Centripetal Force

Purpose: To verify Newton's second law of motion for the case of uniform circular motion.

 Table of Trials and Times

The table above shows the five trails for two different masses for the bob. The radius was the same for both masses. To find the time we spun the bob around in a circle 50 times and that gave us our time. The frequency was found by dividing the revolutions (50) buy the time. The time was different for each trial. To find the velocity it is (2pi*50*radius)/time. To find acceleration, it's just velocity/time. To find force we did the (bob mass*velocity^2)/radius.
Once we did that, we found the hanging mass. To find that we hung weight from the bob. The weight was determined by where the weight leveled out the bob to the radius. After found the hanging mass we could find weight, which is just hanging mass*gravity. Then we found the difference between the weight and the force for each trial. As you can tell, for the first bob mass we have under 6% difference for each. Then for the second bob mass, we have under 6.5% difference.

This is the force diagram for the spring. The spring is what the bob is connected to. There are only two forces acting on it. The force of static friction and the force of tension. The forces are equal.

This is the diagram for the hanging weight that held the bob in place at the radius. There are two forces acting on it. The force of tension and the force of gravity. These two forces are equal.















Conclusion: I learned that the hanging weight should be the objective of the force that we found. For sources of error, we could have timed things wrong, measured things wrong, or any other possible human error. To improve we could do more trials and take the best five. When adding mass to the hanging bob, the centripetal force stays the same, but the radius the bob is at changes.

Drag Force on a Coffee Filter

Purpose: To study the relationship between air drag forces and the velocity of a falling body.

This is the prediction for the position versus time graph. Before the fall, there is a constant position because it is being held in the same place. Once it falls, the coffee filters decrease in position moving to the floor (origin). The once it hits the floor, it stays in the same place because there is nothing causing it to come back up.

These are all of our trials for the different number of coffee filters. We started with nine filters and did five trials. Then from there we took one filter away after five trials with the same number of filters. We ended with one coffee filter.

This is the position versus time graph. This is the best one out of all of our trials. We found the best fit line and our slope was -2.004. The actual would be -2.

This is the curve from out plotted points. The y-axis is the number of coffee filters, and the x-axis is the absolute values of slope averages of the five trials for each value of filters. With the power fit line, the A = k and the B = n in the drag equation we used. Drag = k|v|^n. For our value of n, we have a 2.289. The actual is supposed to be a 2. Our percent error is 14.45%.




The equation for drag moving through a fluid is:

drag = .5*density*v^2*area*drag coefficient 

This is equation is similar to ours where velocity is squared. However, in the fluid equation are is used not surface area. To compare the drag fluid equation to the normal drag equation (drag = 1/4 * Av^2) you can see many more similarities.  

Conclusion: We learned that air slows down the fall of objects. Also, the less mass there is the more the air acts upon it. Our error could be from not dropping from the exact same height each time. Not dropping it at the same height does affect the experiment. The higher we drop the coffee filter, the longer it takes to reach the ground. If we had dropped the filters from the exact same height each time, then we would have better numbers. Next time, we can make sure we drop the filters at the exact same height and even do more trials to have more data.