6.1 Work

In everyday language, the word "work" can mean many things—studying for an exam, doing chores, or earning a living. However, in physics, "work" has a very specific and precise meaning. It is related to force and displacement. Understanding the scientific definition of work is essential for understanding energy, power, and many other concepts in physics.

Definition

Work is said to be done when a force displaces a body in its own direction. Mathematically, work done (W) is the product of the force (F) and the displacement (d) in the direction of the force.

W = F × d

Work is a scalar quantity. The SI unit of work is the joule (J). One joule is equal to the work done by a one-newton (1 N) force acting over a one-metre (1 m) distance.

1 J = 1 N × 1 m

Main Idea

The main idea is that work is done only when a force causes a displacement. If you push against a wall and it doesn't move, you are applying a force, but no work is done (in the physics sense). Work requires both a force and a displacement in the direction of that force. The amount of work done depends on the magnitude of the force and the distance the object moves.

Core Concept

• A force must be applied to an object.
• The object must be displaced in the direction of the force.

The text states: "Work is said to be done when a force displaces a body in its own direction."

The Formula The formula for work is: W = F × d where: - W is the work done (in joules, J). - F is the applied force (in newtons, N). - d is the displacement in the direction of the force (in metres, m).

Units of Work The SI unit of work is the joule (J). One joule is the work done when a force of 1 N moves an object 1 m in the direction of the force. 1 J = 1 N × 1 m

• Given: Force F = 100 N, Distance d = 200 m
• Solution: W = F × d = 100 N × 200 m = 20,000 J = 20 kJ

Vector Representation The text also discusses the vector representation of force and displacement. Force is not always applied perfectly in the direction of motion. For example, consider a toy car moving horizontally with a force F applied at an angle θ to the horizontal. In such situations, the force is resolved into its rectangular components. The component of force in the direction of motion is Fcosθ, and the work done is: W = (Fcosθ) × d

Detailed Explanation

Work is a fundamental concept in physics that connects force and energy. When work is done on an object, energy is transferred to or from the object.

Work and Energy The text states: "When work is done, energy is used. Thus, work and energy are related to each other." Work is the transfer of energy. When you do work on an object, you transfer energy to it. For example, lifting a book transfers energy to the book (gravitational potential energy). Pushing a car transfers kinetic energy to the car.

• Positive work: When the force and displacement are in the same direction, the work done is positive. Example: Pushing a box forward.
• Negative work: When the force and displacement are in opposite directions, the work done is negative. Example: Friction does negative work on a sliding object.
• Zero work: When the force and displacement are perpendicular, the work done is zero. Example: Carrying a book horizontally while walking (the force is upward, displacement is horizontal).

Work Done by a Force at an Angle When the force is applied at an angle θ to the displacement, only the component of the force in the direction of displacement does work. The formula becomes: W = F d cosθ - If θ = 0^°, W = Fd (maximum positive work). - If θ = 90^°, W = 0 (zero work). - If θ = 180^°, W = -Fd (negative work).

Intermediate Level

In physics, work is a scalar quantity defined as the dot product of force and displacement: W = F · d = Fdcosθ. This means that only the component of force in the direction of displacement contributes to work. If the force is perpendicular to the displacement (e.g., centripetal force in circular motion), the work done is zero. If the force is opposite to the displacement (e.g., friction), the work done is negative. Work is measured in joules (J), and one joule is the work done when a force of 1 N moves an object 1 m. The concept of work is closely related to energy—work is the transfer of energy from one system to another.

Important Points

• - Work: Force × displacement in the direction of force.
• - Formula: W = F × d (when force and displacement are in the same direction).
• - Formula (at an angle): W = Fdcosθ.
• - Unit: Joule (J). 1 J = 1 N·m.
• - Work is a scalar quantity.
• - Positive work: Force and displacement in the same direction.
• - Negative work: Force and displacement in opposite directions.
• - Zero work: Force and displacement perpendicular.

Remember

• - Work = Force × Distance.
• - Unit: Joule (J).
• - Scalar quantity.
• - Work is done only if there is displacement in the direction of force.
• - Positive work: Force and motion in the same direction.
• - Negative work: Force and motion in opposite directions.
• - Zero work: Force perpendicular to motion.

Common Mistakes

• - Thinking work is done whenever a force is applied: Work requires displacement. Pushing a wall that doesn't move does no work.
• - Forgetting the direction: Work depends on the component of force in the direction of displacement. A force perpendicular to the motion does no work.
• - Confusing work with power: Work is the amount of energy transferred. Power is the rate at which work is done.

Quick Revision

Work is done when a force displaces a body in the direction of the force. It is calculated as the product of force and displacement (W = F × d) and is measured in joules (J). Work is a scalar quantity. When the force is at an angle to the displacement, the formula becomes W = Fdcosθ. Work can be positive (force and displacement in the same direction), negative (opposite directions), or zero (perpendicular).

60-Second Revision

• Formula: W = Fdcosθ.
• Unit: Joule (J).
• Scalar.
• Positive work: Same direction.
• Negative work: Opposite direction.
• Zero work: Perpendicular.

Frequently Asked Questions (FAQs)

Q1. What is work in physics? Answer: Work is done when a force displaces a body in the direction of the force. It is the product of the force and the displacement in the direction of the force (W = F × d).

• Q2. What is the SI unit of work?
• Answer: The SI unit of work is the joule (J). One joule is the work done when a force of 1 N moves an object 1 m in the direction of the force.

• Q3. Is work a scalar or a vector?
• Answer: Work is a scalar quantity. It has magnitude but no direction.

Q4. Can work be zero? Answer: Yes. Work is zero when the force is perpendicular to the displacement (e.g., carrying a book horizontally). It is also zero when there is no displacement (e.g., pushing a wall that doesn't move).

• Q5. What is positive work?
• Answer: Positive work is done when the force and the displacement are in the same direction. For example, pushing a box forward.

• Q6. What is negative work?
• Answer: Negative work is done when the force and the displacement are in opposite directions. For example, friction does negative work on a sliding object.

Q7. How is work related to energy? Answer: Work is the transfer of energy. When work is done on an object, energy is transferred to or from the object. For example, lifting a book transfers energy to the book (gravitational potential energy).

Multiple Choice Questions (MCQs)

• Q1. Work is defined as:
• A. Force × time
• B. Force × distance
• C. Force / distance
• D. Force / time

• Correct Answer: B
• Explanation: The text defines work as force multiplied by displacement in the direction of the force.

• Q2. The SI unit of work is the:
• A. Newton
• B. Joule
• C. Watt
• D. Pascal

• Correct Answer: B
• Explanation: The SI unit of work is the joule (J).

• Q3. Work is a:
• A. Vector quantity
• B. Scalar quantity
• C. Base quantity
• D. Derived quantity

• Correct Answer: B
• Explanation: The text states that work is a scalar quantity.

• Q4. If a force of 10 N moves an object 5 m in the direction of the force, the work done is:
• A. 2 J
• B. 50 J
• C. 15 J
• D. 0.5 J

• Correct Answer: B
• Explanation: W = F × d = 10 × 5 = 50 J.

• Q5. Work done is zero when:
• A. Force and displacement are in the same direction
• B. Force and displacement are in opposite directions
• C. Force and displacement are perpendicular
• D. Force is zero

• Correct Answer: C
• Explanation: When force is perpendicular to displacement, the work done is zero (e.g., carrying a book horizontally).

• Q6. Positive work is done when:
• A. Force and displacement are in the same direction
• B. Force and displacement are in opposite directions
• C. Force and displacement are perpendicular
• D. Force is zero

• Correct Answer: A
• Explanation: Positive work is done when the force and displacement are in the same direction.

• Q7. Negative work is done when:
• A. Force and displacement are in the same direction
• B. Force and displacement are in opposite directions
• C. Force and displacement are perpendicular
• D. Force is zero

• Correct Answer: B
• Explanation: Negative work is done when force and displacement are in opposite directions (e.g., friction).

• Q8. One joule is equal to:
• A. 1 N × 1 m
• B. 1 N / 1 m
• C. 1 N × 1 s
• D. 1 N / 1 s

• Correct Answer: A
• Explanation: 1 J = 1 N × 1 m.

• Q9. When a force is applied at an angle θ to the displacement, the work done is:
• A. Fd
• B. Fdsinθ
• C. Fdcosθ
• D. Fdtanθ

• Correct Answer: C
• Explanation: The component of force in the direction of displacement is Fcosθ, so W = Fdcosθ.

• Q10. A force of 100 N pushes a box 200 m. The work done is:
• A. 2 J
• B. 200 J
• C. 20,000 J
• D. 200,000 J

• Correct Answer: C
• Explanation: W = 100 × 200 = 20,000 J = 20 kJ, as calculated in the text.

Frequently Asked Questions (FAQs)

Q1. What is the difference between work and power? Answer: Work is the amount of energy transferred when a force moves an object. Power is the rate at which work is done (work divided by time). Work is measured in joules, power in watts.

• Q2. Can work be negative?
• Answer: Yes. Negative work is done when the force is opposite to the direction of motion (e.g., friction). It means energy is removed from the object.

Q3. Why is work zero when force is perpendicular to displacement? Answer: Because the component of force in the direction of displacement is zero. For example, the centripetal force in circular motion is perpendicular to the velocity, so it does no work.

• Q4. How is work related to kinetic energy?
• Answer: The work-energy theorem states that the net work done on an object equals its change in kinetic energy: W_net = Δ KE.

Q5. What is the work done by gravity when an object falls? Answer: When an object falls, gravity does positive work because the force (downward) and displacement (downward) are in the same direction. The work done is W = mgh.

Q6. What is the work done when lifting an object? Answer: When lifting an object at constant speed, the applied force equals the weight (mg), and the displacement is upward. The work done by the applied force is W = mgh. Gravity does negative work.

Q7. How is work calculated when the force is at an angle? Answer: Work is calculated using the component of force in the direction of displacement: W = Fdcosθ, where θ is the angle between the force and displacement vectors.

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