What is Centripetal Force
Definition:
When an object is in curvilinear motion, then the force acting on it is directed towards the centre of curvature or its axis of rotation is known as centripetal force. This force is responsible for making objects move in a circle. The force can include other combinations also like friction, gravity, tension in a cable. The direction of the centripetal force will always be towards the centre of the circle of motion.
The unit of centripetal force is Newton.
The centripetal force is always acted perpendicular to the direction of the objectâ€™s displacement. According to Newtonâ€™s second law of motion, it is found that if a body is moving in a circular path, then the centripetal force always acts towards the centre of the circle.
Calculation of Centripetal Force
The product of mass (kg) and tangential velocity (m/sec) squared, divided by the radius (m), is the formula of centripetal force.
Centripetal force can be mathematically it is written as:
F = mv^{2}/r
Where, F represents the centripetal force, m = mass of the object, v = speed or velocity of the object and r = radius.
What is Centrifugal Force?
Centrifugal force is a virtual or fictitious force needed to make a non-inertial reference in a circular motion; the direction of this force is always away from the centre of the circle because it acts along the radius. This force seems like it pushes you away from the centre of the circle of motion.
It only comes into play when changing our reference frame from inertial to non-inertial, that is, from a ground rotating reference frame.
Calculation of Centrifugal Force
A centrifugal force basically uses the centripetal force formula (which describes a real phenomenon) and reverses the direction of the force to describe the fictitious centrifugal force.
F = – mv^{2}/r
Where, F = Centrifugal force, m = mass of the object, v = speed or velocity of the object and r = radius.
Important Questions on Centripetal and Centrifugal Force
1) A stone of mass 150 g is rotated in a horizontal circle at 10 m/s which is attached to the end of a 1m long string. What will be the acceleration of the stone and its centripetal force?
Since, centripetal force F_{c} = mv^{2}/r = (0.15Ã—10^{2}) /1 = 15 N
Now, by using Newtonâ€™s Second Law, centripetal acceleration can be calculated as
a_{c}=F_{c} / m = 15/0.15 = 100 m/s^{2}
2) In order to allow a car to travel at 60.0 km/h, what will be the compulsory frictional force between the road and the tires, if the car of mass 1500 kg is driven around a curve of radius 60.0 m?
The frictional force between the tyres and the road must deliver enough centripetal force for the circular motion involved.
v = 60 kmph = 60Ã—1000/3600 m/s = 16.6 m/s
Centripetal force F_{c} = mv^{2}/r = 1500 x 16.6^{2} / 60 = 6944.4 N.
This means that the total frictional force provided by the tyres must be at least 6944.4 N, or an average force of 1736 N per tyre.
3) Why does the increasing centripetal force not increase work?
Increasing centripetal force does not increase work for the reason that the work and centripetal force don’t have the same variables.
Since, Centripetal force = mv^{2}/(r) where, m=mass, v=velocity, and r=radius and on the other hand, work = force * displacement. Therefore, to have an impact on work, the centripetal force equation should be similar to the work equation, which is not actually possible.
4) Define Centripetal Acceleration.
The property of the motion of an object navigating a circular path is defined as centripetal acceleration. Centripetal acceleration works on the idea that when an object moves in a circular motion, then its acceleration vector will point out towards the centre of that circle. This phenomenon will be true even if the object is moving at a constant speed.
5) An object of mass 20kg is in a circular orbit of radius 20m at a velocity of 10m/s. Calculate the centripetal force required to maintain this orbit and the acceleration of this object.
Given, m = 20kg
R = 20m and v = 10m/s
According to the formula of centripetal force, F_{c} = mv^{2}/r
= F_{c} = 20* (10)^{2}/20 = 100N
And for acceleration a_{c}=F_{c} / m
= a_{c}= 100/20 = 5 m/s^{2}
6) Explain how centrifugal force acts in the washing machine?
A washing machine is basically a spinning top device; thus, when the machine rotates, the centrifugal force balances itself from both sides. When the force exerted by one side of the machine passes through the centre of the machine to act on the other side, a centrifugal force transits into a centripetal force. Therefore, it can be considered as an example of both centripetal and centrifugal force as it totally hangs on its relationship with the centre of the machine.
7) What is a Centrifuge?
A centrifuge is a machine that uses centrifugal force to detach or separate the contents based on their density. A strong centrifugal force is produced by a centrifuge when it spins, which results in the separation of contents. Centrifuge machine delivers speedy results for laboratory and other applications.
8) Define Centripetal Acceleration and derive the expression for the centripetal acceleration.
Centripetal Acceleration is defined as the rate of change of tangential velocity, i.e. the acceleration of a body traversing in a circular path.
Since,
F =
mv^{2}/r
centripetal acceleration is given by,
a_{c }= m/F
â€‹=(mv^{2}/r)/F
âˆ´ a_{c} = v^{2}/r
9) What is the dimensional formula of centripetal acceleration?
The dimensional formula of centripetal acceleration is given as:
Since the dimensional formula of velocity is M^{0}L^{1}T^{-1 }, and the dimensional formula of the radius is M^{0}L^{1}T^{0}
Therefore, Replacing the above in the centripetal acceleration formula, that is,
a_{c} = v^{2}/r
we can obtain the dimensional formula of centripetal acceleration as M^{0}L^{1}T^{-2}
10) Define Centrifugation and explain the factors affecting it.
The process of concentrating and accelerating the particles of different densities for their separation is termed as centrifugation. This process helps to accelerate the natural process of separation. Either filtration or sedimentation method can be used for centrifugation.
In either method, the particles are separated in the centrifuge machine through suspension.
Centrifugation is affected by these four factors –
- The density of the samples and solution
- Temperature and viscosity of the solution
- The distance at which the particles are displaced
- Speed of rotation of the device
Practice Questions
- Differentiate between centrifugal and centripetal force.
- Give 5 daily life examples of centrifugal and centripetal force.
- Does centripetal force increase or decrease with speed?
- Define Centripetal force.
- Explain the concept of centripetal acceleration.
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