A 100 gram resistive slider (thick line) moves without friction along a vertical U-shaped conducting track (thin line) that is 50 centimeters wide in a magnetic field of 5 Tesla as shown. The slider's resistance is 20 Ohms. It falls under the influence of gravity. What is the terminal velocity of the slider in meters/second? Assume it can reach terminal velocity before it falls off
3.5
The answer is 3.864
You can find it by solving the differential equation.
for me it was 3.2, I think data are variables.
By the way, have you done question 4? because I did
B=uo N/L I,
I from the 3rd quest. but for "a big t" and N/L= loop density, but that wans't the aswer, any hint?
3.864
To determine the terminal velocity of the resistive slider, we need to consider the forces acting on it. There are two primary forces at play: the force due to gravity (its weight) and the electromagnetic force (Lorentz force) due to the interaction of the magnetic field and the current flowing through the slider.
The weight of the slider can be calculated using the formula:
Weight = mass * acceleration due to gravity
Given that the mass of the slider is 100 grams and the acceleration due to gravity is approximately 9.8 m/s^2, we can calculate the weight:
Weight = 0.1 kg * 9.8 m/s^2 = 0.98 N
Next, we need to consider the electromagnetic force acting on the slider. In this case, the force is given by:
Force = (magnetic field strength) * (current through the slider) * (length of the slider) * (sine of the angle between the slider and the magnetic field)
Since the slider is moving vertically, the angle between its motion and the magnetic field is 90 degrees, and the sine of 90 degrees is 1. The length of the slider is not given, but we can assume it is negligible compared to the width of the U-shaped track.
The current through the slider can be calculated using Ohm's Law:
Current = Voltage / Resistance
Where the voltage across the resistor is given by:
Voltage = Force * distance
Here, the distance is the width of the track, which is 50 centimeters or 0.5 meters. The force is the weight of the slider.
Voltage = 0.98 N * 0.5 m = 0.49 N·m
Plugging this value back into Ohm's Law:
Current = 0.49 N·m / 20 Ω = 0.0245 A
Now we can calculate the electromagnetic force:
Force = 5 T * 0.0245 A * 0.5 m * 1 = 0.06125 N
Since the electromagnetic force is acting in the opposite direction of the weight, we subtract the force value:
Net Force = Weight - Force = 0.98 N - 0.06125 N = 0.91875 N
At terminal velocity, the net force becomes zero because the upward electromagnetic force matches the downward force due to gravity. When the net force is zero, the slider reaches a constant velocity, which is the terminal velocity.
To calculate the terminal velocity, we can use the equation for constant velocity motion:
Velocity = sqrt((2 * acceleration * distance) / mass)
In this case, the acceleration is the acceleration due to gravity, which is 9.8 m/s^2, the distance is the width of the track (0.5 m), and the mass is 100 grams or 0.1 kg.
Velocity = sqrt((2 * 9.8 m/s^2 * 0.5 m) / 0.1 kg) = 4.427 m/s
Therefore, the terminal velocity of the slider is approximately 4.427 m/s.