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Laws of Motion

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Physics Part I

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Physics

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A block A of mass m1 rests on a horizontal table. A light string connected to it passes over a frictionless pulley at the edge of the table and from its other end, another block B of mass m2 is suspended. The coefficient of kinetic friction between the block and the table is straight mu subscript straight k. When the block A is sliding on the table, the tension in the string is

  • fraction numerator left parenthesis straight m subscript 2 plus straight mu subscript straight k straight m subscript 1 right parenthesis straight g over denominator left parenthesis straight m subscript 1 plus straight m subscript 2 right parenthesis end fraction
  • fraction numerator left parenthesis straight m subscript 2 minus straight mu subscript straight k straight m subscript 1 right parenthesis straight g over denominator left parenthesis straight m subscript 1 plus straight m subscript 2 right parenthesis end fraction
  • fraction numerator straight m subscript 1 straight m subscript 2 left parenthesis 1 plus straight mu subscript straight k right parenthesis straight g over denominator left parenthesis straight m subscript 1 plus straight m subscript 2 right parenthesis end fraction
  • fraction numerator straight m subscript 1 straight m subscript 2 left parenthesis 1 minus straight mu subscript straight k right parenthesis straight g over denominator left parenthesis straight m subscript 1 plus straight m subscript 2 right parenthesis end fraction

C.

fraction numerator straight m subscript 1 straight m subscript 2 left parenthesis 1 plus straight mu subscript straight k right parenthesis straight g over denominator left parenthesis straight m subscript 1 plus straight m subscript 2 right parenthesis end fraction

FBD of block A,


T -m1afk ..... (i)
FBD  of block B

m2g -T = m2a ... (ii)
Adding Eqs. (i) and (ii), we get
m2g-m1a = m2a +fkrightwards double arrow space straight m subscript 2 straight g minus straight m subscript 1 straight a space equals space straight m subscript 2 straight a space plus straight f subscript straight k
rightwards double arrow space straight a equals space fraction numerator left parenthesis straight m subscript 2 minus straight u subscript straight k straight m subscript 1 right parenthesis straight g over denominator straight m subscript 1 plus straight m subscript 2 end fraction
from space equation space left parenthesis ii right parenthesis
straight T equals space straight m subscript 2 minus left parenthesis straight g minus straight a right parenthesis
equals space straight m subscript 2 open square brackets 1 minus fraction numerator left parenthesis straight m subscript 2 minus straight mu subscript straight k straight m subscript 1 over denominator straight m subscript 1 plus straight m subscript 2 end fraction close square brackets straight g
straight T equals space fraction numerator straight m subscript 1 straight m subscript 2 space left parenthesis 1 plus straight mu subscript straight k right parenthesis over denominator straight m subscript 1 plus straight m subscript 2 end fraction straight g

FBD of block A,


T -m1afk ..... (i)
FBD  of block B

m2g -T = m2a ... (ii)
Adding Eqs. (i) and (ii), we get
m2g-m1a = m2a +fkrightwards double arrow space straight m subscript 2 straight g minus straight m subscript 1 straight a space equals space straight m subscript 2 straight a space plus straight f subscript straight k
rightwards double arrow space straight a equals space fraction numerator left parenthesis straight m subscript 2 minus straight u subscript straight k straight m subscript 1 right parenthesis straight g over denominator straight m subscript 1 plus straight m subscript 2 end fraction
from space equation space left parenthesis ii right parenthesis
straight T equals space straight m subscript 2 minus left parenthesis straight g minus straight a right parenthesis
equals space straight m subscript 2 open square brackets 1 minus fraction numerator left parenthesis straight m subscript 2 minus straight mu subscript straight k straight m subscript 1 over denominator straight m subscript 1 plus straight m subscript 2 end fraction close square brackets straight g
straight T equals space fraction numerator straight m subscript 1 straight m subscript 2 space left parenthesis 1 plus straight mu subscript straight k right parenthesis over denominator straight m subscript 1 plus straight m subscript 2 end fraction straight g
3225 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

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.
2445 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. 
1316 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