Show that terminal velocity equals

In summary, the conducting rectangular loop will reach a terminal velocity of Vt = mgR/B2w2 before its top edge reaches the magnetic field. This can be shown using the formula for the force on a current carrying wire in a uniform magnetic field where the wire is moving with respect to the magnetic field.
  • #1
wayneinsane
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0

Homework Statement



A conducting rectangular loop of Mass M and resistance R and length l and width w falls from rest into a magnetic field B as shown. During the time interval before the top edge of the loop reaches the field, the loop approaches the terminal speed v T .

Show that Terminal velocity (Vt) = MgR
B2w2



Homework Equations



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The Attempt at a Solution



HAve Nooooo Clue!
 
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  • #2
it should be Vt = mgR/B2w2
 
  • #3
Use the formula for the force on a current carrying wire in a uniform magnetic field where the wire is moving with respect to the magnetic field.
 

FAQ: Show that terminal velocity equals

What is terminal velocity?

Terminal velocity is the maximum speed that an object can reach when falling through a fluid, such as air or water. When the force of gravity is balanced by the force of air resistance, the object will no longer accelerate and will maintain a constant velocity.

How is terminal velocity calculated?

Terminal velocity can be calculated using the equation Vt = √(2mg/ρAC), where Vt is terminal velocity, m is the mass of the object, g is the acceleration due to gravity, ρ is the density of the fluid, A is the cross-sectional area of the object, and C is the drag coefficient.

What factors affect terminal velocity?

The factors that affect terminal velocity include the mass and shape of the object, the density and viscosity of the fluid, and the gravitational force. Objects with larger mass and surface area experience greater air resistance and therefore have a lower terminal velocity. Additionally, denser fluids and higher gravitational forces also lead to higher terminal velocities.

How is terminal velocity affected by altitude?

As altitude increases, the air density decreases. This results in a decrease in the force of air resistance and a subsequent increase in terminal velocity. However, the effect of altitude on terminal velocity is relatively small and may not be noticeable in everyday situations.

Can terminal velocity be exceeded?

No, terminal velocity is the maximum speed that an object can reach when falling through a fluid. If external forces, such as a parachute or propulsion, are applied to the object, then the terminal velocity may be exceeded. However, in a free-fall situation, terminal velocity cannot be exceeded.

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