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Laws of Motion

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Physics Part I

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A car is negotiating a curved road of radius R. The road is banked at angle straight theta. The coefficient of friction between the tyres of the car and the road is straight mu subscript straight s. The maximum safe velocity on this road is,

  • square root of gR open parentheses fraction numerator straight mu subscript straight s plus tan space straight theta over denominator 1 minus straight mu subscript straight s space tan space straight theta end fraction close parentheses end root
  • square root of straight g over straight R open parentheses fraction numerator straight mu subscript straight s plus tan space straight theta over denominator 1 minus straight mu subscript straight s space tanθ end fraction close parentheses end root
  • square root of straight g over straight R squared open parentheses fraction numerator mu subscript s plus tan theta over denominator 1 minus mu subscript s tan theta end fraction close parentheses end root
  • square root of g R squared open parentheses fraction numerator straight mu subscript straight s plus tanθ over denominator 1 minus straight mu subscript straight s tanθ end fraction close parentheses end root

A.

square root of gR open parentheses fraction numerator straight mu subscript straight s plus tan space straight theta over denominator 1 minus straight mu subscript straight s space tan space straight theta end fraction close parentheses end root

A car is negotiating a curved road of radius R. The road is banked at angle straight theta and the coefficient of friction between the tyres of car and the road is straight mu subscript straight s.
The given situation is illustrated as:


In the case of vertical equilibrium,

N cos straight theta = mg + f1 sin straight theta
rightwards double arrowmg = N cos straight theta space minus space straight f subscript 1 space sin space straight theta    ... (i)
In the case of horizontal equilibrium,

straight N space sin space straight theta space plus space straight f subscript 1 space cosθ space equals space mv squared over straight R  ... (ii)
Dividing Eqns. (i) and (ii), we get

straight v squared over Rg equals fraction numerator sin space theta space plus space mu subscript s space cos theta over denominator cos space theta space minus space mu subscript s space sin space theta end fraction space open square brackets f subscript 1 proportional to mu subscript s close square brackets

rightwards double arrow v space equals square root of R g open parentheses fraction numerator tan space theta space plus mu subscript s over denominator cos space theta space minus space mu subscript s space sin space theta space end fraction close parentheses end root
rightwards double arrow space v space equals space square root of R g open parentheses fraction numerator tan space theta space plus space mu subscript s over denominator 1 minus mu subscript s space tan space theta end fraction close parentheses end root

A car is negotiating a curved road of radius R. The road is banked at angle straight theta and the coefficient of friction between the tyres of car and the road is straight mu subscript straight s.
The given situation is illustrated as:


In the case of vertical equilibrium,

N cos straight theta = mg + f1 sin straight theta
rightwards double arrowmg = N cos straight theta space minus space straight f subscript 1 space sin space straight theta    ... (i)
In the case of horizontal equilibrium,

straight N space sin space straight theta space plus space straight f subscript 1 space cosθ space equals space mv squared over straight R  ... (ii)
Dividing Eqns. (i) and (ii), we get

straight v squared over Rg equals fraction numerator sin space theta space plus space mu subscript s space cos theta over denominator cos space theta space minus space mu subscript s space sin space theta end fraction space open square brackets f subscript 1 proportional to mu subscript s close square brackets

rightwards double arrow v space equals square root of R g open parentheses fraction numerator tan space theta space plus mu subscript s over denominator cos space theta space minus space mu subscript s space sin space theta space end fraction close parentheses end root
rightwards double arrow space v space equals space square root of R g open parentheses fraction numerator tan space theta space plus space mu subscript s over denominator 1 minus mu subscript s space tan space theta end fraction close parentheses end root

3737 Views

What is Aristotle’s law of motion?

Aristotle’s law of motion states that an external force is required to keep the body in motion.
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Define inertia.

The property by virtue of which the body cannot change its state of rest or uniform motion in a straight line, unless an external force is acting on the body is called as Inertia. 
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When the branches of an apple tree are shaken, the apples fall down. Why?

The apple fall from an apple tree when it shaken because of inertia of rest. Apple is in a state of rest and when the tree is suddenly shaken, apples still tends to remain in it's same state of rest whereas branches move. 

So, the apples fall down. 
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State Galileo’s law of motion.

Galileo’s law of motion states that, a body continues to move in the same direction with constant speed, if no force is acting on the body. 
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Is Aristotle’s law of motion now correct?

No. Aristotl'e law of motion is false. 
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