Question 1: Work done in physics is defined as the transfer of energy when a force causes an object to move in the direction of the force. The formula for work done is W = F × d × cos(θ), where F is the force applied, d is the displacement, and θ is the angle between the force and displacement.

Answer: Work done is the energy transferred when a force moves an object in the direction of the force, calculated as W = F × d × cos(θ).

Question 1: What is the SI unit of work done?

Answer: Joule (J)

Question 2: Explain why the angle θ is important in calculating work done.

Answer: Because work is maximized when force and displacement are in the same direction (θ=0), and no work is done when force is perpendicular to displacement (θ=90).

Question 1: A worker pushes a box with a force of 50 N over a distance of 4 meters in the same direction as the force. Calculate the work done.

Answer: Work done = 50 N × 4 m × cos(0°) = 200 Joules

Question 2: An object is moved 10 meters with a force of 30 N at an angle of 60° to the direction of movement. Find the work done.

Answer: Work done = 30 N × 10 m × cos(60°) = 30 × 10 × 0.5 = 150 Joules

Question 1: Outline the variables that must be controlled and measured in an experiment to determine the work done when lifting a load vertically.

Answer: Variables include the force applied (measured with a force sensor), the height lifted (measured with a ruler or meter stick), and the angle of application of force if not vertical. Controlled variables might include the mass of the load, the surface friction, and the lifting speed to ensure consistent conditions.

Question 1: A crane lifts a 2000 kg load to a height of 20 meters. Ignoring resistance, calculate the work done by the crane. Assume gravity g = 9.8 m/s².

Answer: Work done = mass × gravity × height = 2000 kg × 9.8 m/s² × 20 m = 392,000 Joules

Question 2: In an industrial setting, a conveyor belt moves objects with a force of 150 N over a distance of 30 meters. If the force is applied at an angle of 45°, what is the total work done?

Answer: Work done = 150 N × 30 m × cos(45°) = 150 × 30 × 0.7071 ≈ 3183 Joules

Question 1: Explain in detail how the angle between force and displacement affects the work done, including real-world examples.

Answer: The work done depends on the component of force in the direction of displacement, which is given by F cos(θ). When θ=0°, force is fully in the direction of movement, maximizing work done. When θ=90°, force is perpendicular, and no work is done. For example, pushing a box directly forward does maximum work, whereas pushing at an angle results in less effective work.

Question 1: Describe how understanding work done helps in designing energy-efficient machines, such as electric motors or cranes.

Answer: Understanding work done allows engineers to minimize energy loss and optimize force application, leading to more efficient machines by reducing unnecessary effort and improving energy transfer.

Question 2: Provide a real-life example where calculating work done is essential for safety and efficiency.

Answer: In construction cranes, calculating the work done helps determine the energy required to lift heavy loads safely and efficiently, preventing overloading and accidents.