Q17. The kinetic energy will stay constant since the magnetic force (which is also the net force acting on the particle) is always perpendicular to the velocity. This means acceleration is always perpendicular to velocity, which only occurs when an object is in uniform circular motion. Uniform circular motion is characterized by a constant speed, and by KE = 1/2mv^2, a constant kinetic energy.
17.You can find the acceleration first using kinematics, since you know displacement (1 m), final velocity (30 m/s), and initial velocity of zero since it starts at rest.
a = 450 m/s^2
Using Newton's 2nd and a FBD, you can also find that the magnetic force is the only force acting to accelerate the bar.
Fnetx = IBL = ma so I = ma/BL
I = 1.985 Amperes, magnetic field is directed into the page through the loop formed by the bars and the rails.
66.
a)
Remember that old thing called the Free Body Diagram?
We need to use it here - the magnetic force on the current accelerates the sliding wire down the rails.
Fnetx = Fmag = IBl = ma so a = IBl/m.
We can use v = vo + at to write the velocity as a function of time. The rod starts at rest, so vo = 0.
Thus v(t) = IBLt/m
b) With friction acting, the y-direction (which is directed out of the page in the photo above) becomes more important.
Fnety = Fn - mg = 0 so Fn = mg.
Since friction force Fk = mu*Fn, Fk = mu*mg
The new Fnetx = Fmag - Fk = ma
IBl - mu*mg = ma
a = (IBL/m) - mu*g
Using v = vo + at again, v(t) = 0 + ((IBL/m) - mu*g))t
c) Using the right hand rule, we can point our fingers North, and palm out of the page to go along with B. This leaves our thumb pointing to the right. This is then the direction of force.
Try it - don't guess!
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