What quantity are we going to compare between the two cases ? Yes, I know ... the "amount of work". But how to find that from the numbers given in the question ? Is it the same as the change in speed ? Well ? Is it ? NO. IT's NOT.
In order to reduce the car's speed, the brakes have to absorb the KINETIC ENERGY, and THAT changes in proportion to the SQUARE of the speed. ( KE = 1/2 m V² )
Case 'A' : The car initially has (1/2 m) (100²) = (1/2m) x 10,000 units of KE.
It slows down to (1/2 m) x (70²) = (1/2m) x 4,900 units of KE.
The brakes have absorbed (10,000 - 4,900) = 5,100 units of KE.
Case 'B' : The car initially has (1/2 m) (79²) = (1/2m) x 6,241 units of KE.
It slows down to a stop . . . NO kinetic energy.
The brakes have absorbed all 6,241 units of KE.
Just as we suspected when we first read the problem, the brakes do more work in Case-B, bringing the car to a stop from 79, than they do when slowing the car from 100 to 70 .
But when we first read the problem and formed that snap impression, we did it for the wrong reason. Here, I'll demonstrate:
Change Case-B. Make it "from 70 km/h to a stop".
Here's the new change in kinetic energy for Case-B:
The car initially has (1/2 m) (70²) = (1/2m) x 4,900 units of KE. It slows down to a stop . . . NO kinetic energy. The brakes have absorbed all 4,900 units of KE.
-- To slow from 100 to 70, the brakes absorbed 5,100 units of KE.
-- Then, to slow the whole rest of the way from 70 to a stop, the brakes absorbed only 4,900 units of KE.
-- The brakes did more work to slow the car the first 30 km/hr than to slow it the whole remaining 70 km/hr.
That's why you can't just say that the bigger change in speed requires the greater amount of work. ______________________________________
It works exactly the same in the opposite direction, too.
It takes less energy from the engine to accelerate the car from rest to 70 km/hr than it takes to accelerate it the next 30, to 100 km/hr !
That statement is false. Stored energy is potential energy. Kinetic is a word that refers to motion. Kinetic energy is the energy of motion not stored energy.
Moment of inertia of second shaft is seven times times the rotational speed of the first i.e. If I is the moment of inertia of first wheel so moment of inertia of second is 7 I
As there is no external torque therefore angular momentum is conserved