Download Lab 5 – Circular Motion and Forces

North Carolina State University PY131 Lab Manual Lab 5 – Circular Motion and Forces Lab 5 – Circular Motion and Forces INTRODUCTION Imagine the following scenario: In your hand you hold a rope at the end of which is tied a bucket with a ladybug resting at the bottom. If you swing the bucket around your head fast enough, the ladybug will experience a force sufficient to prevent her from falling. What forces come into play here? Why doesn’t she fall? Consider another scenario. You make a right-­‐hand turn while driving your car. As you turn, you feel that you are pushed against the car door. Is there a force pushing you against the door? It may seem like there is, but there isn’t. In reality, your body is trying to move in a straight line and the car door (and the car seat and anything else in the car that is touching you) turns in front of you and presses against you. The force of the door pushing against you causing you to curve is called the centripetal force. This centripetal force is directed toward the center of the circle. For an object in circular motion, at any given moment during its motion, the centripetal force on the object (and hence the centripetal acceleration) is directed toward the center of the circle. In the absence of the centripetal force, the object will not move in a circular path. Consider the example of a stone tied to the end of a string and whirled in a circle. If the string breaks, the stone will fly in a direction tangential to the circle. The centripetal force is given by the equation Fcentripetal =
mv 2
r
where v is the linear speed of the object and r is the radius of the circular path. €
An object undergoing circular motion has two types of velocity: tangential and rotational. The tangential velocity of the object at a particular instant of time is also known as the linear velocity of the object. This tangential velocity is directed along the tangent to the circle. Since the direction of the tangent changes at different points on the circle, the tangential velocity will change direction as the object moves in a circle. Recall that velocity is a vector quantity that has both magnitude and direction. Speed refers to just the B magnitude of the velocity. So an object moving at constant speed Q around a circle will have changing velocity as the direction of the A tangential velocity changes. P In a given interval of time, a point further from the center of the circle (point A in figure 1) will cover a larger distance than a point closer to the center of the circle (point P in figure 1). Therefore, the tangential 1 Figure 1 North Carolina State University PY131 Lab Manual Lab 5 – Circular Motion and Forces speed (magnitude of velocity) depends on the distance of the point from the center of the circle. The rotational speed (also known as angular speed) is defined as the number of rotations (or revolutions) per unit time. All points on a circle, regardless of distance from the center, will cover the same angular distance in a given interval of time. Therefore, the angular speed does not depend on the distance of the point from the center of the circle. For an object moving in a circle of constant radius, the average linear speed of the object is the total distance travelled divided by the time it took to travel that distance. The total distance is the circumference of the circle (the distance traveled for one revolution) times the number of revolutions made by the satellite. v average =
2πr
T
where T is the time for one rotation (also known as the period of revolution), and r is the radius of the circle. €
In this lab you will you will whirl, a rubber stopper on a string, around in a circle. The tension in the string provides the necessary centripetal force that keeps the rubber stopper in its circular path. As you proceed with this experiment, here are some questions to keep in mind. How is the average speed of the stopper affected by the radius of its circular path? How is the average speed of the stopper affected by the centripetal force? PROCEDURE CAUTION! You will be whirling heavy weights above your head. Conduct the experiment in a place with plenty of room, away from people and breakable stuff (like windows and computer monitors). Make sure your apparatus is securely built. The apparatus for this experiment is shown in Figure 2. A rubber stopper is whirled in a horizontal circle. When the speed of the stopper and the radius of its path are just right, the stopper will travel in a circle of constant radius and the anchor (see Figure 2a) will remain at rest. At this point the centripetal force on the satellite is exactly equal to the force of gravity on the anchor. 2 North Carolina State University PY131 Lab Manual Lab 5 – Circular Motion and Forces Figure 2a: Diagram of apparatus Figure 2b: Photo of apparatus 1. Assemble the apparatus. Run the string through the tube. Run the string through a stack of 5 washers. Attach the spring clip through the loop at the end of the string (see figure 3). Do not put the washers on the clip (see figure 3). 2. You may need to practice using the apparatus before your group can begin. Hold the tube above your head so that 5-­‐10 cm of the tube extends above your hand. Carefully begin to whirl the stopper around the tube in a horizontal circle above your head. Practice whirling the stopper so that the mark on the string stays even with the bottom of the tube. This may take several tries. Figure 3 Once you have become proficient at whirling the stopper so that the mark on the string stays even with the bottom of the tube, you’re ready to take data. 3. In the data table on the worksheet, record the amount of time it takes the stopper to make 20 complete revolutions around the tube (the number of revolutions should remain unchanged for the entire experiment). 4. Calculate the time for a single revolution (the period) and record this in the data table. 5. Record the radius of the circular path. 6. Record the number of washers that make up the Anchor. 7. Using the values of the radius and the period, calculate and record the velocity. 8. Repeat steps 3 through 7 four more times for four different radii of the circular path. CHECKPOINT 1: HAVE YOUR TA CHECK YOUR WORK BEFORE PROCEEDING 3 North Carolina State University PY131 Lab Manual Lab 5 – Circular Motion and Forces CIRCULAR MOTION -­‐ WORKSHEET Data Table Trial Time for 20 Period (s) revolutions (s) Radius (cm) Circumference (cm) Velocity (cm/s) # Of washers 1 2 3 4 5 CHECKPOINT 1: Based on your data, as the radius of the circle increases, what happens to the average speed of the stopper? Based on your data, as the number of washers increases, what happens to the average speed of the stopper? CHECKPOINT 2: 4