If the ration supplementary angle is 11:7,find the measure of the larger angle larger angle?
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:
t = 0.354 hours
Explanation:
given,
coefficient of rolling friction μr=0.002
mass of locomotive = 180,000 Kg
rolling speed = 25 m/s
The force of friction = μ mg
= (.002) x (180000) x (9.8)
= 3528 N
F = m a
now,
m a = 3528 N
180000 x a = 3528
a = 0.0196 m/s²
Then apply
v = u + at
0 = 25 - 0.0196 x t
t = 1275.51 sec
t = 1275.61/3600 hours
t = 0.354 hours
time taken by the locomotive to stop = t = 0.354 hours
Answer:
Induced emf in the loop is 0.0603 volts.
Explanation:
It is given that,
Radius of the circular loop, r = 1.6 cm = 0.016 m
Magnetic field, B = 0.8 T
When released, the radius of the loop starts to shrink at an instantaneous rate of 75.0 cm/s,
We need to find the magnitude of induced emf at that instant. Induced emf is given by :
Where
is the magnetic flux,
, A is the area of cross section
So, the induced emf in the loop is 0.0603 volts. Hence, this is the required solution.