TEST OF PRACTICAL KNOWLEDGE QUESTION
You are provided with a retort stand, boss head, clamp, stopwatch, slotted weights, hanger, grooved pulley, thread, measuring tape, and other necessary materials.
i. Measure and record the radius \(R\) of the pulley.
ii. Setup the apparatus as illustrated in the diagram above, such that the clamp is 1.5 m above the floor.
iii. Tie one end of the thread to the pulley.
iv. Tie the other end of the thread to the hanger.
v. Slot a mass \(m = 50\ \text{g}\) on the hanger.
vi. Wind the thread around the groove of the pulley until the base of the hanger is at a height \(h = 1.4\ \text{m}\) above the floor. Maintain this height \(h\) for every other value of \(m\) through out the experiment.
vii. Release the mass to unwind the thread.
viii. Determine and record the time \(t\) taken by the mass \(m\) to reach the floor.
ix. Evaluate \(t^{2}\)
x. Also evaluate
a = \(\frac{2h}{t^{2}}\), T = \(\frac{m}{1000}(10 - a)\) and \(\propto = \frac{a}{R}\)
xi. Repeat the procedure for four other values of \(m = 70\ \text{g}, 90\ \text{g}, 110\ \text{g}\) and \(130\ \text{g}\)
xii. Tabulate your readings.
xiii. Plot a graph with \(\propto\) on the vertical axis and T on the horizontal axis.
xiv. Determine the slope s, of the graph.
xv. Evaluate \(I = \frac{R}{s}\).
xvi. State two precautions taken to obtain accurate results.
(b)i. Define centripetal force
ii. An object drops to the ground from a height of 2.0 m. Calculate the speed with which it strikes the ground. [g=10 ms\(^{-2}\)]
(a) Moment-of-inertia (pulley) experiment (outline). A falling mass \(m\) unwinds a thread from a pulley of radius \(R\). Timing the fall through a fixed height \(h\) gives the linear acceleration \(a = \dfrac{2h}{t^2}\); the tension is \(T = \dfrac{m}{1000}(10 - a)\) and the angular acceleration \(\alpha = \dfrac{a}{R}\). For a pulley of moment of inertia \(I\) driven by torque \(TR\), \(TR = I\alpha\), so
\[ T = \frac{I}{R}\,\alpha. \]
Thus a graph of \(\alpha\) (vertical) against \(T\) (horizontal) is a straight line of slope \(s = \dfrac{R}{I}\), and the moment of inertia is \(I = \dfrac{R}{s}\).
Precautions: measure the height and time carefully, releasing the mass and starting the stopwatch together, and avoid parallax when reading the metre scale/heights; keep the thread wound in a single layer in the groove.
(b)(i) Centripetal force is the resultant force directed towards the centre of a circular path that keeps a body moving in that circle.
(b)(ii) Object dropping through \(h = 2.0\ \text{m}\): using \(v^2 = 2gh\),
\[ v = \sqrt{2 \times 10 \times 2.0} = \sqrt{40} = 6.32\ \text{m s}^{-1}. \]
(a) Moment-of-inertia (pulley) experiment (outline). A falling mass \(m\) unwinds a thread from a pulley of radius \(R\). Timing the fall through a fixed height \(h\) gives the linear acceleration \(a = \dfrac{2h}{t^2}\); the tension is \(T = \dfrac{m}{1000}(10 - a)\) and the angular acceleration \(\alpha = \dfrac{a}{R}\). For a pulley of moment of inertia \(I\) driven by torque \(TR\), \(TR = I\alpha\), so
\[ T = \frac{I}{R}\,\alpha. \]
Thus a graph of \(\alpha\) (vertical) against \(T\) (horizontal) is a straight line of slope \(s = \dfrac{R}{I}\), and the moment of inertia is \(I = \dfrac{R}{s}\).
Precautions: measure the height and time carefully, releasing the mass and starting the stopwatch together, and avoid parallax when reading the metre scale/heights; keep the thread wound in a single layer in the groove.
(b)(i) Centripetal force is the resultant force directed towards the centre of a circular path that keeps a body moving in that circle.
(b)(ii) Object dropping through \(h = 2.0\ \text{m}\): using \(v^2 = 2gh\),
\[ v = \sqrt{2 \times 10 \times 2.0} = \sqrt{40} = 6.32\ \text{m s}^{-1}. \]
