1.

A car travels on a flat circular track of 200m at 30m/s and centripetal acceleration is 4.5m/s^2 if the car has a mass of 1000 kg find the frictional force requiredIf it’s coefficient of static friction is 0.8 what is the maximum speed at which the car can circle the track

Answer»

Given :

  • A car travels on a flat circular track of 200m at 30m/s

  • centripetal acceleration = 4.5m/s^2

  • mass of car = 1000kg

To find :

  • the frictional force required

  • If its coefficient of STATIC friction is 0.8 what is the maximum speed at which the car can circle the track

Formula used:

  • Force (F) = mass × Acceleration

  • Maximum speed (v) = √(μrg)

where :-

  • μ = coefficient of static friction
  • R = radius
  • G = 10 m/s²

Solution :

⟹mass = 1000kg

⟹Acceleration = 4.5m/s²

⟹Friction Force (F) = mass × Acceleration

⟹F = 1000 × 4.5

⟹F = 4500 N

Now we will find maximum speed at which the car can circle the track :-

⟹ v = √(μrg)

Now PUT :-

  • μ = 0.8
  • r = 200
  • g = 10

⟹v = \sqrt{0.8 \times 200 \times 10}

⟹v = \sqrt{ \dfrac{8}{10} \times 200 \times 10}

⟹v = \sqrt{ {8} \times 200 }

⟹v = \sqrt{ 1600 }

⟹v = \sqrt{ 40 \times 40 }

⟹v = 40 \frac{m}{s}

Answer :

  • frictional force = 4500N
  • maximum speed = 40 m/s

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Learn more :-

  • v = wr

  • ar = r w²

  • F = mv²/r

  • Maximum speed (v) = √(μrg)

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