# Centripetal Acceleration Lab

In this investigation, a mass was attached to a string and was swung horizontally for certain number of rotations (ten). The sole goal for this investigation was to find and verify the relationships between Centripetal Force, Frequency and Radius of circular path. In order to get relationships between the variables mentioned above, this experiment was divided into two parts. In Experiment A, the radius of the path (length of the string), along with the mass was kept constant, and the relation between centripetal force and square of frequency was determined. In Experiment B, the Centripetal force and the mass were kept constant, and the relationship between square of frequency and the Radius was determined. For Experiment A, the results showed that the relationship between the centripetal force and square frequency was linear, such that FC∝0.96f2. On the other hand, for experiment B, the results showed that the relationship between the radius and square of frequency is Inverse, such that 1r∝0.71f2. Purpose:

The purpose of this part in the investigation was to verify the relationships between frequency, centripetal force and radius of rotation for an object moving in a horizontal circular motion. Hypothesis:

Part A:

Assuming that the mass and the radius will be constant in this part of the experiment and considering the base theoretical expression FC=m4π2rf2, it can be stated that FC=kf2, where k is the combined value for all the constants in the expression. After analyzing the new equation, it can be stated that the centripetal force and square of frequency will have a linear relationship and will be directly proportional to each other. Moreover, to further classify the equation, value of constant should be found. An equation to represent constant would be k= m4π2r, after the mass and the radius is available, the value of k can be calculated using the equation mentioned. Part B:

Assuming that the centripetal force and the mass will be constant in this part of the experiment and rearranging the base theoretical expression FC=m4π2rf2, it can be stated that 1r=(m4π2FC)f2, where m4π2FC is the value for the constant. Therefore this equation can be stated as 1r=kf2. After analyzing the new equation, it can be stated that the rotational radius and the square of frequency will have a inverse relationship. Moreover, to further classify the equation, value of constant should be found. An equation to represent constant would be k= m4π2FC, after the mass and the centripetal force is available, the value of k can be calculated using the equation mentioned. Materials:

Apparatus| Uncertainty|

Newton Spring Scale| ±0.1N|

Meter Stick| ±0.1cm|

Mass Balance| ±0.01kg|

Stop Watch| ±0.1s|

Safety Goggles| -|

Fishing Line| -|

String| -|

Rubber Stopper with hole| -|

Diagram:

Procedure:

PART A: Frequency vs. Force

1. The experimental adjustment above was set up using the apparatus listed 2. The length of the string was set at 60.cm, which made up the radius of rotation 3. Then, the string was swung horizontally to practice it’s movement 4. Then the stopper was spun at a constant centripetal force of 1.0N for 10 rotations. The time period it took for 10 rotations was noted in the observation chart 5. Step 4 was repeated for centripetal force value starting at 0.5N, reaching 2.5N by increments of 0.5 6. The time interval it took for each trial was noted in the observations chart PART B: Frequency vs. Radius

1. The experimental adjustment above was set up using the apparatus listed 2. The radius of the string was set at 80cm

3. The stopper was rotated at a constant rate, so that it maintained a force of 1.0N 4. The stopper was rotated ten times, at a constant force of 1.0N 5. Step 3-4 were repeated for various radii values starting from 80cm and reducing to 30cm by increments of 10 6. The time interval it took for each trial was noted in the...

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