Answer:
K = 2 10⁻⁸ J
Explanation:
Let's solve this exercise in parts, we start by finding the charge on each plate of the capacitor
C = Q / ΔV
C = ε₀ A / d
ε₀ A / d = Q / ΔV
Q = ε₀ A ΔV / d (1)
indicate the potential difference ΔV₁ = 12 V, the distance between the plates d₁ = 3 mm = 0.003 m,
as the power supply is disconnected and the capacitor is ideal the charge remains constant
in the second part we separate the plates at d₂ = 5 mm = 0.005 m, using equation 1
ΔV₂ = 
we substitute the equation for Q
ΔV₂ = 
ΔV₂ = 
in the third part we use the concepts of energy
starting point. Test charge near positive plate
Em₀ = U = q ΔV₂
final point. Test charge near negative plate
Em_f = K
energy is conserved
Em₀ = Em_f
q ΔV₂ = K
K = q ΔV₁ 
we calculate
K = 1 10⁻⁹ 12 0.005/0.003
K = 2 10⁻⁸ J
Answer:
Explanation:
1 ) Total mechanical energy of the car at the height of 10 m
1/2 mv² + mgh
.5 x 1800 x 25² + 1800 x 9.8 x 10 m
= 562500 + 176400
738900 J
If v be the velocity at the bottom ,
Total energy of the car at the bottom
1/2 m v² + 0
Applying conservation of energy
1/2 mv² = 738900
.5 x 1800 v² = 738900
v = 28.65 m /s
Energy required by car to ascend height of 15 m
1800 x 9.8 x 15
= 264600 J
b )
This energy is more that total energy of the car at the top that is 738900 J
so car can easily reach gas station .
If V be the velocity at the gas point
Total energy at the gas point
1/2 m V² + 264600
Applying conservation of energy
1/2 m V² + 264600 =738900
.5 x 1800 x V² = 474300
V = 22.95 m / s
d ) If R be the normal reaction at the bottom
net force
R - mg = m v² / r
R = m ( g + v² / r )
1800 ( 9.8 + 28.65² / 5 )
R = 313136 N
Answer:
F = 0.0545 N
Explanation:
Let's use Newton's second law for rotational movement
τ = I α
The moment of inertia for a bar supported by some ends is
I = 1/3 m L²
Torque is
τ = F L
Let's replace
F L = 1/3 m L² α
F = 1/3 m L α
Let's reduce angular acceleration to SI units
Alf = 26º / s² (π rad / 180º) = 0.454 rad / s²
Let's calculate
F = 1/3 0.5 0.72 0.454
F = 0.0545 N
Driving a motor........
chemical energy is converted into kinetic energy.
Falling off of cliff
.........gravitational potential energy is converted into kinetic energy.
Hydroelectric energy generation
.......gravitational potential energy is converted into kinetic energy (i.e. driving a generator), which is then converted into electrical energy.
Nuclear power generation
.........mass is converted into energy, which then drives a steam turbine, which is then converted into electrical energy.
