Question

An engineer is building a bridge that should be able to hold a maximum weight of 1 ton. He builds a model of the bridge that is exactly 4 times smaller than the actual bridge.

16 ounces = 1 pound. 2,000 pounds = 1 ton.

If a test of the model shows that it holds 8,000 ounces, will the bridge hold 1 ton?

8,000 ounces on the model is equal to
ounces on the actual bridge.
Convert ounces to pounds. The actual bridge can hold
pounds.
Therefore, the bridge
hold 1 ton

Answer 1

To determine if the actual bridge will hold 1 ton based on the model's performance, let’s go through the calculations step by step.

1. **Convert model's weight capacity from ounces to pounds:**
- The model can hold 8,000 ounces.
- Since \(16\) ounces = \(1\) pound, we convert ounces to pounds:
\[
8,000 \, \text{ounces} \div 16 \, \text{ounces/pound} = 500 \, \text{pounds}
\]

2. **Determine the equivalent weight capacity of the actual bridge:**
- The model is 4 times smaller in size. When scaling, the weight capacity scales with the cube of the size ratio. This is because weight (or mass) is proportional to volume, and volume is a cubic measurement.
- Therefore, the actual bridge can hold:
\[
500 \, \text{pounds} \times 4^3 = 500 \, \text{pounds} \times 64 = 32,000 \, \text{pounds}
\]

3. **Convert pounds to tons:**
- Since \(2,000\) pounds = \(1\) ton, we convert pounds to tons:
\[
32,000 \, \text{pounds} \div 2,000 \, \text{pounds/ton} = 16 \, \text{tons}
\]

4. **Conclusion:**
- The actual bridge can hold \(16\) tons.

Thus, based on the findings:

- The model holds 8,000 ounces, which is equal to **500 pounds** on the model.
- The actual bridge can hold **32,000 pounds**, which is equal to **16 tons**.

Therefore, the bridge **will** hold 1 ton.