Laws of Motion

Physics Part I

Physics

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A batsman deflects a ball by an angle of 45Â° without changing its initial speed which is equal to 54 km/h. What is the impulse imparted to the ball? (Mass of the ball is 0.15 kg.)

The given question can be illustrated as in the following fig. below.

Here,Â

AO = incident path of the ball,Â

OB = Path followed by ball after deflection,Â

< AOB =Â Angle between the incident and deflected paths of the ball = 45^{o}

Therefore,Â ^{}âˆ AOP = âˆ BOP = 22.5Â° =Â *Î¸*

Initial velocity of the ball = Final velocity of the ball = v

On resolving the component of velocity along v, we have

Horizontal component of the initial velocity =Â *v*cos Î¸, along ROÂ

Vertical component of the initial velocity =Â *v*sin Î¸, along PO

Horizontal component of the final velocity =Â *v*cos Î¸, along OS

Vertical component of the final velocity =Â *vÂ *sin Î¸, Â along OP

The horizontal components of velocities suffer no change.

The vertical components of velocities are in the opposite directions.

So, change in linear momentum of the ball gives us the impulse which is imparted to the ball.Â

That is,Â *Impulse = mvCos*Î¸ - (-*mvCos*Î¸)Â

Â Â Â Â Â Â Â =Â 2*mvCos*Î¸Â

Mass of the ball, m = 0.15 kgÂ

Velocity of the ball,Â *v*Â = 54 km/h

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = 15 m/s

Therefore,Â

Impulse = 2 x 0.15 x 15 cos 22.5^{oÂ Â Â Â Â Â Â }= 4.16 kg m/sÂ

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State Galileoâ€™s law of motion.

Galileoâ€™s law of motion states that, a bodyÂ continues to move in the same direction with constant speed, if no force is acting on the body.Â

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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.Â

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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.Â

So, the apples fall down.Â

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