Your challenge for this laboratory period will be to design and execute an experiment that will demonstrate that the net force exerted on a mass moving in a circular path is the same as the force necessary to extend the spring. You will be expected to pay particular attention to the problems of accuracy and precision. The following information is presented to give you some guidance, on possible alternatives, but part of your grade will be based on your experimental design.

According to Newton's Second Law, for an object moving in a circular path, the acceleration is given the equation:

when v is the linear speed of the object and R is the radius of the circle in which the object is moving. The centripetal force can be expressed by:

or if the velocity is expressed in terms of radians:

Also, if the velocity is expressed in terms of the number of revolutions per second (N), the centripetal force can also be expressed in the following manner:

From Hooke’s Law, F=kx, when F is the force needed to extend a spring through a distance x.

The apparatus consists of an electric motor which drives a "driving disc". A friction disc contacts the driving disc and rotates the centripetal force apparatus. As the apparatus rotates, the inertia of the mass moves it away from the center. At a measured distance from the center of rotation, the mass contacts a pivoted pointer. When the pointer is aligned with the small screw, the system is in equilibrium. Force can be added to the spring of the removed apparatus to extend the spring to the distance of equilibrium when the apparatus is in rotation. Then the calculated centripetal force can be compared with the force necessary to extend the spring.

Procedure: The Centripetal force apparatus must be configured so that it will rotate on a vertical axis. Adjust the threaded collar holding the spring so that there is minimum tension on the spring. Set the friction disc so that it is near the center of the driving disc. Start the motor. Adjust the speed control device until the pointer is just opposite the index screw. The speed control should be adjusted so that there is as little oscillation as possible about the point. When the apparatus has been adjusted, simultaneously start the counter & the timer. Observe & record 5 one-minute intervals. List these in a table. Stop the motor, remove the apparatus, & determine the gravitational force necessary to extend the spring. Measure the extension of the spring. Record F (the gravitational force) & R. Reassemble the apparatus. Change the tension in the spring & repeat the observations & recording.

From the number of revolutions & the time, determine the frequency (N) in revolutions per second. From your values of m, R, & N, calculate Fc. From your measurements for gravitational force, compare Fc & Fg & calculate the percent difference. As part of your write-up, include the answers to the following questions:

a) Which would be more serious, a 1% error in observing the time or a 1% error in measuring the radius? Why?

b) Could a horizontal axis of rotation, rather than a vertical axis be used? Explain why.

c)What was the angular velocity in rad/sec of the rotating body in each case?

d) How is the centripetal force on the rotating body affected by each of the following

i) doubling the radius, keeping the linear velocity constant?

ii) doubling the radius, keeping the angular velocity constant?