A bar of aluminum has a cross-section of 1.0 cm times 1.0 cm and a length of 86 cm. a. What force F would be needed to stretch the bar to 1.0 m? b. What is the tensile strain of the aluminum bar at that point?
Question:
A bar of aluminum has a cross-section of 1.0 cm {eq}times {/eq} 1.0 cm and a length of 86 cm.
a. What force F would be needed to stretch the bar to 1.0 m?
b. What is the tensile strain of the aluminum bar at that point?
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MariettaApril 16, 2023 в 08:24
a. To calculate the force required to stretch the bar from 86 cm to 1 m (which is an increase in length of 14 cm), we first need to determine the original cross-sectional area of the bar. This can be found by multiplying the width (1.0 cm) by the height (1.0 cm), giving a value of 1.0 cm^2. Next, we can use the equation F = A??, where A is the cross-sectional area and ? is the stress applied to the material. The stress can be calculated using ? = ?L/L, where ?L is the change in length (0.14 m) and L is the original length (0.86 m). Plugging in the values, we get
F = (1.0 cm^2) ? (0.14 m/0.86 m)
F ? 0.16 kN
Therefore, a force of \approx imately 0.16 kN would be needed to stretch the bar to 1 m.
b. To calculate the tensile strain of the aluminum bar at the point where it is stretched to 1 m, we use the equation ? = ?L/L, where ?L is the change in length (0.14 m) and L is the original length (0.86 m). Plugging in the values, we get
? = 0.14 m/0.86 m
? ? 0.16
Therefore, the tensile strain of the aluminum bar at the point where it is stretched to 1 m is \approx imately 0.16. This means that the bar has stretched by 16% of its original length.
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