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What is the Work Done by a Force Field (Introduction)?
Grade Level:
Class 12
AI/ML, Physics, Biotechnology, FinTech, EVs, Space Technology, Climate Science, Blockchain, Medicine, Engineering, Law, Economics
Definition
What is it?
The 'work done' by a force field is the energy transferred when an object moves through that field. It tells us how much 'effort' the force field puts in to move the object from one point to another.
Simple Example
Quick Example
Imagine pushing a small toy car across your room. You are applying a force, and the car moves a certain distance. The 'work done' by your push is how much energy you used to move the car. If you push it further, you do more work.
Worked Example
Step-by-Step
Let's calculate the work done by a constant force.
STEP 1: Identify the force (F) and the distance (d) over which the force acts. Assume a force of 10 Newtons (N) pushes a box.
---STEP 2: Identify the distance the box moves. Assume the box moves 5 meters (m) in the direction of the force.
---STEP 3: Use the formula for work done when force and displacement are in the same direction: Work (W) = Force (F) x Distance (d).
---STEP 4: Substitute the values: W = 10 N x 5 m.
---STEP 5: Calculate the product: W = 50 Newton-meters (Nm).
---STEP 6: Express the answer in Joules (J), which is the standard unit for work. 1 Nm = 1 Joule.
---Answer: The work done is 50 Joules.
Why It Matters
Understanding work done by force fields is crucial for designing everything from electric vehicles (EVs) that move efficiently to complex robotics in AI/ML. Engineers use this concept to calculate the energy needed for rockets to escape Earth's gravity, and even in medicine to understand how forces affect blood flow.
Common Mistakes
MISTAKE: Thinking work is always done when a force is applied. | CORRECTION: Work is only done if the object moves in the direction of the force. If you push a wall, no work is done because the wall doesn't move.
MISTAKE: Confusing work done with just force or just distance. | CORRECTION: Work done is the product of force AND the distance moved in the direction of the force. Both are essential.
MISTAKE: Not considering the direction of force and displacement. | CORRECTION: If the force is perpendicular to the direction of motion (like carrying a bag horizontally), no work is done by that specific force on the bag's vertical position.
Practice Questions
Try It Yourself
QUESTION: A coolie lifts a suitcase weighing 200 N from the ground to a height of 1.5 m. How much work does he do? | ANSWER: Work = Force x Distance = 200 N x 1.5 m = 300 Joules.
QUESTION: A boy pulls a toy car with a force of 5 N over a distance of 10 m on a smooth floor. What is the work done by the boy? | ANSWER: Work = Force x Distance = 5 N x 10 m = 50 Joules.
QUESTION: A satellite is orbiting the Earth in a circular path. Does the Earth's gravitational force do work on the satellite? Explain why. | ANSWER: No, the Earth's gravitational force does no work on the satellite. This is because the gravitational force acts towards the center of the Earth (radially inwards), while the satellite's displacement is always tangential (perpendicular) to the force. When force and displacement are perpendicular, work done is zero.
MCQ
Quick Quiz
When is the work done by a force considered zero?
When the force applied is very small.
When the object does not move, even if a force is applied.
When the object moves very slowly.
When the force is applied for a very short time.
The Correct Answer Is:
B
Work is done only when there is displacement in the direction of the force. If the object does not move (displacement is zero), then the work done is zero, regardless of the force applied.
Real World Connection
In the Real World
Think about Zepto or Swiggy delivery riders. The work done by their vehicle's engine is what moves the bike and the food from the restaurant to your home. Engineers calculate this work to design more fuel-efficient bikes or electric scooters, helping reduce pollution in Indian cities.
Key Vocabulary
Key Terms
WORK DONE: Energy transferred when a force moves an object | FORCE: A push or pull on an object | DISPLACEMENT: The change in an object's position | JOULE: The standard unit of work and energy | FORCE FIELD: A region where a force can be felt by an object (like gravity or magnetism)
What's Next
What to Learn Next
Next, you can explore how work done changes when the force is not constant or when it acts at an angle to the displacement. This will help you understand more complex real-world situations, like how cranes lift heavy materials.
