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

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?

and the first questoin?

Well, before I calculate the terminal velocity, I must say, this resistive slider seems quite electrifying! It's going to have a shocking velocity!

To find the terminal velocity, we need to consider the balance of forces acting on the slider. We have the force due to gravity pulling it downward and the magnetic force pushing it upward. At terminal velocity, these forces cancel out, resulting in no net force.

The force due to gravity acting on the slider can be calculated using the formula:

F_gravity = m * g

Where:
m = mass of the slider, given as 100 grams = 0.1 kg
g = acceleration due to gravity, approximately 9.8 m/s^2

Plugging in the values:
F_gravity = 0.1 kg * 9.8 m/s^2

Now, the magnetic force acting on the slider can be calculated using the formula:

F_magnetic = B * I * L

Where:
B = magnetic field strength, given as 5 Tesla
I = current flowing through the slider
L = length of the slider moving in the magnetic field

Since the slider is moving without friction, we know that the EMF (electromotive force) is equal to the force due to gravity. The EMF can be calculated using Ohm's Law:

EMF = I * R

Where:
R = resistance of the slider, given as 20 Ohms

Since we know both the resistance and the EMF, we can rearrange this equation to solve for the current I:

I = EMF / R

Now we can calculate the magnetic force:

F_magnetic = B * (EMF / R) * L

Finally, at terminal velocity, F_gravity equals F_magnetic. We can set up an equation and solve for L, which will give us the length of the slider moving in the magnetic field:

F_gravity = F_magnetic
0.1 kg * 9.8 m/s^2 = B * (EMF / R) * L

Solving for L, we can calculate the terminal velocity! But since I'm more of a clown than a mathematician, I'll have to leave that part to you. Good luck calculating, and may the magnetic force be with you!

To determine the terminal velocity of the slider, you will need to consider the forces acting on it. In this case, there are two main forces: the gravitational force and the magnetic force.

1. Gravitational Force (Fg):
The gravitational force acting on the slider is given by the equation:
Fg = m * g
where m is the mass of the slider and g is the acceleration due to gravity (approximately 9.8 m/s^2). We need to convert the mass from grams to kilograms by dividing it by 1000. So, the gravitational force can be calculated as:
Fg = (100 g / 1000) kg * 9.8 m/s^2

2. Magnetic Force (Fm):
The magnetic force on the slider is given by the equation:
Fm = q * v * B
where q is the charge of the slider, v is the velocity, and B is the magnetic field strength. The charge (q) can be determined using Ohm's Law: V = I * R, where V is the voltage across the resistor, I is the current, and R is the resistance. The voltage across the resistor can be calculated as V = I * R. We know the resistance (R = 20 Ω) and the current can be calculated using Ohm's Law: I = V / R.

Assuming the voltage is constant, the current will also be constant. Therefore, we can determine the charge (q) as:
q = I * t
where t is the time it takes for the slider to reach terminal velocity. Since the terminal velocity is constant, the current will also be constant, and we can assume t = 1 s for simplicity.

To calculate the magnetic force, we can plug in the values:
Fm = q * v * B = (I * t) * v * B

To reach terminal velocity, the magnetic force must be equal and opposite to the gravitational force. Therefore, we can set Fg = -Fm:
m * g = -(I * t) * v * B

Simplifying the equation, we can solve for terminal velocity (v):
v = -m * g / (I * t * B)

Now, we can plug in the provided values and calculate the terminal velocity.

Note: The given dimensions of the conducting track, as well as its shape, are not relevant for calculating the terminal velocity in this case.

Given:
Mass of slider (m) = 100 grams = 0.1 kg
Resistance of slider (R) = 20 Ω
Magnetic field strength (B) = 5 T
Acceleration due to gravity (g) = 9.8 m/s^2

First, calculate the current (I):
V = I * R
V = 1 Volt (assuming a constant voltage)
I = V / R = 1 V / 20 Ω

Now, calculate the terminal velocity (v):
v = -m * g / (I * t * B)
v = -(0.1 kg * 9.8 m/s^2) / (I * 1 s * 5 T)

To determine the terminal velocity of the slider, we need to consider the forces acting on it. There are two main forces at play in this situation: the gravitational force and the electromagnetic force due to the magnetic field.

1. Gravitational Force:
The gravitational force acting on the slider is given by the equation: F_gravity = m*g, where m is the mass of the slider and g is the acceleration due to gravity. In this case, the mass of the slider is 100 grams, which is equivalent to 0.1 kg, and the acceleration due to gravity is approximately 9.8 m/s^2.

So, the gravitational force is: F_gravity = 0.1 kg * 9.8 m/s^2 = 0.98 N.

2. Electromagnetic Force:
The electromagnetic force acting on the slider is given by the equation: F_em = B * I * L, where B is the magnetic field strength, I is the current flowing through the slider, and L is the length of the slider across the magnetic field.

In this case, the magnetic field strength is 5 Tesla, and the length of the slider is the width of the U-shaped track, which is 50 cm or 0.5 meters.

The current flowing through the slider can be determined using Ohm's Law: V = I * R, where V is the voltage across the slider and R is its resistance. The voltage across the slider can be approximated to the gravitational potential energy difference between its highest and lowest positions.

The gravitational potential energy difference is given by: ΔPE = m * g * h, where h is the height difference between the highest and lowest positions. In this case, since the slider is falling freely, the height difference is the height of the U-shaped track, which is also 0.5 meters.

So, the voltage across the slider is: V = ΔPE = 0.1 kg * 9.8 m/s^2 * 0.5 m = 0.49 J.

Now, we can use Ohm's Law to find the current: I = V / R = 0.49 J / 20 Ω = 0.0245 A.

Substituting the values into the electromagnetic force equation, we have: F_em = 5 T * 0.0245 A * 0.5 m = 0.06125 N.

3. Terminal Velocity:
The terminal velocity occurs when the gravitational force and the electromagnetic force are balanced. So, we can equate these forces and solve for the velocity.

F_gravity = F_em
0.98 N = 0.06125 N

Now, we can use Newton's second law (F = m*a) to determine the acceleration at terminal velocity. The acceleration is given by a = F_net / m, where F_net is the net force acting on the slider.

At terminal velocity, the net force is zero, so:

0 = F_net = F_gravity - F_em
0 = 0.98 N - 0.06125 N

Now, we can solve for the acceleration:

a = 0 / 0.1 kg = 0 m/s^2

Since the acceleration is zero, the slider is at its terminal velocity. Therefore, the terminal velocity of the slider is 0 m/s.

To summarize, the terminal velocity of the resistive slider in this scenario is 0 meters/second, indicating that it will not continue to fall once it reaches this speed.