Let's return to our friend the sphere, with surface charge density σ(θ, f) = σ0sinθcos2f . Find the net polarization of this sph
ere, assuming the charge density is bound charge. You can assume the sphere is not rotating (f is azimuthal angle). What is the electric potential a large distance from the sphere?
1 answer:
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The elastic potential energy of a spring is given by
where k is the spring's constant and x is the displacement with respect to the relaxed position of the spring.
The work done by the spring is the negative of the potential energy difference between the final and initial condition of the spring:
In our problem, initially the spring is uncompressed, so
. Therefore, the work done by the spring when it is compressed until 
is
And this value is actually negative, because the box is responsible for the spring's compression, so the work is done by the box.
where k is the spring's constant and x is the displacement with respect to the relaxed position of the spring.
The work done by the spring is the negative of the potential energy difference between the final and initial condition of the spring:
In our problem, initially the spring is uncompressed, so
And this value is actually negative, because the box is responsible for the spring's compression, so the work is done by the box.
Answer:
ΔK = 2.45 J
Explanation:
a) Using the law of the conservation of the linear momentum:
Where:
Now:
Where is the mass of the car,
is the initial velocity of the car,
is the mass of train,
is the final velocity of the car and
is the final velocity of the train.
Replacing data:
Solving for :
Changed to cm/s, we get:
b) The kinetic energy K is calculated as:
K =
where M is the mass and V is the velocity.
So, the initial K is:
And the final K is:
Finally, the change in the total kinetic energy is:
ΔK = Kf - Ki = 22.06 - 19.61 = 2.45 J