Lab 7: 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, triple beam balance.

Introduction: Then centripetal force apparatus is designed to rotate a known mass through a circular path of known radius. By timing the motion for a definite number of revolutions and knowing the total distance that the mass has traveled, the velocity can be calculated. Thus the centripetal force, F, necessary to cause the mass to follow its circular path can be determined from Newton's second law.
                                                           F=mv^2/r
Where m is the mass, v is the velocity, and r is the radius of the circular path.
Here we have used the fact that for uniform circular motion, the acceleration, a, is given by:
                                                           a=v^2/r


Procedure:
1. For each trail the position of the horizontal crossarm and the verticle indicator post must be such that the mass hangs freely over the post when the spring is detached. After making this adjustment, connect the spring to the mass and practice aligning the bottom of the hanging mass with the indicator post while rotating the assembly.

2.Measure the time for 50 revolutions of the apparatus. Keep the velocity as constant as possible by keeping the pointer on the bottom of the mass aligned with the indicator post. A while sheet of paper placed as a background behind the apparatus can be helpful in getting the alignment as close as possible. Using the same mass and radius, measure the time for three different trials. Record all data in a neat excel table.

3.Using the average time obtained above, calculate the velocity of the mass. From this calculation the centripetal force exerted on the mass during its motion.

4.Independently determine the centripetal force by attaching a hanging a weight to the mass until it once again is positioned over the indicator post (this time at rest). Since the spring is being stretched by the same amount as when the apparatus was rotating, the force stretching the spring should be the same in each case.

Centripetal apparatus

    Data:
    mass= 475grams
    radius= 16.5cm
                                                                v= 2πr·f                 
                                                                f=50/t
                                                                a=v^2/r
                                                                F=mv^2/r
(r= radius, f= frequency, t= time of 50 revolutions, m= mass, a= acceleration, F=calculated centripetal force)  

The apparatus to find the measured force 

 
 The force diagram for the hanging weight:

Our five trials when m=475grams, r=16.5cm

The average calculated force: 7.36N

The average measured force: 7.066N

Percent difference: 4.44%

5.Add 100g to the mass and repeat steps 2,3,4 above.

    Data:

    mass= 575grams
    radius= 16.5cm

The average calculated force: 7.53N

The average measured force: 7.252N

Percent difference: 3.83%

Conclusion:

      According to our data, we find that when radius is constant, the greater mass, the lower centripetal force. Our average calculated force is really close to measured force, that's means our data is convincing. Because the centripetal force is from the spring. The radius is constant means the length of spring doesn't change, so when the mass changes, the centripetal force is still constant. The formula: F=mv^2/r, F and r are constant, when mass increases, the velocity will decrease.
      In this lab, we verify Newton's second law of motion for the case of uniform circular motion. That the acceleration a of a body is parallel and directly proportional to the net force F acting on the body, is in the direction of the net force, and is inversely proportional to the mass m of the body, F = ma. In this case, the direction of net force points to the center of circle, F= ma, where a=v^2/r. 
      The causes of error:
      (1) When we measure the time for 50 revolutions of apparatus we can't keep the speed exactly constant. So, our frequency is not accurate.
      (2) Our experiment is influenced by air resistance, so our centripetal force actually is not only from the spring.