Centripetal Force

In this lab we are verifying Newton's Second law of Motion for the case of uniform circular motion. To better understand this, we are going to try and show that the force of circular motion to cause a spring to stretch is equal to the force of a mass hanging to stretch the spring the same amount.

The materials needed for this lab are:

• Centripetal force apparatus
• Metric scale
• Verneir Caliper
• Stop Watch
• Slotted weight set
• Weight hanger
• Triple beam balance

INTRODUCTION
Before starting this lab we need to understand a couple concepts first. The centripetal force apparatus rotates a known mass in a circular path with a known radius. When we time the motion for a number of revolutions we can find the distance traveled and calculate the velocity. We can use Newton's Second Law to determine the velocity with the equation:

F = (mv^2)/r

 m: mass of the object

v: velocity

r: radius

F: centripetal force

This is derived from the equation F = ma and in uniform circular motion the value for acceleration, a, is given by:

a = (v^2)/r

PROCEDURE

To set up this lab we first measured the mass of the weight. We then put a centripetal force apparatus on the table and leveled it by adjusting the legs appropriately. Next, attached the weight to the end of arm of the apparatus on a string and let it hang until it stopped moving. We adjusted the post to where the weight was directly above the post. Once the post was tightened down, we attached the spring to it.

Once everything was set up, we then measured the radius of the apparatus from the center of the rotating pole to the string where the weight hung from. This is going to be our radius, r, for the equations we use.

After having the measurements we spun the apparatus until the spring stretched far enough to where the tip of the weight reached the post. We timed how long it took the apparatus to go around 50 complete revolutions. We took 3 trials of this and put our measurements on to a table.

The next part of the lab is to now find the Force that is required to stretch the spring the same distance that spinning the apparatus did. In order to do that you must attach a string to the weight opposite of the spring and hang a mass hanger over the pulley of the apparatus. Once doing that, begin adding slotted weights to the hanger until the weight is over the post just as it was when we were spinning the apparatus. Record the mass and calculate the force that was required to stretch the spring. 

Repeat this experiment except this time around, add a 100 g slotted weight to the hanging weight. 

DATA ANALYSIS

All the data that was collected we put into tables. In order to do so we first had to do some calculations. We had to find the linear speed, the centripetal force, the force of the hanging mass, and the percent difference.

First we calculated the linear speed for each trial and found an average.

Once we had and average velocity, we could then calculate for our centripetal force with the given equation F = (mv^2)/r. We also solved for the force of the hanging mass

These were the calculations for the mass of 0.4492 kg. We also did the calculations for the mass of 0.5492 kg. The table represents all of our calculations.

DISCUSSION

In this lab I learned how to calculate the centripetal force of an object in a circular motion. I also learned that the centripetal force to stretch the spring with a weight attached moving in a circular path is equal to the force required to pull the string. This makes sense because the faster you spin something, the force on that object that is pulling it away is greater. 

Some sources of error that could have occurred in this lab is that we may not have given a completely constant velocity on while rotating the apparatus. Also there were a couple of times where the weight wasn't completely over post; sometimes the spring was not stretched enough and sometimes it was stretched too much.