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A car is moving on a circular track of radius 100 m. If the maximum speed at whi

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Question: A car is moving on a circular track of radius 100 m. If the maximum speed at which it can move without skidding is 20 m/s, what is the coefficient of friction between the tires and the road?

Options:

  1. 0.1
  2. 0.2
  3. 0.3
  4. 0.4

Correct Answer: 0.3

Solution: 

The centripetal force required is provided by friction: F = mv^2/r. The frictional force is μmg. Setting them equal gives μ = v^2/(rg). Here, μ = (20^2)/(100*9.8) ≈ 0.4.

A car is moving on a circular track of radius 100 m. If the maximum speed at whi

Practice Questions

Q1
A car is moving on a circular track of radius 100 m. If the maximum speed at which it can move without skidding is 20 m/s, what is the coefficient of friction between the tires and the road?
  1. 0.1
  2. 0.2
  3. 0.3
  4. 0.4

Questions & Step-by-Step Solutions

A car is moving on a circular track of radius 100 m. If the maximum speed at which it can move without skidding is 20 m/s, what is the coefficient of friction between the tires and the road?
Correct Answer: 0.4
  • Step 1: Understand that the car is moving in a circle, which means it needs a force to keep it moving in that circular path. This force is called centripetal force.
  • Step 2: The formula for centripetal force (F) is F = mv^2/r, where m is the mass of the car, v is the speed of the car, and r is the radius of the circular track.
  • Step 3: Identify the values given in the problem: the radius (r) is 100 m and the maximum speed (v) is 20 m/s.
  • Step 4: The frictional force that prevents the car from skidding is given by the formula F_friction = μmg, where μ is the coefficient of friction, m is the mass of the car, and g is the acceleration due to gravity (approximately 9.8 m/s²).
  • Step 5: Set the centripetal force equal to the frictional force: mv^2/r = μmg.
  • Step 6: Notice that the mass (m) cancels out from both sides of the equation, simplifying it to v^2/r = μg.
  • Step 7: Rearrange the equation to solve for μ: μ = v^2/(rg).
  • Step 8: Substitute the known values into the equation: μ = (20^2)/(100 * 9.8).
  • Step 9: Calculate the value: μ = 400/(100 * 9.8) = 400/980 ≈ 0.408.
  • Step 10: Round the answer to two decimal places if needed, which gives μ ≈ 0.4.
  • Centripetal Force – The force required to keep an object moving in a circular path, which is provided by friction in this scenario.
  • Friction – The force that opposes the motion of the car, which is calculated using the coefficient of friction.
  • Coefficient of Friction – A dimensionless scalar value that represents the frictional force between two surfaces.
  • Circular Motion – The motion of an object in a circular path, which requires a centripetal force to maintain.
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