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Laws of Motion

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Physics Part I

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Physics

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Class 10 Class 12

A particle of mass m is driven by a machine that delivers a constant power K watts. If the particle starts from rest, the force on the particle at time t is

  • square root of mk over 2 end root t to the power of negative 1 divided by 2 end exponent
  • square root of mk space t to the power of negative 1 divided by 2 end exponent
  • square root of 2 mk end root space t to the power of negative 1 divided by 2 end exponent
  • 1 half square root of m t end root to the power of negative 1 divided by 2 end exponent

A.

square root of mk over 2 end root t to the power of negative 1 divided by 2 end exponent

As the machine delivers a constant power
So F, v =constant = k (watts)
rightwards double arrow space straight m dv over dt. straight v space equals straight k
rightwards double arrow integral vdv space equals straight k over straight m integral dt
rightwards double arrow straight v squared over 2 equals straight k over straight m straight t space space
rightwards double arrow space straight v equals space square root of fraction numerator 2 straight k over denominator straight m end fraction end root straight t
Now comma space force space on space the space particles space is space given space by
straight F equals space straight m fraction numerator d straight v over denominator d straight t end fraction space equals straight m straight d over dt open parentheses fraction numerator 2 kt over denominator straight m end fraction close parentheses to the power of 1 divided by 2 end exponent
equals space square root of 2 km end root space open parentheses 1 half straight t to the power of negative 1 half end exponent close parentheses
equals space square root of mk over 2 end root. straight t to the power of fraction numerator negative 1 over denominator 2 end fraction end exponent

As the machine delivers a constant power
So F, v =constant = k (watts)
rightwards double arrow space straight m dv over dt. straight v space equals straight k
rightwards double arrow integral vdv space equals straight k over straight m integral dt
rightwards double arrow straight v squared over 2 equals straight k over straight m straight t space space
rightwards double arrow space straight v equals space square root of fraction numerator 2 straight k over denominator straight m end fraction end root straight t
Now comma space force space on space the space particles space is space given space by
straight F equals space straight m fraction numerator d straight v over denominator d straight t end fraction space equals straight m straight d over dt open parentheses fraction numerator 2 kt over denominator straight m end fraction close parentheses to the power of 1 divided by 2 end exponent
equals space square root of 2 km end root space open parentheses 1 half straight t to the power of negative 1 half end exponent close parentheses
equals space square root of mk over 2 end root. straight t to the power of fraction numerator negative 1 over denominator 2 end fraction end exponent

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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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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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Is Aristotle’s law of motion now correct?

No. Aristotl'e law of motion is false. 
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