Vernier Centripetal Force Lab Report

Theory Centripetal force is a force that makes and object move in a circular path. When an object moves in a circle it can have a constant speed where the magnitude of the velocity is the same but the direction is always changing so the velocity cannot be considered constant. For the velocity to change there must be an acceleration and from there on we can calculate the centripetal force. There are also instances where we don’t know the velocity but we know the time it takes to so from that we can get the velocity of the object that is traveling in the circle. Then by using the laws of conservation of energy we can figure out the height a ball must be dropped from to over come the force of gravity so it can make it around the loop.

Experimental

First we took the cart off the mass and weighed it obtaining a value of .05kg. Then we attached the cart back to the apparatus and added a 100g mass to it making the total mass of the cart .15kg. Then we adjusted the radius between the cart and center of the apparatus to be .09m. When the cart was finally set up properly we made sure that loggerpro was synched and began to spin the apparatus by hand. The results were recorded in loggerpro over a span of about four seconds and the data was recorded. We then picked three angular velocities off of the plot, and decided to use the values 14.83 rad/s, 15.15 rad/s, and 16.07 rad/s. these values would then be used to calculate the centripetal force by plugging them into the formula F=mV^2/R. After all of the values were plugged in the centripetal force was calculated and those value were 2.94N, 3.10N, and 3.49N. They were then compared with the measured values of centripetal force and those values were 2.47N, 2.65N, and 2.83N. These values do not quite matchup so we also took the percent error for each of the values and obtained errors of -.19, -.17,-.23. One reason why we may not of been able to get the same results as the calculated values is that we did not take into account any kind of friction that the apparatus may have been experiencing while being spun

The apparatus was spun around and the angular velocities measured were 10.47rad/s, 14.40 rad/s, and 15.76 rad/s. Then using those values and the equation F=mV^2/R we calculated the centripetal force one more time and the values were 4.39N, 8.29N, and 9.94N. Those results were compared with the measured results, which were 3.44N, 7.15N, and 8.41N. Since these values did not matchup perfectly with the calculated value we found the percent error and those values were -.28, -.16, and -.18. Then we took and average of all nine percent errors that were obtained and a value of -.17. This number wouldn’t be considered the best number but its not too bad. Reasons of what could of caused the error to be a little high can be due to factors such as friction and air