Centrifugal force

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Centrifugal force equation
Centrifugal force equation | Image: Learnool

Centrifugal force, also known as a fictitious force or pseudo force, is the apparent force that pushes an object outward when it is rotating around a center. Although it is not a real force, but rather a result of inertia, it appears to act on objects in a rotating reference frame. For instance, when you take a sharp turn in a car, you feel pushed outward against the car door. This sensation is due to your body’s inertia trying to keep you moving in a straight line while the car turns. In reality, it is the car exerting a centripetal force on you, pulling you inward. Centrifugal force is often observed in scenarios involving circular motion, such as amusement park rides and the spinning of a washing machine drum.

The equation for centrifugal force (Fcf) in a rotating reference frame is given by:

$$F_{cf} = \frac{mv^{2}}{r}$$

where m is the mass of the object, v is the velocity of the object, and r is the radius of the circular path. This equation is similar to that of centripetal force, showing that centrifugal force is the apparent force felt in a rotating system, acting outward from the center of rotation.

Practice problems

Problem #1

Determine the centrifugal force acting on a scooter weighing 80 kg as it moves in a circular path with a radius of 16 m and a speed of 2 m/s.

Solution

Given data:

  • Centrifugal force acting on a scooter, Fc = ?
  • Mass of a scooter, m = 80 kg
  • Radius of a circular path, r = 16 m
  • Velocity of a scooter, v = 2 m/s

Applying the formula:

  • Fc = (m × v2) ÷ r
  • Fc = [80 × (2)2] ÷ 16
  • Fc = 320 ÷ 16
  • Fc = 20 N

Therefore, the centrifugal force acting on a scooter is 20 N.

Problem #2

Calculate the centrifugal force acting on a bike weighing 150 kg, which moves with a speed of 1 km/h in a circular path of radius 5 m.

Solution

Given data:

  • Centrifugal force acting on a bike, Fc = ?
  • Mass of a bike, m = 150 kg
  • Velocity of a bike, v = 1 km/h = 0.27 m/s
  • Radius of a circular path, r = 5 m

Applying the formula:

  • Fc = (m × v2) ÷ r
  • Fc = [150 × (0.27)2] ÷ 5
  • Fc = 10.935 ÷ 5
  • Fc = 2.18 N

Therefore, the centrifugal force acting on a bike is 2.18 N.

Problem #3

Find the centrifugal force acting on a girl weighing 24 kg who is enjoying a carousel ride. The girl sits on a carousel rotating in a circular path with a radius of 8 m and a speed of 1 m/s.

Solution

Given data:

  • Centrifugal force acting on a girl, Fc = ?
  • Mass of a girl, m = 24 kg
  • Radius of a circular path, r = 8 m
  • Velocity of a girl, v = 1 m/s

Applying the formula:

  • Fc = (m × v2) ÷ r
  • Fc = [24 × (1)2] ÷ 8
  • Fc = 24 ÷ 8
  • Fc = 3 N

Therefore, the centrifugal force acting on a girl is 3 N.

Problem #4

Determine the centrifugal force acting on a bus weighing 700 kg as it moves in a circular path with a speed of 0.8 km/h. The radius of the circular path is 8 m.

Solution

Given data:

  • Centrifugal force acting on a bus, Fc = ?
  • Mass of a bus, m = 700 kg
  • Velocity of a bus, v = 0.8 km/h = 0.22 m/s
  • Radius of a circular path, r = 8 m

Applying the formula:

  • Fc = (m × v2) ÷ r
  • Fc = [700 × (0.22)2] ÷ 8
  • Fc = 33.88 ÷ 8
  • Fc = 4.23 N

Therefore, the centrifugal force acting on a bus is 4.23 N.

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Deep

Learnool.com was founded by Deep Rana, who is a mechanical engineer by profession and a blogger by passion. He has a good conceptual knowledge on different educational topics and he provides the same on this website. He loves to learn something new everyday and believes that the best utilization of free time is developing a new skill.

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