizontal movement and the role of gravity in carrying the bag.