When an object is lifted at a constant speed, the work done depends on both the weight of the object being lifted and the distance over which it is lifted.
The work done, W, is given by the equation:
W = F × d × cosθ
Where:
- F is the force applied (in this case, the weight of the object being lifted),
- d is the distance over which the object is lifted, and
- θ is the angle between the direction of the force and the direction of motion (in this case, the force is acting vertically upward, and the motion is also vertical, so cosθ = 1).
Since we are considering lifting an object at a constant speed, the applied force is equal to the weight of the object. The weight of an object is given by the equation:
F = m × g
Where:
- m is the mass of the object, and
- g is the acceleration due to gravity (approximately 9.8 m/s^2 on Earth).
Substituting the weight into the work equation, we get:
W = (m × g) × d × cosθ
Since cosθ = 1, the equation simplifies to:
W = m × g × d
From this equation, we can see that the work done is directly proportional to both the weight of the object (m × g) and the distance over which it is lifted (d). Doubling the weight of the object or doubling the distance will result in twice the amount of work done. Similarly, halving the weight or the distance will result in half the amount of work done.
It's important to note that the work done is a measure of the energy transferred to the object as it is lifted. In this case, since the object is lifted at a constant speed, the work done is equal to the gravitational potential energy gained by the object.