**Mag**

**-lift**

Joshua Cage

Chris Potters

Magnetic Levitation

Mg = Mass X Gravity

V = Velocity

R = Reaction

Fr = Force of Resistance

μ = Coefficient of friction = Tan(θ)

Mg = Mass X Gravity

V = Velocity

R = Reaction

Fr = Force of Resistance

μ = Coefficient of friction = Tan(θ)

Mg = R

Mg (Maglev) = 144g = R

Mg (Car) = 76g = R

For the first instance before the car moves, Mg = R

The force Mg and the Reaction (R) make an angle that is equal to angle θ (which defines the slope of the surface).

To calculate the force of R, we can use the Cos(θ). Since Cos = Adjacent / Hypotenuse, we plug in the numbers accordingly.

Cos(0.003266) = (R / 144)

(144)Cos(0.003266) = (R / 144) (144)������

(144)Cos(0.003266) = R

Cos(3.67) = (R / 144)

(144)Cos(3.67) = (R / 144) (144)������

(144)Cos(3.67) = R

Mg (Maglev) = 144g = R

Mg (Car) = 76g = R

For the first instance before the car moves, Mg = R

The force Mg and the Reaction (R) make an angle that is equal to angle θ (which defines the slope of the surface).

To calculate the force of R, we can use the Cos(θ). Since Cos = Adjacent / Hypotenuse, we plug in the numbers accordingly.

**Mag****Lev:**Cos(0.003266) = (R / 144)

(144)Cos(0.003266) = (R / 144) (144)������

(144)Cos(0.003266) = R

**144 = R****Car:**Cos(3.67) = (R / 144)

(144)Cos(3.67) = (R / 144) (144)������

(144)Cos(3.67) = R

**143.705 = R**

Since we now know what the force of reaction is at angle θ, we can now use the formula:

Fr = μ * R

Since [R = Mg * Sin(θ)] , we can plug that in for R. And since [Fr = Mg * μ * Cos (θ)], we can set them equal to each other.

Mg * Sin(θ) = Mg * μ * Cos(θ)

Divide both sides by Mg.

Sin(θ) = μ * Cos(θ)

Divide by Cos(θ)

Sin(θ) / Cos(θ) = μ

μ = Tan(θ)

Fr = μ * R

Since [R = Mg * Sin(θ)] , we can plug that in for R. And since [Fr = Mg * μ * Cos (θ)], we can set them equal to each other.

Mg * Sin(θ) = Mg * μ * Cos(θ)

Divide both sides by Mg.

Sin(θ) = μ * Cos(θ)

Divide by Cos(θ)

Sin(θ) / Cos(θ) = μ

μ = Tan(θ)

**μ****(Car) = Tan(3.67) = 0.06572****μ****(Mag- Lev) = Tan(0.003266) = 0.000057**

When car begins to move it means that Mg > R