Unit 3 Centripetal Force

Transcription

1 Unit 3 Centripetal Force Objective Circular motion is one of the basic motions among the universe. Electrons in an atom, turning of a car, and revolution of planets all utilize centripetal force. In this experiment we use an electric motor to rotate an object and demonstrate the relations between the mass of the object, rotation radius, time period, and the centripetal force. Apparatus Centripetal force device (rotation platform, springs, weights, hanger etc.), optical timer, optical gates, horizontal level device. Side post Springs Center post Pulley1 Pulley 1 c Thread a Thread r b Indicator bracket Pulley Balance Rotating platform Mass Belt & Motor Weights Knob Fig. 1. Centripetal force device. (Equilibrium without rotating)

2 Principles When an object of mass m making circular motion with a constant speed v and the radius r on a horizontal plane, the centripetal force of this object is mv = = =..(1). r F mrω Mg (M= mass of the hanger and weights) v is the speed along tangential direction, and ω is the angular speed (ω=r v). Furthermore, v in Eq. (1) can be expressed as π r v = () T From Eq. (1) and (), we have the centripetal force as a function of T 4π mr F =..(3). T In this experiment, we vary m, F, and r in Eq. (3) and measure the periods of those circular motions under different conditions to discus and demonstrate the relations of centripetal force F with other physical quantities. Instructions I. Preparations 1. Adjust the horizontal level of the centripetal force device. Make sure that the device is horizontal in every direction.. Measure the weights of the hanger and all the weights, and put the numbers down. 3. Put 7 weights on the hanger, and tight 3 threads on the three hooks of the rotation object. Thread a and b go through pulley 1 and respectively (as shown in Fig. 1); a is fasten on the hook, and b on the spring. Thread c is fasten on the top of the side post. 4. Adjust the height of pulley 1 and the position of the side post (16 cm from the center post), making thread a and b horizontal, and c vertical. The distance of the side post from the center post is required to set as 16 cm. 5. As shown in Fig., adjust the indicator bracket on the center post making the upper edge of the indicator disk (orange and circular plate) just pass the indicator bracket. This is set as an indicator showing that thread a and b are horizontal. Q1: What are the physical meanings when the upper edge (surface) of the indicator disk (orange plate) just passes the indicator bracket except that thread a and b are horizontal.

3 Fig.. Fig. 3. (Equilibrium without rotating)

4 Balanced condtition. Unbalanced condition. II. Vary the mass of the object m under static rotation radius r and centripetal force F 1. Put 7 weights on the hanger, and adjust the position of the post, making thread c aim at the reference line (vertical line on the post). Record the position of the side post as the rotation radius r. And the weights on the hanger provide the centripetal force F.. Adjust the indicator bracket on the center post, making the upper edge of the indicator disk just pass the indicator bracket. 3. Remove the hanger, and install the optical gates to let pulley 1 pass this optical gate when making rotation (as shown in Fig. 3). Increase the voltage of the power supply smoothly until the indicator disk return to the initial position (upper edge of the indicator disk pass the indicator bracket). Select function 5 of the optical timer. Q: What is the centripetal force under such condition? 4. Record the time period of 5 cycles and get the time period T. Repeat 5 times, and calculate the average value and standard deviation. 5. Unfasten a slice from the object, and measure the new mass m of the object. Repeat step, 3 and 4 for time period T. 6. Unfasten another slice, and measure another new mass m. Repeat step, 3, and 4 for T. 7. Do the plot of m versus T.

5 Q3: If the indicator disk cannot match the indicator bracket steadily but oscillate through the indicator bracket, what do you think the reasons are? Can you overcome this problem? III. Vary the rotation radius r under static F and m 1. Put 7 weights on the hanger. Fasten 3 slices and measure the mass of the object. Adjust the position of the side post making thread c aim at the reference line (vertical line) on the side post. Measure the rotation radius (position of the side post).. Adjust the indicator bracket on the center post and make the indicator disk aim at the indicator bracket (as described previously). 3. Remove the hanger, and place the optical gate across pulley 1. Then smoothly increase the voltage to start the rotation until indicator disk is back to the initial position. Select function 5 of the optical timer. 4. Record the time period of 5 rounds and get the period of each cycle. Repeat 5 times and get the average value and standard deviation. 5. Change the rotation radius: reduce 1 cm each time, and be sure to re-adjust thread a and b to horizontal level, and c to vertical level. The easiest way is to wind thread b on the hook which it is fastened to reduce its length. 6. Repeat step, 3, and 4 and get the new time period T. 7. Change the radius again (you are required to get T of 5 different radius). 8. Do the plot of r versus T. IV. Vary centripetal force F under static r and m. 1. Put 7 weights on the hanger, and set the radius as 1 cm. Fasten 3 slices of the object as the rotation object. Get the average period T and the standard deviation.. Remove a weight from the hanger to change the centripetal force. Re-adjust threads a, b, and c (to the horizontal and vertical level). Start the rotation and get the period (in the same way as mentioned previously). 3. Repeat step until 5 weights are removed (you are required to set 5 different F). 4. Do the plot of F versus T. Q4: Can you derive Eq. (3) from II, III, and IV?

6 Remarks 1. Make sure that the power supply is at C.V. mode and then increase the voltage. Utilize FINE knob for fine tune, and do not over increase the voltage or you may damage the rotation device. Start the measurement after the rotation is stable.. Wipe off the dust of the device and check whether there s dust on the bearing. 3. The object may shift when you change the centripetal force. Remember to adjust thread b to make the object back to the required position, or otherwise the rotation radius r may not be the position of the post. 4. All the quantities are required to be in the form of error propagation. X ± σ, and be careful of the X