Work, Energy and Power

Physics Part I

Physics

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A trolley of mass 200 kg moves with a uniform speed of 36 km/h on a frictionless track. A child of mass 20 kg runs on the trolley from one end to the other (10 m away) with a speed of 4 m s^{â€“1}Â relative to the trolley in a direction opposite to the its motion, and jumps out of the trolley. What is the final speed of the trolley? How much has the trolley moved from the time the child begins to run?

Given,

Mass of the trolley,Â

Speed of the trolley,Â

Mass of the boy,Â

Initial momentum of the system of the boy and the trolley,Â

= (

= (200 + 20) Ã— 10Â

= 2200 kg m/sÂ

LetÂ

Final velocity of the boy with respect to the ground = v' - 4Â

Final momentum = Mv' + m(v' - 4)Â

Â

Â Â Â Â Â Â Â Â Â Â Â Â Â Â = 200v' + 20v' - 80Â

Â Â Â Â Â Â Â Â Â Â Â Â Â Â = 220

As per the law of conservation of momentum,

Â

Initial momentum = Final momentumÂ

Â Â Â Â Â Â Â Â Â Â 2200 = 220

âˆ´ Â Â Â Â Â Â Â Â Â Â Â v' =

Length of the trolley,Â

Speed of the boy,Â

Time taken by the boy to run, t = = 2.5 s

âˆ´ Distance moved by the trolley =Â

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = 25.9 m

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Define the unit joule.

Work done is said to be one joule if one newton of Â force displaces the body through a distance of one meter in the direction of applied Â forceÂ .

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Is work a scalar or a vector quantity?

Work is dot product of two vectors. i.e.Â .

And dot product is a scalar quantity. Therefore, work is a scalar quantity.Â

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