A rod of mass 0 . 51 kg and radius 0 . 048 m rests on two parallel rails that ar

Question

A rod of mass 0.51 kg and radius 0.048 m rests on two parallel rails that are 0.14 m apart and longer than 0.15 m. The rod carries a upward current of 76 A and rolls along the rails without slipping. There is a uniform magnetic field of magnitude 0.45 T directed into the page and perpendicular to the rod and the rails. If it starts from rest, what is the speed of the rod after moving a distance 0.15 m? Answer in units of m/s.

Question 10, chap 129, sect 3. part 1 of 2 10 points A rod of mass 0.51 kg and radius 0.048 m rests on two parallel rails that are 0.14 m apart and longer than 0.15 m. The rod carries a upward current of 76 A and rolls along the rails without slipping. There is a uniform magnetic field of mag- nitude 0.45 T directed into the page and per- pendicular to the rod and the rails. 0.45 T 0.45 T If it starts from rest, what is the speed of An woer int mithsoing a distance 0.15 mf

Explanation / Answer

Given,

B = 0.45 T ; I = 76 A ; d = 0.14 ; L = 0.15 m ; m = 0.51 kg ;

Let the required speed be v.

The magnetic force on the rod is:

F = B I d

moment of inertia of the rod is:

I = m r^2/2 ;

from conservation of energy:

W = K

(B I d) L = Ke(rot) + Ke(trans)

B I d L = 1/2 I w^2 + 1/2 m v^2

B I d L = 1/2 x 1/2 m r^2 vf^2/r^2 + 1/2 m v^2 = 3/4 m v^2

v = sqrt (4 B I d L/3 m)

v = sqrt (4 x 0.45 x 76 x 0.14 x 0.15/3 x 0.51) = 1.37 m/s

Hence, v = 1.37 m/s

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