Uniform Circular Motion: Centripetal Force

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- ANALYSIS AND OBSERVATION

• During our experiment, I observed that the smaller velocity of the object, the less centripetal force you will have to apply. And I have notice that the centripetal force and the centripetal acceleration are always pointing in the same direction. The centripetal acceleration can be derived for the case of circular motion since the curved path at any point can be extended to a circle. Without a net centripetal force, an object cannot travel in circular motion. If the forces are balanced then an object in motion continues in motion in a straight line at constant speed.

- EVALUATION, QUESTIONS, AND PROBLEMS

- Describe the relation of the centripetal force and the frequency squared when the mass varies and when the radius varies.

• As we can see in the formula f=m*(v2/r), if the mass and circular velocity remain constant, increasing the radius will decrease the force and vice versa. When more mass was added the centripetal force and frequency squared both increases. The smaller the length of rope (radius), the more centripetal force you will have to apply to the rope.

- Consider the case where an object is rotating in a uniform circle of radius 2.0 at a rate of 25.0 revolutions in 30 seconds.

- What is the period of motion of the object?

- Determine the velocity and the acceleration of the object in its circular path.

Solution:

r = 2.0

t = 30 second

f = 0.83

v = 2∏ x r x f

= 2∏ x 2.0 x 0.83

= 10.43

a = v2/r

= 10.432/ 2

= 54.39

- What centripetal force is needed to keep a 3kg mass moving in a circle of radius 0.5m at a speed of 8m/s?

Solution:

m = 3kg

r = 0.5 m

v = 8m/s

Fc = m x (v2/r)

= 3kg x ((8m/s)2/0.5m)

= 384 N

- CONCLUSION

• I therefore conclude that Uniform Circular motion refers to the case of constant rate of rotation. The mass is directly proportion to the centripetal force so we can easily say that the bigger the mass, the bigger the value of the force. Centripetal force is a center seeking force which means that the force is always directed toward the center of the circle, without that force, an object will simply continue moving in a straight line motion.