Answer:
Explanation:
Hi!
In order to obtain the Lagrangian of the system we must first write the Kinetic and Potential Energies. Lets orient our axes such that the axis of the cone coincide with the z axis. In cilindrical coordinates we have
- (1)
But, since the particle is constrained to move on the surface of the cilinder, we have the following relation between r and z:
or:
- (2)
and:
replacing (2) in (1) we obtain:
- (3)
Now the kinetic energy is given as:
- (4)
And the potential energy is given by:
So the Langrangian is given by:
And the equations of motion are:
For θ
For r
Obtained from the Euler-Langrange equations
Here the conserved quantity is given by the first equation of motion, namely:
Which is the magnitude of the angular momentum
Answer:
Final energy will be 40 KJ
Explanation:
We have given that 30 KJ of the heat is transferred to the water
So
And 5 KJ of heat is lost to the surrounding air
So
So total heat
The paddle-wheel work amounts to 5000 N -m
So work done W = -5 KJ ( as work is done by the paddle wheel )
We know that
We have given initial kinetic energy = 10 KJ
So
So final energy = 30+10 =40 KJ
F - False.
Electric charges can also be transferred by Contact.