Centripetal acceleration lab report

Lab Exercise 5: Centripetal Acceleration
Follow the instructions and directions below for this lab. Disregard the outline in the manual for your LabPaq Kit.

Read this document entirely before starting your work.

Do not forget to record your measurements and partial results.

Submit a Laboratory Report through Moodle, as shown in the last section of this outline. Remember that the Laboratory Report should include the answers to the questions below.

GOALS
(1) To calculate the angular velocity of a spinning object using varying hanging and rotational masses and varying radii

(2) To calculate the theoretical centripetal force;

(3) To calculate the experimental centripetal force.

INTRODUCTION
When objects, such as a carousel, move in a uniform circular motion, they are moving at a constant speed, while their direction of velocity is changing. The word centripetal means center seeking. When acceleration of a circular moving object is directed toward the center, the acceleration is centripetal and the acceleration is called centripetal acceleration.

Newton’s first and second laws of motion state that an object moves at a constant speed in a straight line unless an external force acts upon that object and that a force causes an object’s acceleration. By following theses laws, the force on a circular moving object is called centripetal force. Centripetal force accelerates an object by changing the direction of its velocity without changing its speed.

Mathematically, centripetal acceleration is represented as:

PHY-115_Lab-5_introduction.PNG

with ac being the centripetal acceleration, v the velocity and r the radius of the circle.

The centripetal force, in turn, can be represented as:

PHY-115_Lab-5_introduction-2.PNG

with Fc being the centripetal force and m the mass of the object.

An example of centripetal acceleration is the Earth/Moon relationship. Earth and the Moon exert gravitational forces on each other and the Moon undergoes centripetal acceleration toward the center of Earth.

PROCEDURE
In this experiment, a rubber stopper is connected to a string and is rotated in a horizontal circle. The tension in the string causes the stopper to undergo centripetal acceleration.

Rotational Velocity

The period of revolution or period—the time it takes for the object to complete one revolution— is represented by T (this is similar to the notation we used in the previous laboratory with the pendulum apparatus). The speed v of the rotating object is calculated by dividing the circumference of the circle of radius r (2πr) by T. This velocity can be referred to as rotational velocity or angular velocity.

PHY-115_Lab-5_equation 3.PNG

Therefore, to determine the constant velocity of a rotating object, we need to measure the time T required to make one revolution using the following equations:

PHY-115_Lab-5.PNG

In addition to centripetal acceleration, the force of gravity acts on the rubber stopper as it is whirled along a horizontal plane. Because gravity acts perpendicular to the centripetal force, the orbital plane of the rotating mass lies below the horizontal plane at the top end of the vertical tube. Despite these factors, the data obtained from this experiment should be reasonable approximations that demonstrate the basic relationships among the variables.

Constant mass, variable radius.

In this section we will investigate the effects of changing the radius of the system on the centripetal force.

Choose an area that is free from obstructions and breakable objects. You will be swinging weights on a string and if these weights break free, they could potentially hit objects or people. Choose an area where only your assistant is present to reduce the risk of people being injured.

Wear goggles so that the rotating stopper does not hit your eyes.

Record the number of washers from your kit in Table 1. Place all of the washers into a bag to weigh their mass and record the total mass in Table 1. Find the average mass of each washer in kilograms and record it in Table 1. Also weigh the mass of the rubber stopper.

Pull out the 4.0 m of string provided in your apparatus kit.

Tie a the 4m string to a rubber stopper (the rotating mass), slide the string through a glass cylinder, and tie the string to our hanging mass. Before threading the string through the glass rod, make sure the smooth end of the glass rod is at the top nearest the rotating rubber stopper.

Thread about 30 g of washers onto the end of the string opposite from the stopper. Record this constant hanging mass. User paper clips to ensure that the washers do not fly away. If needed, open up the paper clip to secure the washers. Figure 3 shows a detail of this.

QUESTION 1

What is the actual (measured) mass of the washers?

Figures 1, 2 and 3 show the experimental setup.