Help it turn!

Classical Mechanics Level 2

A car has to move on a level turn of radius 20m. The coefficient of static friction between the tires and the road is 2.00. Find the maximum speed the car can take without skidding.

Details and assumptions :

  • g = 10 m/s 2 g = 10 \text{m/s}^2

  • Give your answer in m/s \text{m/s} .

Image Credit: Flickr Dan Fegent


The answer is 20.00.

Harsh Shrivastava by Harsh Shrivastava , 20, India

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2 solutions

Vaibhav Prasad
Apr 8, 2015

Only the frictional force would help it to not skid and stay on track. The frictional force here would be μ m g \mu mg

The outward force would be the centrifugal force, which would be m v 2 r \frac {mv^2}{r}

The frictional force must be greater than the centrifugal force.

Thus for a car to turn on a circle: μ m g ≥ m v 2 r \large {\mu mg \ge \frac{mv^2}{r}}

Applying it here gives answer as 20 20

4 Helpful 0 Interesting 0 Brilliant 0 Confused

That's right but u need to show the derivation :)

Harsh Shrivastava - 6 years, 2 months ago

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Ok ...edited

Vaibhav Prasad - 6 years, 2 months ago
Abhishek Mb
Apr 10, 2015

V=sqrt (ugr)

0 Helpful 0 Interesting 0 Brilliant 0 Confused

It's not equal to that it's the maximum velocity and if the car moves with a velocity marginally more than than that the friction wouldn't be able to provide it with the necessary centripetal force. This is because umg is not the value of frictional force, it's the maximum value of static friction.

Kushagra Sahni - 5 years, 3 months ago

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