cos0 = m M The horizontal component of the force of tension, Mg sin 0 is not balanced; it is the centripetal force that keeps the small mass orbiting: 411 mr Mg sin0 = F = From the triangles formed in the figure above: r = L sin 0. Replacing this value of r in the last equation, we have: 411 ml sin 0 Mg sine = 72 Dividing both sides by sin 0: 41I'mL Mg = T2 And rewriting the equation in terms of T? T2 = 41I'mL Mg This last equation predicts three things: . T' is directly proportional to L if m and M are constant. . T' is directly proportional to m if L and M are constant. . T' is inversely proportional to M if m and L are constant. Please make sure you have followed the previous analysis. In your lab work, you are going to prove that these predictions can be verified by analysing the following data. The measurements were made as shown in Figure 2.1 (circular motion). I was measured with a stop watch, L with a meter stick, and M and m with a scale and standard masses. Data: Three experiments were conducted. Mass m was allowed to turn 10 times in order to obtain more accurate values. You will have to divide each time by 10 in order to obtain the time for one period of rotation.Data analysis: 1. Graph: O T - m O T -L O T - I M 2. Write the equations in each case for the best line passing through the plotted points. 3. Compare the actual equation of each graph with the theoretical equation. 4. Find the percent errors obtained. Comment on the value of the error. 5. The friction of the string is a definite source of error. List several ways of reducing this error or describe alternate techniques that would reduce friction. 6. What is the effect of friction on the graphs? 7. Write a conclusion in which you explain what the investigation has proven.Experiment 1: Varying m . M and L constant: M =0.200 kg L = 0.400 m Measuring 10 T m (kg) 0.050 0.075 0.100 0.130 0.150 10 T (S) 6.5 7.8 8.8 10.2 11.0 Experiment 2: Varying L . M and m constant: M=0.100 kg m = 0.050 kg . Measuring 10 T Experiment 3: L (m) 0.200 0.400 0.600 0.800 1.00 10 T (s) 6.2 9.0 11.0 13.0 14.0 Varying M . m and L constant: m = 0.050 kg L = 0.80 m . Measuring 10 T M (kg) 0.100 0.200 0.300 0.400 0.500 10 T (s) 13.0 9.0 7.3 6.3 5.7Section B2 INVESTIGATION-CIRCULAR MOTION Before you begin this investigation, we recommend that you refer to the Open Learning Faculty Member Guidelines for Investigations in the Introduction section of this Study Guide to verify what is needed to complete your lab report and to determine the basis on which it will be evaluated. Most of the information applies here, particularly the way in which your work will be evaluated. It is well worth spending a few minutes looking back before proceeding. Materials Required: . A 15 cm or 30 cm ruler graduated in millimetres . A well-sharpened pencil . Graph paper (4 sheets) glass tube m M Figure 2.1: Circular motion In Figure 2.1, a rotating mass m is connected to a larger hanging mass M by a thread going through a glass tube. The glass tube is held by hand and made to rotate in order for mass m to swirl around it: If the speed of mass m is: . Too small: Mass M will slide down toward the ground. . Too large: Mass M will move up and hit the glass tube. Mg represents the force of tension in the string. It is the force exerted by each end of the string on each of the masses. The vertical component of this force, Mg cos 0, must be equal and opposite to balance the force of gravity on the small mass: Mg cos0 = mg, from where