HOUSTON COMMUNITY COLLEGE SYSTEMS SOUTHWEST COLLEGE COLLEGE PHYSICS I – PHYS 1401 Uniform Circular Motion Professor: David Cantu PRE LAB QUESTIONS 1) What is the difference between centrifugal and centripetal force? 2) A ball on a string is swung in a vertical circle. The string happens to break when it is parallel to the ground and the ball is moving up. What trajectory does the ball follow? 3) If an airplane propeller of radius 5 ft rotates at 2000 rev/min. What is the speed of a point at the tip of the propeller? 4) The period of rotation of the earth about its axis is 24 h. What should be its new rotational velocity for an object at the equator to be weightless, meaning the normal force on it is zero? 5) Correct this statement: “ the racing car rounds the turn at a constant velocity of 50 miles/hr “ OBJECTIVE The purpose of this experiment is to calculate the centripetal force needed to keep an object in uniform circular path. We accomplish that in two ways; by finding the weight needed to stretch a rotating mass until it reaches a sensitive probe and also by allowing this mass to rotate at a speed necessary to make it reach the same probe. MATERIALS Centripetal force apparatus Slotted weights Vernier Caliper Weight hanger INTRODUCTION When a particle of mass m moves in a uniform circular motion of radius r, its velocity v changes direction and the centripetal force Fc needed for the object to stay around this path is directed toward the center of curvature of the path and has magnitude given by Fc = m r ω2 where ω is the angular velocity of the object in radian/sec. It is measured by measuring f which is the number of revolutions per second the apparatus rotates through where ω = 2πf. By substitution we get the theoretical value for centripetal force: Fc = 4 π2 f2 m r (1) The apparatus, see figure ( 2 ), consists of an electric motor that rotates the centripetal force apparatus. As the apparatus rotates, the inertia of the mass m moves it away from the center. At a measured distance from the center of rotation, the mass contacts a pivoted pointer P. When the pointer is aligned with the small screw I, the system is in equilibrium. Weights of mass M can be hung from the spring of the removed apparatus to extend the spring to the distance of equilibrium. This gives us another way to calculate the centripetal force given by: Fc = (m + M)g (2) Then the calculated centripetal force can be compared with the force necessary to extend the spring. EXPERIMENTAL PROCEDURES 1) Clamp the centripetal force apparatus to the chuck of the rotator. Make sure everything is tight enough Slowly increase the speed of rotation until the pointer is deflected up to the index mark. Keep the rotor maintained at this speed at which the pointer is against the index. Now measure the speed of rotation by simultaneously starting the revolution counter and timing a counted number of turns. Let the timing be at least 30 sec. Take a total of four sets of measurements and record them. 2) Remove the centripetal force apparatus and suspend it from a secure support. Determine the total amount of weight that should be hung from the rotating mass to cause the pointer to be deflected to the index mark. Make sure to include the mass of the rotating object. 3) Using a vernier caliper, measure the radius of the rotational motion; it is the distance from the point above the index to the line engraved on the rotating mass. REPORT FORM Part I Centripetal force from the rotational motion Radius of circle Measurement 1 2 3 4 _______ Time, s Rotating mass m ________ Number of revolution Centripetal force from ( 1 ) _____________ Part II Centripetal force from the total weight Value of M ___________ Total mass hung from spring __________ Centripetal force from ( 2 ) ____________ Percent difference between the two values of force _____________ f, rev/s Average CALCULATION 1) Compute the number of revolution per second from procedure 1 and record it. 2) Using the average value for f, compute the theoretical value for the centripetal force from equation ( 1 ) and record it. 3) Compute the value for the centripetal force using equation ( 2 ) and record it. 4) Compute the percent difference between the two values for the centripetal force. POST LAB QUESTIONS 1) How is the centripetal force on the rotating body affected by doubling the linear velocity and keeping the radius constant? 2) Explain why the spring stretches while the system is rotating? 3) Calculate the linear velocity of the rotating mass and its period of motion. 4) Discuss the sources of the errors in this experiment? 5) What is your conclusion from this experiment.