A force of 10 N acts on an object. The object is displaced by 2 metres in the direction of the force. The force acts on the object all through the displacement. What is the work done?
- AOption (a)
5 J
- BOption (b)
10 J
- COption (c)
15 J
- DOption (d)
20 J
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Correct answer
20 J
Why this answer is correct
The correct answer is 20 J.
Key Points
- Work done is calculated using the formula: W = F × d × cos(θ), where F is the force applied, d is the displacement, and θ is the angle between the force and the direction of displacement.
- In this case, the force applied is 10 N, and the displacement is 2 m.
- The force acts in the same direction as the displacement, so the angle θ = 0°. For θ = 0°, cos(0°) = 1.
- Using the formula: W = F × d × cos(θ), we get W = 10 × 2 × 1 = 20 J.
- Therefore, the work done by the force on the object is 20 Joules.
Additional Information
- Work:
- Work is a measure of energy transfer when a force is applied over a distance.
- It is expressed in units of Joule (J) in the SI system, where 1 Joule is equivalent to 1 Newton-meter.
- Work is said to be done only when there is displacement and the force has a component along the direction of displacement.
- Force:
- Force is any interaction that can change the motion of an object. It is measured in Newtons (N) in the SI system.
- 1 Newton is the force required to accelerate a 1 kg mass by 1 m/s².
- In this problem, a constant force of 10 N acts on the object.
- Displacement:
- Displacement refers to the straight-line distance between the initial and final positions of an object.
- It is a vector quantity and has both magnitude and direction.
- Here, the displacement is 2 meters in the direction of the force.
- Angle between Force and Displacement:
- The angle between the force and displacement determines the effective component of the force contributing to the work.
- If the angle is 0°, the entire force contributes to the work, as cos(0°) = 1.
- If the angle is 90°, no work is done, as cos(90°) = 0.
- In this problem, the angle is 0°, ensuring maximum work.
Important Points
- Work Done in Physics:
- Work done is positive when the force and displacement are in the same direction.
- Work done is negative when the force is opposite to the direction of displacement.
- Work done is zero if there is no displacement or if the force is perpendicular to the displacement.
- Real-life applications of work:
- Examples include lifting objects, pushing a cart, or pulling a rope.
- Mechanical work is essential in machines and engines to convert energy into motion.