A stiff spring with a spring constant of 1600.0 N/m is connected to a bar on a s

Question

A stiff spring with a spring constant of 1600.0 N/m is connected to a bar on a slide generator as shown in the figure below. Assume the bar has length 61.0 cm and mass m-0.75 kg, and it slides without friction. The bar connects to a U-shaped wire to form a loop that has width w 40.0 cm and total resistance 28 ? and that sits in a uniform magnetic field B = 0.35 T. The bar is initially pulled 5.0 cm to the left and released so that it begins to oscillate. what is the induced current in the loop as a function of time, I(t)? (Ignore a effects due to the magnetic force on the oscillating bar. Assume clockwise current is positive. Use the following as necessary: t. Do not use other variables, substitute numeric values. Assume that I is in amps and t is in seconds. Do not include units in your answer.) I(t)

Explanation / Answer

angular frequency of the scillations,

w = sqrt(k/m)

= sqrt(1600/0.75)

= 46.2 rad/s

position of rod as a function of time,

x = -A*cos(w*t)

= -0.05*cos(46.2*t)

velocity of the rod,

v = dx/dt

= -0.05*(-sin(46.2*t))*46.2

= 2.31*sin(46.2*t)

we know, inducd emf = B*v*L

= 0.35*2.31*sin(46.2*t)*0.61

= 0.493*sin(46.2*t)

I(t) = emf/R

= 0.493*sin(46.2*t)/28

= 0.0176*sin(46.2*t) <<<<<<<------------------Answer

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