TLDR: It will reach a maximum when the angle between the area vector and the magnetic field vector are perpendicular to one another.
This is an example that requires you to investigate the properties that occur in electric generators; for example, hydroelectric dams produce electricity by forcing a coil to rotate in the presence of a magnetic field, generating a current.
To solve this, we need to understand the principles of electromotive forces and Lenz’ Law; changing the magnetic field conditions around anything with this potential causes an induced current in the wire that resists this change. This principle is known as Lenz’ Law, and can be described using equations that are specific to certain situations. For this, we need the two that are useful here:
e = -N•dI/dt; dI = ABcos(theta)
where “e” describes the electromotive force, “N” describes the number of loops in the coil, “dI” describes the change in magnetic flux, “dt” describes the change in time, “A” describes the area vector of the coil (this points perpendicular to the loops, intersecting it in open space), “B” describes the magnetic field vector, and theta describes the angle between the area and mag vectors.
Because the number of loops remains constant and the speed of the coils rotation isn’t up for us to decide, the only thing that can increase or decrease the emf is the change in magnetic flux, represented by ABcos(theta). The magnetic field and the size of the loop are also constant, so all we can control is the angle between the two. To generate the largest emf, we need cos(theta) to be as large as possible. To do this, we can search a graph of cos(theta) for the highest point. This occurs when theta equals 90 degrees, or a right angle. Therefore, the electromotive potential will reach a maximum when the angle between the area vector and the magnetic field vector are perpendicular to one another.
Hope this helps!
Answer:
0.06 N
1.08 m/s
Explanation:
m = mass of the fan cart = 0.250 kg
a = acceleration of the fan cart = 24 cm/s² = 0.24 m/s²
F = Net force on the cart
Net force on the cart is given as
F = ma
F = (0.250) (0.24)
F = 0.06 N
v₀ = initial velocity of the cart = 0 m/s
v = final velocity of the cart
t = time interval = 4.5 s
Using the equation
v = v₀ + a t
v = 0 + (0.24) (4.5)
v = 1.08 m/s
Answer:
0.505 m
Explanation:
From the question,
The kinetic energy of the car = energy stored in the spring
1/2mv² = 1/2ke²...................... Equation 1
Where m = mass of the car, v = velocity of the car, k = spring constant of the car, e = extension/compression
make e the subject of the equation
e = v√(m/k)............... Equation 2
We can calculate the value of v, by applying,
v² = u²+2gH...................... Equation 3
Where u = initial velocity of the car, H = height of the car, g = acceleration due to gravity.
Given: u = 0 m/s (from rest), H, 10 m, g = 9.8 m/s²
Substitute into equation 2
v² = 2(10×9.8)
v² = 196
v = √196
v = 14 m/s
Also given: m = 1300 kg, e = 1.0×10⁶ N/m =1000000 N/m
Substitute into equation 2
e = 14√(1300/1000000)
e = 14√(0.00013)
e = 14(0.036)
e = 0.505 m
Hence the maximum distance of the spring is compressed = 0.505 m
