Answer:
Option (e)
Explanation:
A = 45 cm^2 = 0.0045 m^2, d = 0.080 mm = 0.080 x 10^-3 m,
Energy density = 100 J/m
Let Q be the charge on the plates.
Energy density = 1/2 x ε0 x E^2
100 = 0.5 x 8.854 x 10^-12 x E^2
E = 4.75 x 10^6 V/m
V = E x d
V = 4.75 x 10^6 x 0.080 x 10^-3 = 380.22 V
C = ε0 A / d
C = 8.854 x 10^-12 x 45 x 10^-4 / (0.080 x 10^-3) = 4.98 x 10^-10 F
Q = C x V = 4.98 x 10^-10 x 380.22 = 1.9 x 10^-7 C
Q = 190 nC
Answer:
W = 1,307 10⁶ J
Explanation:
Work is the product of force by distance, in this case it is the force of gravitational attraction between the moon (M) and the capsule (m₁)
F = G m₁ M / r²
W = ∫ F. dr
W = G m₁ M ∫ dr / r²
we integrate
W = G m₁ M (-1 / r)
We evaluate between the limits, lower r = R_ Moon and r = ∞
W = -G m₁ M (1 /∞ - 1 / R_moon)
W = G m1 M / r_moon
Body weight is
W = mg
m = W / g
The mass is constant, so we can find it with the initial data
For the capsule
m = 1000/32 = 165 / g_moon
g_moom = 165 32/1000
.g_moon = 5.28 ft / s²
I think it is easier to follow the exercise in SI system
W_capsule = 1000 pound (1 kg / 2.20 pounds)
W_capsule = 454 N
W = m_capsule g
m_capsule = W / g
m = 454 /9.8
m_capsule = 46,327 kg
Let's calculate
W = 6.67 10⁻¹¹ 46,327 7.36 10²² / 1.74 10⁶
W = 1,307 10⁶ J
C most of the Earths weather occurs in this layer.
The formula to use is the one that connects the acceleration,
the distance fallen, and the time spent falling:
Distance = 1/2 a T² .
You said 2.1 meters in 0.6 second .
2.1 m = 1/2 a (0.6 sec)²
Multiply each side by 2 : 4.2 m = a (0.6 sec)²
Divide each side by (0.6 sec)² = (4.2/0.36) m/s² = a
a = (11 and 2/3) m/s²
(about 19% more than Earth's gravity)
You can do this two ways:
1). Whatever kinetic energy the rolling ball has is the amount
of energy you have to absorb in order to stop it.
2). Whatever momentum the rolling ball has is the amount of
momentum you have to provide in the other direction to cancel it.
Since you asked about force and time, we sense 'impulse' in the
air, and we know that impulse is exactly a change in momentum.
So let's use #2 and talk about momentum and impulse.
Impulse = (force) x (time)
Momentum of a moving object is (mass) x (speed) .
-- Momentum of the first ball: (8 kg) x (0.2 m/s) = 1.6 kg-m/s
Impulse required to stop it = 1.6 kg-m/s
(force) x (10 sec) = 1.6
Force required = 1.6 / 10 = 0.16 Newton .
-- Momentum of the second ball: (4 kg) x (1 m/s) = 4 kg-m/s
Impulse required to stop it = 4 kg-m/s
(force) x (10 sec) = 4
Force required = 4 / 10 = 0.4 Newton .
You need more force o stop the second ball. Although its mass
is only 1/2 the mass of the 8kg ball, it's moving 5 times as fast,
and has 2.5 times the momentum of the bigger ball.
So you need 2.5 times as much impulse to stop it.
If you're going to push on each ball for the same length of time,
then you need to push 2.5 times as hard on the smaller ball in
order to stop it.
