Physics 5054 · O Level · Elastic deformation

Elastic deformation — practice question

A student determines the spring constant $k$ of a spring by two separate methods. The spring constant $k$ of a spring indicates how stiff the spring is. The greater the spring constant $k$, the harder the spring is to extend. A full-size drawing of the spring appears in Fig. 1.1. The setup of apparatus is shown in Fig. 1.2.
(a(i))[1]

Determine the unstretched length $l_0$ of the spring to the closest $0.1\,\text{cm}$. Exclude the end loops from the measurement.

(a(ii))[1]

Calculate the extension $e$ of the spring caused by the mass. Use the equation $e = l_1 - l_0$ given that $l_1 = 17.6\,\text{cm}$.

(a(iii))[1]

Calculate the spring constant $k_1$ of the spring. Apply the equation $k_1 = \frac{300}{e}$.

(a(iv))[2]

Explain what is meant by parallax errors and how to avoid parallax errors when finding the extension of the spring.

(b(i))[1]

Record the time $t_1$ displayed on the stop-watch in Fig. 1.3 to one decimal place.

(b(ii))[1]

Calculate the mean time $t$ for $20$ oscillations.

(b(iii))[1]

Calculate the mean period $T$ of the oscillation. Determine the value of $T^2$.

(b(iv))[1]

Use your value of $T^2$ to calculate the spring constant $k_2$ of the spring using the equation $k_2 = \frac{11.8}{T^2}$.

(c)[1]

Explain why the value for the mean period $T$ obtained by timing $20$ oscillations twice is more accurate than the value obtained by timing $1$ oscillation twice.

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