TEST OF PRACTICAL KNOWLEDGE QUESTION
You are provided with a stopwatch, a meter rule, a split cork, retort stand and clamp, a pendulum bob, a piece of thread, and other necessary apparatus.
i. Place the retort stand on a laboratory stool. Clamp the split cork.
ii. Suspend the pendulum bob from the split cork such that the point of support P of the bob is at height H = 100cm above the floor Q. The bob should not touch the floor and H should be kept constant throughout the experiment.
iii. Adjust the length of the thread such that the center A of the bob is at a height y= AQ= 20cm from the floor.
iv. Displace the bob such that it oscillates in a horizontal plane.
v. Take the time t for 20 complete oscillations.
vi. Determine the period T of oscillation and evaluate T
vii. Repeat the procedure for four other values of y = 30cm, 40cm, 50cm, and 60cm. In each case, determine T and T.
viii. Tabulate the results.
ix. Plot a graph of T on the vertical axis and y on the horizontal axis, starting both axes from the origin (0,0).
x. Determine the slope, s, of the graph and the intercept c on the vertical axis.
xi. If in this experiment SR= c, calculate R.
x. State two precautions taken to ensure accurate results.
(b) i. The bob of a simple pendulum is displaced a small distance from the equilibrium position and then released to perform simple harmonic motion Identify where its:
(\(\propto\)) kinetic energy is maximum
(\(\beta\)) acceleration is maximum
ii. An object of weight 120N vibrates with a period of 4.0s when hung from a spring. Calculate the force per unit length of the spring. [g= 10ms\(^{-2}\), \(\pi\)=3.142]
For the first part of the question:
- To conduct the experiment, you will first need to place the retort stand on a laboratory stool and clamp the split cork to the stand.
- Next, you will need to suspend the pendulum bob from the split cork using a piece of thread. The point of support, P, should be at a height of 100 cm above the floor, Q, and the center of the bob, A, should be at a height of 20 cm from the floor.
- After suspending the pendulum, you will need to displace the bob slightly so that it oscillates in a horizontal plane.
- Using the stopwatch, you will need to measure the time it takes for 20 complete oscillations and record this value as t.
- To determine the period of oscillation, T, you can use the formula: T = t/20.
- Repeat this procedure for four other values of y = 30 cm, 40 cm, 50 cm, and 60 cm, and determine T and T for each case.
- Tabulate the results in a table.
- Plot a graph of T on the vertical axis and y on the horizontal axis, starting both axes from the origin (0,0).
- Determine the slope, s, of the graph and the intercept c on the vertical axis.
- If in this experiment SR = c, you can calculate R by using the formula: R = SR/s.
- To ensure accurate results, you should take two precautions: first, make sure that the length of the thread is kept constant throughout the experiment and second, ensure that the height H is kept constant as well.
For the second part of the question:
- In a simple pendulum undergoing simple harmonic motion, the kinetic energy is maximum at the extremes of its motion, where the velocity is maximum. The acceleration is maximum at the equilibrium position, where it is equal to the maximum restoring force.
- The period of a simple pendulum is given by the formula T = 2π√(m/k), where m is the mass of the object and k is the spring constant. In this case, the period is 4.0 s and the weight of the object is 120 N. Using the formula, we can calculate the spring constant as k = (4π^2)m/T^2 = (4π^2)(120 N)/(4.0 s)^2 = 180 N/m. The force per unit length of the spring is equal to the spring constant, so in this case it is equal to 180 N/m.