Okay, first off, the formula for Kinetic Energy is:
<em>KE = 1/2(m)(v)^2</em>
<em>m = mass</em>
<em>v = velcoity (m/s)</em>
Using this formula, we can then calculate the kinetic energy in each scenario:
1) KE = 1/2(100)(5)^2 = 1,250 J
2) KE = 1/2(1000)(5)^2 = 12,500 J
3) KE = 1/2(10)(5)^2 = 125 J
4) KE = 1/2(100)(5)^2 = 1,250 J
Answer:
18.1 × 10⁻⁶ A = 18.1 μA
Explanation:
The current I in the wire is I = ∫∫J(r)rdrdθ
Since J(r) = Br, in the cylindrical wire. With width of 10.0 μm, dr = 10.0 μm. r = 1.20 mm. We have a differential current dI. We integrate first by integrating dθ from θ = 0 to θ = 2π.
So, dI = J(r)rdrdθ
dI/dr = ∫J(r)rdθ = ∫Br²dθ = Br²∫dθ = 2πBr²
Now I = (dI/dr)dr at r = 1.20 mm = 1.20 × 10⁻³ m and dr = 10.0 μm = 0.010 mm = 0.010 × 10⁻³ m
I = (2πBr²)dr = 2π × 2.00 × 10⁵ A/m³ × (1.20 × 10⁻³ m)² × 0.010 × 10⁻³ m = 0.181 × 10⁻⁴ A = 18.1 × 10⁻⁶ A = 18.1 μA
To solve this problem we will apply the concepts related to energy conservation. Here we will understand that the potential energy accumulated on the object is equal to the work it has. Therefore the relationship that will allow us to calculate the height will be
Here,
m = mass
g = Acceleration due to gravity
h = Height
our values are,
Replacing,
Then the height is 32.83m.
