@KnightadmiresChappo this is very easy in the rotating frame: The only force acting radially is the centrifugal pseudoforce mw^2 *x ( at a doistance x from the center)
thus, You get the differential equation: $m\dfrac{d^2x}{dt^2}=mw^2x$
@satan29 suppose a block with velocity v is projected on a horizontal table
The work done here will be the displacement of block time friction on table?
For table?
Actually in various book they don't mention work is force component along displacement of point of application Times displacement of point of application so i found in some questions i am confused
Sir suppose a block with velocity v is projected on a horizontal table The work done here will be the displacement of block time friction on table? For table? Actually in various book they don't mention work is force component along displacement of point of application Times displacement of point of application so i found in some questions i am confused
It's always worth taking a step back and considering how the energy is moving. In this case the block starts with some KE and it loses that energy as the KE is turned to heat by the friction. So energy is flowing out of the block, and that means the block is doing work.
By Newton's third law the force the block exerts on the table is the same as the force the table exerts on the block, and that is just the frictional force. Yes?
100% of the KE that the block has goes into the work done by the block. The question is where that energy goes. If we assume the table is fixed then the velocity and KE of the table cannot change, so all the work done by the block goes into heat.
The work is always force times distance, or ∫F.dx if the force varies. The work done by the block is equal to the change in its KE i.e. all the KE the block originally had is used to do work.
The block gets back some of that energy as heat, so the total energy of the block decreases by the work done and increases by the amount of heat it gets back from the friction.
Energy is always conserved. We know the KE of the block decreases to zero so that energy must go somewhere, and it goes somewhere by the block doing work.
@PrateekMourya yes, that's the work-energy theorem.
@PrateekMourya this point is a bit subtle since we mostly are accustomed to point particles. This point comes in handy when we talk aboutt rigid bodies.
for instnace, suppose we apply 10N force at the top of a rolling wheel
and suppose we apply it till the COM of the ring moves 10 metres in front
Can you give the final statement of juice law with the with all the the final points to be kept in mind
Sorry joules law
if a portion of mechanical work is converted to heat energy then the portion of mechanical work can be mathematically related to the heat energy generated by the joules law
An iron ball won't shrink much because iron is very hard. But it will shrink a bit. The amount its volume decreases under pressure is determined by the bulk modulus.
It depends what the cone is made of, so the question can't be answered. If the cone is made of a very soft metal like lead it will squish out sideways. The volume will stay constant but it will be some weird shape that's complicated.
Oh, OK, yes the book is assuming all the energy goes into the water and the bullet respectively. That is an approximation because some of the heat would go into the stream bed and the target respectively.
@RewCie there is an advantage to little endian notation because it means an int* pointer can be cast to any size of int and the pointer still works. OK this isn't an amazing advantage, but it is nevertheless a real one.
If you consider a solid then when we talk about it containing some heat what we actually mean is that the atoms in the solid are vibrating around, and the "heat" is actually energy stored in these oscillations.
If we start at absolute zero the atoms are not oscillating at all, so the solid contains no "heat".
Then as we raise the temperature the atoms vibrate more and more, so more and more energy is stored on those vibrations.
If we heat the solid enough the vibrations get so large that the solid shakes itself to bits, and that's exactly what melting is.
Now consider what happens if you place a hot solid and a cold solid in contact.
The atoms in the hot solid are vibrating more than the atoms in the cold solid, and those vibrating atoms literally bump into the atoms in the cold solid and make them vibrate more.
So the energy is transferred from the hot solid to the cold solid as kinetic energy when atoms at the junction between the two solids bump into each other.
