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CENTRIPETAL AND CENTRIFUGAL FORCE:
Centripetal force is an inward force that act on an object that is moving round a circle. The force help to stop the object from skidding out of the circular path.
Centripetal force = m X v² /r ….. equation. 1
Where m is the Mass of the object, v is the velocity of the object, r is the radius of the circular path
From the formula of force,
force = mass X acceleration. ( f = m X a ). ….. equation. 2
If we equate equation 1 and equation 2, then we will get,
M X a = M V² / r.
M will cancel M. Therefore, we will get, a = V² / r
Centripetal acceleration a = V² / r
Example:
Calculate the magnitude if centripetal force on a car of mass 5.23kg that is moving round a circle of radius 0.5m with a a velocity of 10m/s.Also, determine the centripetal acceleration of the object.
Solution:
Data: mass = 5.23kg, radius = 0.5m, velocity = 10 m/s
Formula : F = M XV² / r
Substitution:
F = 5.23kg X ( 10m/s )² / 0.5
F = 5.23 X 100 / 0.5 = 523 / 0.5 m = 100 / 0.5 = 1046N
Centripetal acceleration of the car:
Centripetal acceleration = V² / r
= C. A = ( 10m/s )² / 0.5 m = 100 / 0.5 = 200 m/s²
Example 2:
If 200 N force act on a train of mass 34.5 kg that is moving round a circle with a velocity V, of radius 2.10 m, calculate the velocity of the train and hence what is its centripetal acceleration?
Solution:
data: mass = 34.5 kg, velocity = V, radius = 2.10 m, force = 200N, c.a = ?
Formula: F = M X V² / r
Substitution: 200 = 34.5 kg X V² / 2.10.
Make V the subject: 200 X 2.10 / 34.5 = V²
V² = 420 / 34.5 = 12.174
V = √12.174.
V = 3.49 m/s
Centripetal acceleration = V² / r
c.a = 3.49² / 2.10 = 12.18 / 2.10 = 5.80 m/s²
C.A = 5.80 m/s²
Centrifugal Force:
Centrifugal force is an outward force which act on an object that moves round a circle. Centrifugal force is a balancing force which counterbalances the centripetal force so as to prevent the centripetal force from pushing the object to the centre of the circle. It is opposite to centripetal force.
Since centrifugal force is a balancing force, it is equal in magnitude but opposite in direction centripetal force.
Therefore, Centripetal force = centrifugal force = M X V² / r
Same formulae is used to calculate centrifugal force
Centrifugal force = M X V² / r
Advantages of Centripetal Force:
Centripetal force is responsible for the force that keeps the satellites in their orbits.
Centripetal force helps to maintain an object that is moving in a circular path
Centripetal force overcomes inertia
According to Newton’s Law of Inertia, an object in motion tends to follow a straight line. If a force is applied to an object at an angle to the direction of motion, that force will overcome the object’s inertia, such that it will follow a curved path, depending on the amount of the force and how long it is applied.
Advantages of Centrifugal Force:
- Centrifugal for e balances /centripetal force.
- Centrifugal is used in laboratory to separate solute from solution.