A cylindrical steel rod with negligible weight has a diameter of \(1.5\,\mathrm{cm}\) and a length of \(5.2\,\mathrm{cm}\).
The rod is firmly attached at the top end.
The rod is firmly attached to a machine at the other end that applies a constant force of \(363\,\mathrm{N}\) to the rod.
This causes the rod to extend to a length of \(7.4\,\mathrm{cm}\) and to have a minimum diameter of \(0.60\,\mathrm{cm}\) in the position shown.
What is the maximum stress acting on the steel rod when the length is \(7.4\,\mathrm{cm}\)?
Correct Answer: \( \boxed{\mathrm{D}} \)
Stress is given by
\( \sigma=\dfrac{F}{A} \).
The minimum cross-sectional area occurs where the diameter is \(0.60\,\mathrm{cm}=0.0060\,\mathrm{m}\).
\(A=\dfrac{\pi(0.0060)^2}{4}=2.83\times10^{-5}\,\mathrm{m^2}\).
Hence,
\( \sigma=\dfrac{363}{2.83\times10^{-5}}\approx1.28\times10^{7}\,\mathrm{Pa}\).
Therefore, the correct answer is (D).
Which expression gives the formula for the spring constant?
Correct Answer: \( \boxed{\mathrm{C}} \)
Hooke’s law states that \(F=kx\).
Rearranging gives
\(k=\dfrac{F}{x}\).
Therefore, the correct answer is (C).
A platform is supported by a spring. A box is placed onto the platform. The diagram shows the spring before and after the box is placed onto it.
What is the term for the quantity marked as \(x\)?
Correct Answer: \( \boxed{\mathrm{A}} \)
The quantity \(x\) is the decrease in the spring’s length after the load is applied.
This decrease in length is called the compression of the spring.
Therefore, the correct answer is (A).
