Answer:
a) [tex]\vec{d} =B-A[/tex]
b) [tex]I=\frac{B*v*d*\sin 90 \textdegree}{R}[/tex]
c) [tex]v \approx 0.6m/s[/tex]
Explanation:
From the question we are told that
Magnetic field strength [tex]B=3.6T[/tex]
Distance traveled [tex]d=7m[/tex]
Mass [tex]m=4.7 kg[/tex]
Resistance [tex]r=8.2 ohm[/tex]
Gravitational acceleration [tex]g=9.8m/s^2[/tex]
[tex]\theta =90 \textdegree[/tex] Because of perpendicularity
a)
Generally the direction of the current will be given as
[tex]\vec{d} =B-A[/tex]
Because it opposes increases of magnetic flux
b)
Generally the equation for induced EMF [tex]E[/tex] is mathematically given as
[tex]E=B*v*d*\sin \theta[/tex]
[tex]E=B*v*d*\sin 90 \textdegree[/tex]
Generally the equation for induced current [tex]I[/tex] is mathematically given as
[tex]I=E/R[/tex]
[tex]I=\frac{B*v*d*\sin 90 \textdegree}{R}[/tex]
c)
Generally the the equation for force F at terminal speed is mathematically given as
[tex]F=mg[/tex]
[tex]mg=B*I*d*\sin 90 \textdegree[/tex]
[tex]mg=B*(\frac{B * v * d }{R}) *d[/tex]
[tex]v=\frac{m*g*R}{B^2*D^2}[/tex]
[tex]v=\frac{4.7*9.8*8.2}{3.6^2*7^2}[/tex]
[tex]v=0.59475m/s[/tex]
[tex]v \approx 0.6m/s[/tex]
