Yes the plot dose make it with out baking out
Answer:
ΔT = 302 °c
Explanation:
mass (m) = 4.6 g = 0.0046 kg
velocity (v) = 278 m/s
specific heat of lead (c) = 128 J/kg. °c
kinetic energy = 0.5 mx 
kinetic energy = 0.5 x 0.0046 x 
kinetic energy = 177.8 J
since all the kinetic energy is converted to thermal energy,
kinetic energy = thermal energy (E) = 177.8 J
thermal energy = m x c x ΔT
where ΔT is the temperature change
177.8 = 0.0046 x 128 x ΔT
ΔT = 177.8 / 0.59
ΔT = 302 °c
Answer:
ΔΦ = -3.39*10^-6
Explanation:
Given:-
- The given magnetic field strength B = 0.50 gauss
- The angle between earth magnetic field and garage floor ∅ = 20 °
- The loop is rotated by 90 degree.
- The radius of the coil r = 19 cm
Find:
calculate the change in the magnetic flux δφb, in wb, through one of the loops of the coil during the rotation.
Solution:
- The change on flux ΔΦ occurs due to change in angle θ of earth's magnetic field B and the normal to circular coil.
- The strength of magnetic field B and the are of the loop A remains constant. So we have:
Φ = B*A*cos(θ)
ΔΦ = B*A*( cos(θ_1) - cos(θ_2) )
- The initial angle θ_1 between the normal to the coil and B was:
θ_1 = 90° - ∅
θ_1 = 90° - 20° = 70°
The angle θ_2 after rotation between the normal to the coil and B was:
θ_2 = ∅
θ_2 = 20°
- Hence, the change in flux can be calculated:
ΔΦ = 0.5*10^-4*π*0.19*( cos(70) - cos(20) )
ΔΦ = -3.39*10^-6
To minimize the material usage we have to have the volume requested with the minimum surface area.
The volume is:

And the surface is:

From the first equation we get:

I will use k instead of a number just for the conveince.
We plug this into the second equation and we get:

To find the minimum of this function we have to find the zeros of its first derivative.
Sx will denote the first derivative with respect to x and Sy will denote the first derivative with respect to Sy.

Now let both derivatives go to zero and solve the system (this will give us the so-called critical points).

Now we plug in the first equation into the other and we get:

Now we can calculate y:

And finaly we calculate z:

And finaly let's check our result:
Explanation:
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