Lab 4: Uniform Circular Motion, Study notes of Physics

Uniform circular motion occurs when an object goes around in a circle at constant speed. Note that although the object's velocity is constant in magnitude, it ...

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Lab 4: Uniform Circular Motion
SP211: Physics I
Fall 2018
Dr. M.E. Jamer
1 Introduction
Uniform circular motion occurs when an object go es around in a circle at constant speed. Note
that although the object’s velocity is constant in magnitude, it is not constant in direction, and thus the object
is accelerating even though its speed is constant! Since the object is accelerating, there must be a net force on
it. One of our goals for this laboratory is to remind ourselves that the force on and acceleration of an object
traveling in a circle with a constant speed are inward, i.e., toward the center of the circle. We will determine
the magnitude of the inward (centripetal) acceleration experimentally and then multiply it by the mass to cal-
culate the magnitude of the required centripetal force. We will then attempt to show that, for this experiment,
the force responsible for centripetal acceleration is provided by a spring. The tension in the spring is equal to
Fspring =mac. For the rotating machine we will use in this exercise, we can measure the mass of the plumb bob
and the orbital radius directly. We can measure the period of revolution by using a stopwatch to measure the
time required for 10 rotations, and then we can calculate a measured value for the tangential speed, velocity, and
the centripetal acceleration (ac). We can measure the tension in the spring by measuring the weight required to
stretch the spring to the same degree it was stretched while the system was rotating.
2 Procedure
2.1 Measure the Bob Mass
1. Measure the mass of bob using an electronic balance.
Mass =
1
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Lab 4: Uniform Circular Motion

SP211: Physics I

Fall 2018

Dr. M.E. Jamer

1 Introduction

Uniform circular motion occurs when an object goes around in a circle at constant speed. Note that although the object’s velocity is constant in magnitude, it is not constant in direction, and thus the object is accelerating even though its speed is constant! Since the object is accelerating, there must be a net force on it. One of our goals for this laboratory is to remind ourselves that the force on and acceleration of an object traveling in a circle with a constant speed are inward, i.e., toward the center of the circle. We will determine the magnitude of the inward (centripetal) acceleration experimentally and then multiply it by the mass to cal- culate the magnitude of the required centripetal force. We will then attempt to show that, for this experiment, the force responsible for centripetal acceleration is provided by a spring. The tension in the spring is equal to Fspring = mac. For the rotating machine we will use in this exercise, we can measure the mass of the plumb bob and the orbital radius directly. We can measure the period of revolution by using a stopwatch to measure the time required for 10 rotations, and then we can calculate a measured value for the tangential speed, velocity, and the centripetal acceleration (ac). We can measure the tension in the spring by measuring the weight required to stretch the spring to the same degree it was stretched while the system was rotating.

2 Procedure

2.1 Measure the Bob Mass

  1. Measure the mass of bob using an electronic balance. Mass =

2.2 Calibrate the Spring

If the spring is an ”ideal” spring, the force it can apply is equal to Fspring = −k∆x, where k is the spring constant, and ∆x is the distance the spring stretches or compressed from it’s relaxed, equilibrium length.

  1. Set up the apparatus in the figure but WITHOUT THE SPRING. Remove the spring and the mass hook, and make it so that the bob is hanging straight down over the pointer. Line up the vertical pointer under the tip of the bob as a reference for your measurement. Measure the distance from the pointer to the center of the spindle as accurately as you can. This is the equilibrium distance. This is x 0.
  2. Replace the the mass holder hook, making sure the string goes over the pulley smoothly. Hand a slotted mass on the hook. Hang enough mass to stretch the spring about 20 %. Record the weight of the hanging mass (masses added and the mass holder hook). This weight is equal to the tension in the string that goes over the pulley, and this is equal to Fspring. (So, Fspring = −k∆x = mg). For the non-rotating apparatus, the bob hangs straight down when the hanging mass’ weight is equal to the tension in the spring, so by measuring the weight required to keep the mass vertical at various lengths for the stretched spring, you will be able to calibrate the spring.

Data Table Mass Weight (m*g)

Spring Length (x)

x-x 0

Find the spring constant by taking the slope of the line after plotting in Excel Weight versus x-x 0.

3 Starting your experiment

Force = MASS * g = Find the mass it takes on the pulley to have the bob perfectly centered over the pointer. Record this mass. Mass = Force = MASS * g =

4 Measuring Centripetal Force

  1. Detach the weights and hook. Make sure the cross-arm is locked in position. Adjust the position of the counterweight if needed to have the bob rotate smoothly.
  2. Rotated the apparatus and let the spring provide the centripetal force. The spring will pull the bob inward. Practice rotating the system until you can achieve a smooth motion that will cause the bob to pass directly over the pointer as the apparatus rotates. By doing this you have found a speed such that the inward pull of the stretched spring provides exatly enough Centripetal Force to keep the bob moving in a circle at a constant radius, x 0 at a constant speed.
  3. Note that the only Forces on the bob are the upward force of the string, which balances the downward force of the weight of the bob, and the inward force of the stretched spring. The forces are therefore ”unbalanced”. There is an inward force on the Bob applied by the spring. The bob seems to ”want” to go outward simply because its own inertia is trying to keep it moving in a straight line, and an inward force is required to force it to move in a circle. The necessary force is called the Centripetal Force and the spring is what is providing the Centripetal Force in this case.
  4. Spin the bob at a roughly constant speed so that the point of the bob passes over the Pointer at the distance you have chosen. Use your stopwatch to measure the average period of revolution, T. To do this accurately, measure the time it takes to complete 10 turns (if possible), then divide the total time by the number of turns. Repeat this process four more times until you get nearly repeatable results. Have one lab partner checking to make sure that the point of the bob is hanging over the vertical marker through