CIRCULAR MOTION OBJECT

Transcription

1 6 M4 M4. CIRCULAR MOTION OBJECT The purpose of this experiment is to study the motion of an object that is following a circular trajectory. THEORY References: Sections 7. and 7.4, College Physics, Serway and Vuille v Acceleration is defined as the time rate of change of velocity: a = where a is the acceleration t (a vector), v is the change in velocity, and t is the corresponding time interval. Since velocity is a vector quantity, the change in velocity can arise from a change in the direction of v, a change in its magnitude, or both. The direction of the acceleration is the same as that of the change in velocity. EXPERIMENT Equipment: protractor, ruler, parallel rulers, spark table, spark timer, puck, air supply:

2 7 M4. Figure The spark timer produces High Voltage electrical pulses. Do not touch the spark table, puck, or wire when the spark timer is in operation. Follow the lab instructor s instructions. The apparatus, shown in the photograph and Figure, consists of an aluminum plate over which a sheet of sensitized carbon paper is placed with a sheet of white paper above it. A metal puck which can be supported on an air cushion in an almost frictionless state is anchored with a piece of wire to the centre of the plate. A spark timer, connected between the plate and the centre of the puck, delivers a pulse at regular intervals. The spark jumps from a pin located in the centre of the puck to the plate and in so-doing deposits a dot of carbon onto the bottom surface of the white paper, thus recording the position of the puck as a function of time. The spark timer frequency is 0 Hz ± %, i.e. there are 0 dots/second, so the time between each successive dot is 0.00 s. Procedure:. Level the apparatus. Without using the spark timer, turn on the air and practise projecting the puck into a smooth circular trajectory. The puck should take approximately seconds for one revolution.. Turn on the air, project the puck into a smooth circular trajectory, and make a spark trace of its path. Avoid overlapping the trace. Before removing the paper, mark the approximate start point of the spark trace and the direction of motion of the puck. If an appropriate puck speed was used, successive dots on the trace should be spaced at ~6 to ~8 cm intervals. To perform the analysis discussed below, your trace must have at least 7 dots (numbered from 0 to 6), and should not have more than dots. Checkpoint ask the TA to review your work for items and. ANALYSIS 3. Measure the radius r of the circular trajectory. Consider the portion of a typical spark trace shown in Figure.

3 8 M4.3 s (arc 0-) v v 3 v (translated) s 3 (arc -4) 3 4 v 3 0 v 3 v v Figure Recall that the direction of the instantaneous velocity at any location is tangent to the trajectory. The magnitude of the instantaneous velocity at a location can be approximated by determining the average speed over a small time interval around the location. Recall the equation for converting angles in degrees into angles in radians: 360 and the equation for arclength (obtained from the definition of radian angle measure): s = r rad () For example, the magnitude of the velocity at point is given by rad rad o o () s (3) t where s is the arclength travelled during the time interval t (= 0.00 s). Note that s = r where r is the radius of the trajectory and is the angle through which the radius sweeps as the object moves from point 0 to point. 4. Use a protractor to measure the angles, 3, 7, 9, 3, and Calculate the arclengths for points 0-, -4, 6-8, 8-0, -4, and Calculate the magnitudes of the velocities at points, 3, 7, 9, 3, and 5. Checkpoint ask the TA to review your work for items 3 through 6.

4 9 M Choose an appropriate scale and draw the velocity vectors at points, 3, 7, 9, 3, and 5 on the spark trace. (Note that if the speed is constant, then the tangent to the circle at point will be parallel to the chord between ponts 0 and. This may help with ensuring that the velocity vectors are drawn in the correct directions. Alternatively, use a straightedge and large triangle to construct the tangents.) Checkpoint 3 ask the TA to review your work for item 7. The average acceleration, a, over the time interval t (= 0.00 s) is defined as v 3 v3 v a (4) t t where v 3 v is the vector that results from the vector subtraction of vectors v 3 and v (see next paragraph). 8. Use the parallel rulers to construct the resultant of the vector subtraction v 3 v. Use the parallel rulers to translate the resultant so that it acts at point. Note that from equation (4) the direction of this resultant is also the direction of the acceleration a. Measure the length of the resultant vector and, using your velocity-to-length scale and equation (4), calculate the magnitude of the acceleration a. 9. Using the graphical vector subtraction method discussed above, also determine the accelerations a 8 and a 4. Calculate the average and average deviation (see p. xvi of the Introduction) of your acceleration values. Checkpoint 4 ask the TA to review your work for items 8 and 9. In the text it is shown that the magnitude of the acceleration of an object moving in a circular path of radius r with constant speed υ is a c (5) r CONCLUSION 0. In what direction do the acceleration vectors point?. Can anything be concluded regarding the magnitudes of the acceleration vectors?. Is there a force acting on the puck while it is in circular motion, and if so, what is the origin of this force? 3. How does the average of your acceleration magnitudes compare with the value calculated using equation (5)? 4. In your own words, describe what you have determined, from this experiment, regarding the motion of an object that is following a circular trajectory. SOURCES OF ERROR 5. In addition to discussing any factors that likely affected the experiment, answer the following question(s): was the puck moving with constant speed and, if not, what factors could have affected its speed? Checkpoint 5 ask the TA to join your discussion of items 0 through 5.

5 0 M4 CIRCULAR MOTION DATA & RESULTS Frequency and Period of timer: f = 0.0 Hz ± % ; T = 0.00 s ± % Radius of circular trajectory: r = ± cm Points on spark trace Angle (± ) Angle (± rad) (eq n ()) Arclength s (cm) (eq n ()) Velocity, υ (cm/s) (eq n (3)) vector subtraction of velocities (cm/s) Average Acceleration (cm/s ) (eq n (4)) 0- ± -4 ± 6-8 ± 8-0 ± -4 ± 4-6 ± Average Ave. Dev. (= error in avg.)