A bicycle chain of length 1.6 m and of mass 1 kg is lying on a horizontal floor. If g=10ms−2, the work done in lifting it with one end touching the floor and the other end 1.6 m above the floor

To find the work done in lifting a bicycle chain from the floor to a height of 1.6 meters, we can use the concept of gravitational potential energy. The work done against gravity when lifting an object is equal to the change in gravitational potential energy of that object. Let's break this down step by step.

Understanding the Problem

The bicycle chain has a length of 1.6 meters and a mass of 1 kg. When lifting it, one end remains on the floor while the other end is raised to a height of 1.6 meters. This means that the entire chain is not lifted uniformly; rather, different parts of the chain are at different heights during the lift.

Calculating the Average Height

Since the chain is uniform, we can find the average height of the chain as it is lifted. The average height can be calculated as follows:

• The lowest point (one end) is at 0 m.
• The highest point (the other end) is at 1.6 m.

The average height (h) of the chain can be calculated using the formula:

h = (0 + 1.6) / 2 = 0.8 m

Calculating the Work Done

Now that we have the average height, we can calculate the work done (W) in lifting the chain using the formula for gravitational potential energy:

W = m * g * h

Where:

• m = mass of the chain = 1 kg
• g = acceleration due to gravity = 10 m/s²
• h = average height = 0.8 m

Substituting the values into the formula gives:

W = 1 kg * 10 m/s² * 0.8 m = 8 J

Final Result

The work done in lifting the bicycle chain with one end touching the floor and the other end raised to 1.6 meters above the floor is 8 joules.

This example illustrates how to apply the concepts of average height and gravitational potential energy to calculate work done in lifting an object. By understanding the distribution of mass and height, we can accurately determine the energy required for such tasks.