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.

Question

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, we need to perform the following calculations step-by-step:

1. Calculate the weight that 8,000 ounces represents on the actual bridge:

Since the model is 4 times smaller than the actual bridge, the forces will scale with the square of the linear dimensions (because weight is a volume-related measure in structural contexts).

The scale factor for the model is 4, so the actual bridge will be able to handle the weight on the model multiplied by the square of the scale factor:

\[ \text{Weight Capacity of Actual Bridge} = \text{Weight Capacity of Model} \times (\text{Scale Factor})^2 \]

Given the model holds 8,000 ounces, we calculate:

\[ \text{Weight Capacity of Actual Bridge} = 8,000 \text{ ounces} \times (4^2) \] \[ \text{Weight Capacity of Actual Bridge} = 8,000 \text{ ounces} \times 16 = 128,000 \text{ ounces} \]

2. Convert ounces to pounds:

Since 1 pound = 16 ounces, we can convert the weight held by the actual bridge from ounces to pounds:

\[ \text{Weight in Pounds} = \frac{128,000 \text{ ounces}}{16} = 8,000 \text{ pounds} \]

3. Convert pounds to tons:

Since 2,000 pounds = 1 ton, we convert the weight into tons:

\[ \text{Weight in Tons} = \frac{8,000 \text{ pounds}}{2,000} = 4 \text{ tons} \]

4. Conclusion:

Since the actual bridge can hold 4 tons and the maximum weight it is designed to hold is 1 ton, we conclude:

Therefore, the bridge will hold 1 ton.