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Sunday, May 28, 2006

The Lion MUST be caught ?!?

Car pulls ( engine pulls rather ) with force F.
Car moves with constant velocity V.
:. Net force on car = 0
Force by dissipiative forces such as friction = -F.

Now ; P = δW/δt = δ(F.s)/δt = F.δs/δt
Now since velocity is always relative, δs/δt = u is always relative!

However, since there are two powers acting, one by friction & one by engine, & net F = 0 , the net power on car is 0. This is from ground frame.

If a cycle follows at velocity U, in frame of cycle, the cars velocity = V-U. It is wrong to say that cyclist would say the power delivered by engine is F.(V-U) because the cyclist finds the car not accelerating & hence he caculates the work done by engine to be 0. The cyclist has no direct means to find from his frame what the work done by the engine alone is. ( Cyclist can't measure F, the internal force )

Besides, whenever engine applies a POWER, it makes the car accelerate. And acceleration is independant of relative refrence frames.Both someone on the car and on the cycle would measure the same Acceleration & hence find out the engine's power ( in absence of dissipiative forces ).

To get my point, try to sit on a cycle & follow a car (running at constant velocity) & think of an experiment to determine the power of its engine! You can do so by guessing at its friction, but not directly! This is the key to the problem. Work done is relative.

Therez another realated interesting thought. WHEN WE CLIMB STAIRS UPSTAIRS OR DOWNSTAIRS, THE NET CHANGE IN POTENTIAL E IS THE SAME. THEN WHY DO WE GET TIRED WHILE CLIMBING UPSTAIRS TO A GRATER DEGREE ???

6 comments:

saurya_time_travel said...

wait a minute .. isnt some thing going wrong ? I mean it is the lion that ought to catch the people .. not the other way round ..
just joking ...

TwIsTeR said...

hi time ... sent u a gmail invitatiobn... chek it n make an account there

Pravar D Mahajan said...
This comment has been removed by a blog administrator.
Pravar D Mahajan said...

Simple, we do some work against gravity in climbing the stairs and hence get tired

bravura said...

Hey Twish
When u say that the cyclist can't measure the internal force delivered by the engine u r talking about a practical hinderance not a conceptual one. What if he invents a device that tells him the force being given by the engine or i say i tell him what the force is. What happens then.
Swetabh

TwIsTeR said...

Wrong Bhaktji...

Imagine a cyclist & a car ... thats all there is to the universe. Then the cyclist can't MEASURE the power of engine since force applied by engine is an internal force & not measurable by cyclist. The cyclist can however ask someone on the car, about the power, but then that person would calculate the power from the car frame not cycle! There is thus no direct means to measure the power from the cycle!

~ Twish ~