Centripetal Force
Purpose: To verify Newton's second law of motion for the case of uniform circular motion.
Equipment: Centripetal force apparatus, metric scale, vernier caliper, stop watch, slotted weight set, weight hanger, & a triple beam balance.
In this lab we will look at the centripetal force necessary to cause the mass to follow its circular path. To determine this we will have to use Newton's second law.
F = mv^2 / r Acceleration a is given by; a = V^2 / r
Procedure: We began by setting up our Centripetal force apparatus. We hanged the mass from the horizontal crossarm so that the mass hanged freely over the indicator post. Once the mass was aligned with the indicator post, we took a spring and connected the mass to the vertical post connected to the horizontal crossarm. Then we began to practice rotating the assembly to align the bottom of the hanging mass with the indicater post. We were now ready to start our experiment.
The measurement from the indicator post to the vertical post of the apparatus was taken to be used as our radius for future calculations. We placed a white sheet of paper behind the apparatus to be used as background in the intent of a precise alignment. We began the rotation of the assemby, when the velocity of the mass was as constant as possible we hit the go on our stop watch. To insure accuracy we distributed duties throughout our team. One turned the assembly, another held the white paper, somebody else was incharge of the stop watch, while 3 of us keept count. 
Our measurement consisted of 50 revolutions. Using the same mass and radius we measured the time for three different trials. All data was recorded to later be put into an excel table. When we were done with our trials, we took our average time obtaineed and calculated the velocity of the mass.
V = T/ 2pi (r)
Then we used the velocity to calculate the centripetal force exerted on the mass. After our findings we went ahead and took a different path to finding the centripetal force. With the spring attached to one side of the mass we attached a string to the other side and hung wight until it was once again positioned over the post indicator. It turns out that the spring is being stretched by the same amount of force as when the apparatus was rotating. 
When we compare the centripetal force obtained by the spring experiment to the one from the hanging weight experiment we see that there is slight diffrence. Well, if we take into consideration all the possible places where there is room for error we can account for this diffrence.
Places where there
could be room for Error:
The measurment from the indicator post to the vertical post of the apparatus for our radius.
When twisting the apparatus tring to get a perfect alignment of the mass to the pole.
The reaction time from when the counter said "go" to start the stop watch and "stop" to end it.
Last but not least we added 100g to the mass and repeated both experiments.
Conclusion:
Our findings were almost the same exept that with the bigger mass we had a smaller acceleration. To be more precise a smaller velocity
This makes sence because
Fcentripetal = M v^2/r and acceleration = v^2/r
so if our Forces & radius stay the same but one of our masses increase, the velocity of that mass has to be smaller to be equivalent to the other Fcentripetal with the smaller mass. These experiments were both interesting and helpful to the understanding of the concept of centripetal force. We know that it is center seeking force that experiences change in velocity with the change in mass when radius stays the same. But when the radius and mass stay the same we can see by the relationship between Fcentripetal and acceleration that Fc & V are proportional to each other. Meaning change in one will cause change in the other. For example, if velocity doubles, it would take 4 times the amount of force to keep the object in the same circular path. In these experiment it seems like there were a lot of room for source of error. One of the main ones was when we tried to keep the apparatus moving at a constant speed while passing throught he same point. If there was a spinning device that could be added to the apparatus that would regulate the speed it would probably help with the source of error.
Places where there
could be room for Error:
The measurment from the indicator post to the vertical post of the apparatus for our radius.
When twisting the apparatus tring to get a perfect alignment of the mass to the pole.
The reaction time from when the counter said "go" to start the stop watch and "stop" to end it.
Last but not least we added 100g to the mass and repeated both experiments.
Conclusion:
Our findings were almost the same exept that with the bigger mass we had a smaller acceleration. To be more precise a smaller velocity
This makes sence because
Fcentripetal = M v^2/r and acceleration = v^2/r
so if our Forces & radius stay the same but one of our masses increase, the velocity of that mass has to be smaller to be equivalent to the other Fcentripetal with the smaller mass. These experiments were both interesting and helpful to the understanding of the concept of centripetal force. We know that it is center seeking force that experiences change in velocity with the change in mass when radius stays the same. But when the radius and mass stay the same we can see by the relationship between Fcentripetal and acceleration that Fc & V are proportional to each other. Meaning change in one will cause change in the other. For example, if velocity doubles, it would take 4 times the amount of force to keep the object in the same circular path. In these experiment it seems like there were a lot of room for source of error. One of the main ones was when we tried to keep the apparatus moving at a constant speed while passing throught he same point. If there was a spinning device that could be added to the apparatus that would regulate the speed it would probably help with the source of error.
Where you buy the Centripetal force apparatus. I need two of them. Thx.
ReplyDeleteacordobautp@gmail.com