A metal wire of mass m = 0.450 kg slides without friction on two horizontal rail
ID: 1459983 • Letter: A
Question
A metal wire of mass m = 0.450 kg slides without friction on two horizontal rails spaced a distance d = 0.20 m apart, as in the figure. The track lies in a vertical uniform magnetic field B = 0.80 T. There is a constant current i = 0.20 A through generator G, along one rail, across the wire, and back down the other rail. Find the speed and direction of the wire's motion as a function of time, assuming it to be stationary at t = 0. Evaluate for t = 1.2 s. Take positive to the right and negative to the left.
Explanation / Answer
Magnetic force acting on the metal wire, F = B*I*d*sin(90)
= 0.8*0.2*0.2*1
= 0.032 N (towards left)
acceleration of metal wire, a = F/m
= 0.032/0.45
= 0.071 m/s^2
speed at time t seconds,
v = u + a*t
= 0 + 0.071*t
= 0.071*t
direction : towards left (-x axis)
at t = 1.2 s
v = 0.071*1.2
= 0.0853 m/s