<span>The value of the constant needed to complete in joules to three significant figures is 2.18 x 10^-18 J.</span>
Answer:

Explanation:
The instantaneous velocity of a point mass that executes a simple harmonic movement is given by:

Where:

Express the amplitude in meters:

The angular frequency can be found using the next equation:

Using the data provided:

At the equilibrium position:


Answer:
dx/Dt x B . x =0
Explanation:
Let's calculate the work and the magnetic force, the expression for magnetic force is
F = qv x B
Bold indicate vector quantities, the expression for the job is
W = F. X
Let's replace in this equation
W = q v x B . X
The definition of speed is
v = dX / dt
With what work is left
W = q dX / dt x B . X
As we can see the vector product gives us a vector perpendicular to dX and its scalar product by X of zero
Second part
The speed a vector and although the magnitude is constant the change of direction implies a change in the speed.
Let's calculate the magnitudes of speed (speed)
F = qv B sin θ
F = ma
q v B sin θ = ma
a = qvB / m senT
This acceleration is perpendicular to the magnetic field and the velocity, so it does not change if magnitude but its direction, it is directed to the center of the circle.
| v | = q vB/m sin θ
If you divide miles by minutes, the answer will have units of
miles per minute, which is exactly what you want.
(1 mile) / (10 minutes) = 1/10 mile/minute = 0.1 mile per minute
We have that F=ma from the 2nd Newton law where F is the force, m is the mass and a is the acceleration. Suppose we have that F' is the new force and m' is the new mass. Then, we have that a'=F'/m' still, by rearranging Newton's law. We are given that F'=2F and m'=m/2. Hence,

But now, we have from F=ma, that a=F/m and we are given that a=1m/s^2.
We can substitute thus, a'=4a=4*1m/s^2=4m/s^2.