Lab5 Circular Motion FORMAL

PHY111: Uniform Circular Motion (UCM) Objectives :  Experiment 1: investigate how the magnitude of radius affects the time period of an object undergoing circular motion.  Skill: Linearize a non-linear data set and utilize the constant slope to experimentally determine a constant. Introduction : An object experiencing uniform circular motion (UCM) will be influenced by a net force that causes this motion and spins in a circle with constant radius. Any object in UCM will experience a net force and, according to N2L, will therefore experience an acceleration. In UCM, this acceleration is called the centripetal acceleration. Since the net force and acceleration are directly proportional to one another, they will be directed towards the center of the circle. Specific forces cause UCM and these forces are nicknamed centripetal forces. Be mindful to always articulate what specific force is causing the object to undergo UCM. Pre-Lab Questions: (Be sure to write using complete sentences) 1) In this lab, you will be rotating a mass on one side of a string that is balanced by a second mass on the other end of the string (Figure 6). A free-body diagram will show that the centripetal force on the rotating mass m 1 , is provided by the weight of the hanging mass m 2 . Since those forces must be equal, we can write the equation: m 2 g = m 1 v 2 /r, where v is the velocity of m 1 , and r is the radius of its circular path. Since the magnitude of the velocity is the average distance divided by the average time, we can write the velocity = the circumference / the period, or v = 2π r /T = r  , where the period T is the time to complete one revolution. Assume m 2 = 4m 1 . Write an expression for the period in terms of r and g . You should find the mass terms will drop out. a) Below are the steps to obtain the period T in terms of r and g, the key to solving is replacing v with the formula for radial velocity, r  , i) m 2 g = m 1 v 2 /r ii) m 2 g = m 1 (2π r /T) 2 /r iii) r*m 2 g = m 1 4π 2 r 2 /T 2 iv) T 2 = (m 1 4π 2 r 2 )/( r*m 2 g) v) T =  (m 1 4π 2 r)/( m 2 g) vi) T = π*  (m 1 4 r)/( m 2 g) b) If m 2 = 4m 1 i) T = π*  (m 1 4 r)/(4 m 1 g) ii) T = π*  (r /g) 2) The around the world yo-yo trick is completed when you twirl a yo-yo in a vertical circle. If the yo-yo was in uniform circular motion, compare the force of tension at the top of the circle to the force of tension at the bottom of the circle. Include a free-body diagram in your answer. a) The force of the tension in the rope is less when at the top of the circle than when it’s at the bottom of the circle. Since the force of gravity is in the same direction as the tension force when it’s at the top, the centripetal net force is equal to the two forces added together. When the yo-yo is at the bottom of Figure 6: Rotating Mass 1

it’s revolution the tension force is pointed up but the gravitational force is pointed down so the centripetal net force is the difference between the two. 3) The wheel of fortune is 2.6 meters in diameter. A contestant gives the wheel an initial velocity of 2 m/s. Calculate the centripetal acceleration and force that an 8 kg mass would have. a) D = 2.6 m, v = 2 m/s, m = 8kg b) Centripetal acceleration: i) a = v 2 /r = 4/1.3 = 3.07692 ii) a = 3.08 m/s 2 c) Centripetal force: i) F c = m*a = 8*(3.07692) = 24.6154 ii) F c = 24.6154 N EXPERIMENT 1: Balancing Centripetal Force Procedure 1. Measure out and cut one meter of fishing line. 2. Tie a single metal washer around one end, and string the other end through the tube. Tie four washers at the other end in a group (Figure 6). 3. Measure 0.25 m from the single washer and use a permanent mark to mark this point on the line. 4. Hold the tube vertically at arm’s length to your side so that the washer near the mark is hanging from the top. 5. Hold a stopwatch in your other hand or get a willing participant to help you make time measurements. 6. Begin swinging the tube so that the top washer rotates in a circle. Increasing the speed of rotation (careful, not too fast!) should change the radius of rotation.

linear trendline equation to your graph and display the second plot below. The slope of the linear data is equal to pi 2 /g. Use your experimental slope value to determine an experimental value for gravity and use a percent difference to compare it to the accepted value of 9.81 m/s 2 . 4. What can you say about the centripetal force on the rotating mass throughout the experiment? Did it change with the changing radius too, or was it held constant? Explain your reasoning. 5. Refer to the picture in Figure 3 (next page). Before the apparatus begins to spin the wires connecting the swings to the top of the structure will be completely vertical. Once the apparatus begins to spin the swings move outward radially, but also upwards vertically. Hypothesize where the force causing this vertical acceleration comes from. Be sure to review the requirements for a formal lab report and include all the appropriate sections to receive full credit! Always cite at least one credible source 