Please solve (a) and (b) Answer (a)0.00156n-m An erratic engineer, who lives in
ID: 1429967 • Letter: P
Question
Please solve (a) and (b)
Answer (a)0.00156n-m
An erratic engineer, who lives in a residence infested by small, fast, intelligent bugs, conceives the device shown as a method of driving a disk. The bugs are taught to climb up the axle of the disk, emerge through a hole O at its center, and run radially outward at constant velocity. At the edge, the bugs fall off and drop into a bug-catching tray, where they are rewarded in some way prescribed by psychologists. By means of a seat of e.m.f. not shown, each bug acquires an electric positive charge as it ascends, and carries the charge with it as it runs across the disk. A magnetic field of flux density varying with radius according to B = 0.1 r^2 acts upward over the disk. Suppose that 1000 bugs/sec emerge from O, each carrying charge +.001 Coulomb, and move out radially. The radius of the disk is 0.5 meters. Find the torque on the disk The rough sketch of the device shown here hardly does justice to the grandeur of the scheme, which, although inchoate, surely has possibilities.) Where does the increasing kinetic energy of the disk come from (i.e., from what sources of energy ?)Explanation / Answer
let,
B=0.1*r^2 T
charge q=0.001 C
radius, r=0.5 m
no of bugs emerging, n=1000 bugs/sec
current i=n*q/t
i=1000*0.001
i=1 A
a)
torque dT=r*dF*sin(theta) (with r=0 to 0.5 m)
dT=r*dF*sin(90)
dT=r*(i*dr*B)
dT=r*(i*Bdr)
dT=r*(i*0.1*r^2*dr)
dT=0.1*i*r^3*dr
====>
( with the limits r=0 to 0.5)
T=i*0.1*(r^4/4)
T=1*0.1*(0.5^4)/4
T=0.00156 N.m
===>
torque T=0.00156 N.m
b)
source of increasing kinetic enegry is magnetic energy ( magnetic field)