The increase in kinetic energy must have come from a reduction in rest mass. In other words the mass of the two alphas is less than the mass of X and the proton. You have values for the rest mass of the alphas and the proton and the mass equivalent of the kinetic energy gained.
For question 1 find the difference between the initial kinetic energy and the final kinetic energy. Then use E=mc^2 to convert energy to a mass equivalent.
There is nothing wrong with this calculation. All velocities relative to the observer are below c. It appears that the projectile has a relative velocity to the station of 1.1c from the ship's view but this is ok becuase relative to the ship all velocities are less than c. The velocity of the...
The guiding principle is mass/energy conservation.
initial (rest mass energy + kinetic energy)= final (rest mass energy + kinetic energy)
Question 1 is just concerned with the increase of kinetic energy expressed as a mass equivalence.
Question 2 just use the above equation. Be careful to...
I would agree with what you have said. However you are perhaps expected to say something more about the cyclotron.
Even at non-relativistic speeds r increases with v. However r is directly proportional to v and since time for 1 rev=2∏r/v the frequency of revolution is a constant which...
I was thinking L was the extension of the springs when at equilibrium and x was the displacement from equilibrium. Anyhow it does not matter much since the constants drop out during differentiation.
The pitch of a spiral is the distance moved after one complete revolution.
The diagram in section 2.5 of this wiki article is fairly clear:-
http://en.wikipedia.org/wiki/Screw_thread
The two velocity components would be
vsinθ perpendicular to B
vcosθ parallel to B
vsinθ should be used...
I think unfortunately this question as stated is meaningless. Tuning forks only make one frequency so why is the question asking about the quantity of resonant frequencies? This has misdirected your thinking.
If the question actually is asking " at what lengths of tube up to 1m does...
The 2 is correct. I got 16 because I used r=1/2 separation of masses. When cubed in the final equation this leads to a factor of 8 difference. 2 x 8 =16
One approach might be to make an equation for the electric potential. Because potential is a scalar this is easier than trying to find an equation for force or field strength, which would require vector addition.
Now field strength is equal to -potential gradient (E=-dV/dr or more generally...
E = 1/2 mv^2 + k(x-l)^2 + 2k(l-x)^2 -mgx - don't think this is quite right
I am guessing that we have one spring above the mass and one below?
The terms for elastic spring energy are based on 1/2ke^2. Where e is spring extension.
Isn't the extension of the springs l+x and l-x?
Are...
I sort of agree with you but would quibble over the wording.
The resultant force is always given by ma.
When going up the slope a=g(sinα+μ*cosα)
But when going down a=g(sinα-μ*cosα)
Resultant F=ma=mg*sinα+ reaction force from plates.
Reaction force from plates=±mgμ*cosα
So when going...
let r= distance between centre of sphere and midpoint between spheres.
then distance between centres of spheres=2r
We then get
F=-\frac{Gm^2}{4r^2}=-\frac{mv^2}{r}
which simplifies to
\frac{Gm}{4r}=v^2
Subbing in
v^2=\frac{4\pi^2 r^2}{T^2}
leads to
T=(\frac{16\pi^2r^3}{Gm})^{1/2}
Sorry I should have stated that I was assuming that the situation had settled to a steady equilibrium situation. Indeed initially heat will flow faster through the more conductive material. This will change the temperature at the interface until the temperature gradient in the less conductive...
You should get
T=(\frac{16\pi^2r^3}{Gm})^{1/2}
With r being the distance between the centre of a sphere and the midpoint about which the spheres rotate.
Now I suspect you need to replace the mass m with density x volume of a sphere. This introduces another distance: the radius of the...
Let a source of light give 1mW/sr.
The Irradiance at 1cm away is 1mW/cm2
At 2 cm away it is 0.25mW/cm2
At 10cm away it is 0.01mW/cm2
This is because area subtended by solid angle = solid angle in steradians x distance squared.
Essentially I agree with what you have said. To add some more detail it might be useful to consider this equation
\frac{ΔQ}{Δt}=-kA\frac{Δθ}{Δx}
This basically says that the rate of flow of heat through a material depends on the conductivity times the contact area times the temperature...
In your attempt you've added the two vector components together as if they are scalar quantities ie 1006 + 2765 = 3771. I suggest you draw a free body force diagram for the 300kg block. Are we to assume it is on the point moving upwards?
I analyzed it from the stationary frame where all masses share a common acceleration and got the same results.
I dislike working with pseudo forces because it encourages engineers to believe centrifugal forces are real.:grumpy:
Your final equation suggests that as r tends to infinity then T tends to zero. Does that sound reasonable?
Your method is essentially right but you have got errors in the details of your equations.
Applying Newton's law of gravity gives a force of F=-\frac{Gm^2}{r_d^2}
Which should be...
Wiki says:-In classical mechanics, the gravitational potential at a location is equal to the work (energy transferred) per unit mass that is done by the force of gravity to move an object to a fixed reference location.
By fixed reference location they mean infinity. It is the work done by...