Question

calculate the work required to be done to stop a car of 2000kg moving a velocity of 50km/h​

Answer 1

Answer:

Explanation:

mass of car= 2000 kg

velocity= 50 km/h = $50\times\frac{5}{18}=2.77m/s$

So, kinetic energy of car= $\frac{1}{2}mv^2=\frac{1}{2}\times2000\times(2.77)^2=7672.9 J\;of K.E.$

So, if car has that much energy while moving

THEN

The energy required to stop it will be equal to the K.E. of car, because if we provide force = K.E. of car in opposite direction to it, it will cancel out the K.E. and car will stop.

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[  Here, is an example to understand it:

Suppose that you have 2 friends, $Sumit$ and $Pankaj$ one is about 50 kg in weight($Sumit$), while the other is a slim boy, about 40 kg($Pankaj$).

Now, suppose that both are running towards each other at same speed and by chance they collide.

What will happen?

Of course, the slim boy($pankaj$) will fall down in the direction of $Sumit's\;\;$ movement.

yeah! you've seen it?

At least you are sure it would happen :)

Now, suppose another boy comes, let's name him $Prakhar$ who is same as $Sumit$, in weight ,height, etc.

Although it's hard that it is possible, but just suppose it.

Now, suppose that both were running in the ground( with full stability) directly towards each other, unaware that both are about to collide.

NOW

When they'll collide, what will happen?

Will one of the boy fall down?

Will one of the boy fall down so hard that a hole will form till the core of earth? ..... Laugh out! Just joking :)

You know that neither of them will fall down, as both were exactly of same height, weight, muscle, $bla\; bla\; bla$

So, you know why they didn't fell?

There is a word in physics called Kinetic energy.

And both had same kinetic energy ( because both had same weight and speed direction, $bla\;bla\;bla$)

Now, This is the concept that I am applying here.

Now, Let's return back to the question :)

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K.E. of car= $7672.9J\approx7673J$

Now, applying the same concept above

The energy required to stop the car should be 7672.9 J

BUT ................. wait!

The force should be applied to the opposite direction of car, right?

$Aisa\;to\;hai\;ni\;ki\;gaadi\;ko\;dhakka\;maaro\\aur\;phir\;bolo\;ki\;gaadi\;ruk\;ni\;re$☺☺☺☺

TRANSLATION:  That's not a right reason to say that car is not stopping when you are yourself pushing the car☺☺☺☺

SO!

The energy is applied in opposite direction or the work has to be done in opposite direction, so!

The energy/work required to stop the car is $= (-7672.9 J) \approx (-7673 J)$

Hope you liked my answer☺

$Learning\;\;Together:)$