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Laws of Motion

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Physics Part I

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Physics

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CBSE Gujarat Board Haryana Board

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Class 10 Class 12

Three forces acting on a body are shown in the figure. To have the resultant force only along the y-direction, the magnitude of the minimum additional force needed is

  • 0.5 N

  • 1.5 N

  • fraction numerator square root of 3 over denominator 4 end fraction space straight N
  • square root of 3 space straight N

B.

1.5 N

Minimum additional force needed

F = - (Fresultant)x

straight F subscript resultant space equals space left square bracket left parenthesis 4 minus 2 right parenthesis left parenthesis cos space 30 space bold j with hat on top space minus space sin space 30 space bold i with hat on top right parenthesis space plus space left parenthesis cos space 60 space bold i with hat on top space plus sin space 60 space bold j with hat on top right parenthesis
space equals space open square brackets 2 open parentheses fraction numerator square root of 3 over denominator 2 end fraction bold j with hat on top minus 1 half bold i with hat on top close parentheses space plus open parentheses 1 half bold i with hat on top space plus fraction numerator square root of 3 over denominator 2 end fraction bold j with hat on top close parentheses close square brackets
equals open square brackets open parentheses square root of 3 space plus fraction numerator square root of 3 over denominator 2 end fraction close parentheses bold j with hat on top space plus open parentheses negative bold i with bold hat on top space plus fraction numerator bold i with bold hat on top over denominator 2 end fraction close parentheses close square brackets
equals open square brackets negative 1 half bold i with bold hat on top space plus fraction numerator 3 square root of 3 over denominator 2 end fraction bold j with hat on top close square brackets
equals fraction numerator bold i with hat on top over denominator 2 end fraction plus fraction numerator 3 square root of 3 over denominator 2 end fraction space bold j with hat on top
therefore comma
straight F space equals space minus space open parentheses fraction numerator bold i with hat on top over denominator 2 end fraction close parentheses space equals space 1 half bold i with bold hat on top
Hence comma space space vertical line straight F vertical line space equals space 0.5 space straight N

Minimum additional force needed

F = - (Fresultant)x

straight F subscript resultant space equals space left square bracket left parenthesis 4 minus 2 right parenthesis left parenthesis cos space 30 space bold j with hat on top space minus space sin space 30 space bold i with hat on top right parenthesis space plus space left parenthesis cos space 60 space bold i with hat on top space plus sin space 60 space bold j with hat on top right parenthesis
space equals space open square brackets 2 open parentheses fraction numerator square root of 3 over denominator 2 end fraction bold j with hat on top minus 1 half bold i with hat on top close parentheses space plus open parentheses 1 half bold i with hat on top space plus fraction numerator square root of 3 over denominator 2 end fraction bold j with hat on top close parentheses close square brackets
equals open square brackets open parentheses square root of 3 space plus fraction numerator square root of 3 over denominator 2 end fraction close parentheses bold j with hat on top space plus open parentheses negative bold i with bold hat on top space plus fraction numerator bold i with bold hat on top over denominator 2 end fraction close parentheses close square brackets
equals open square brackets negative 1 half bold i with bold hat on top space plus fraction numerator 3 square root of 3 over denominator 2 end fraction bold j with hat on top close square brackets
equals fraction numerator bold i with hat on top over denominator 2 end fraction plus fraction numerator 3 square root of 3 over denominator 2 end fraction space bold j with hat on top
therefore comma
straight F space equals space minus space open parentheses fraction numerator bold i with hat on top over denominator 2 end fraction close parentheses space equals space 1 half bold i with bold hat on top
Hence comma space space vertical line straight F vertical line space equals space 0.5 space straight N

938 Views

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. 
1332 Views

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. 
1475 Views

Is Aristotle’s law of motion now correct?

No. Aristotl'e law of motion is false. 
1233 Views

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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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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