A weightlifter holds a 1,800 N barbell 1 meter above the ground. One end of a 2-meter-long chain hangs from the center of the barbell. The chain has a total weight of 600 N. How much work (in J) is required to lift the barbell to a height of 2 m?


To calculate the work required to lift the barbell to a height of 2 meters, we can use the basic formula for work:

\[
W = F \cdot d
\]

Where:
- \( W \) is the work done (in joules),
- \( F \) is the force applied (in newtons),
- \( d \) is the distance moved by the object (in meters).

### Step 1: Calculate the work required to lift the barbell
- The force applied is the weight of the barbell: \( F_{\text{barbell}} = 1,800 \, \text{N} \),
- The distance lifted is \( d = 2 \, \text{m} - 1 \, \text{m} = 1 \, \text{m} \).

So, the work done to lift the barbell is:

\[
W_{\text{barbell}} = 1,800 \, \text{N} \times 1 \, \text{m} = 1,800 \, \text{J}
\]

### Step 2: Calculate the work required to lift the chain
The chain's weight is distributed along its length, so different parts of the chain are lifted different distances. The center of mass of the chain is located at its midpoint, which is 1 meter below the barbell. Initially, this midpoint is 0.5 meters above the ground, and after lifting, it will be 1.5 meters above the ground.

- The chain's weight is \( F_{\text{chain}} = 600 \, \text{N} \),
- The distance the chain’s center of mass is lifted is \( 1.5 \, \text{m} - 0.5 \, \text{m} = 1 \, \text{m} \).

So, the work done to lift the chain is:

\[
W_{\text{chain}} = 600 \, \text{N} \times 1 \, \text{m} = 600 \, \text{J}
\]

### Step 3: Total work done
The total work required to lift both the barbell and the chain is:

\[
W_{\text{total}} = W_{\text{barbell}} + W_{\text{chain}} = 1,800 \, \text{J} + 600 \, \text{J} = 2,400 \, \text{J}
\]

Thus, the total work required is **2,400 J**.

Would you like more details or have any questions?

Here are 5 related questions to explore:
1. How does the center of mass affect the work required for non-uniform objects?
2. What would happen if the chain were longer or shorter?
3. How would the work change if the barbell had a different weight?
4. What happens to the work if we lifted the barbell at an angle instead of vertically?
5. How would the calculation differ if the chain were uniform but lighter?

**Tip:** When dealing with objects that have distributed mass, always find the center of mass to simplify work and energy calculations.

A weightlifter holds a 1,800 N barbell 1 meter above the ground. One end of a 2-meter-long chain hangs from the center of the barbell. The chain has a total weight of 600 N. How much work (in J) is required to lift the barbell to a height of 2 m?

Learn how to calculate the work required to lift a 1,800 N barbell and a 600 N chain in a detailed physics problem. This solution uses concepts like work, energy, and center of mass to compute the total work of 2,400 J. Suitable for high school students.

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