John is traveling north at 20 meters/second and his friend Betty is traveling south at 20 meters/second. If north is the positiv
2 answers:
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A) The power delivered to the lines is
And the voltage at which the lines work is
Since the power delivered is the product between the voltage and the current:
We can find the current flowing in the lines:
b) The voltage change along each line can be found by using Ohm's law:
c) The power wasted as heat along each line is given by:
And since we have 2 lines, the total power wasted as heat in both lines is
And the voltage at which the lines work is
Since the power delivered is the product between the voltage and the current:
We can find the current flowing in the lines:
b) The voltage change along each line can be found by using Ohm's law:
c) The power wasted as heat along each line is given by:
And since we have 2 lines, the total power wasted as heat in both lines is
Answer:
Explanation:
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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