Answer:
Explanation:
1) Basic concepts
Apogee: is the maximum distance for an object orbiting the Earth. For this case the distance for the apogee would be the sum of radius for the earth and 2289 km.
Perigee: Minimum distance of an object orbiting the Earth. For this case the distance for the perigee would be the sum of radius for the earth and 459 km.
A good approximation for these terms are related to the figure atached.
Isolated system: That happens when the system is not subdued to an external torque, on this case the change of angular momentum would be 0.
2) Notation and data
radius for the Earth, looking for this value on a book we got
, represent the radius for perigee
, represent the radius for perigee
, period
velocity of the perigee
velocity of the apogee
is the variable of interest represented the ratio for the speed of the perigee to the speed of the apogee
3) Formulas to use
We don't have torque from the gravitational force since is a centered force. So the change of momentum is 0
(1)
(2)
From the definition of angular momentum we have , replacing this into equation (2) we got:
(3)
We can cancel the mass on both sides
(4)
And solving we got:
(5)
And replacing the values obtained into equation (5) we got:
And this would be the final answer
Answer: d = 33 cm or 0.33 m
Explanation: In physics, Work is the amount of energy transferred to an object to make it move. It can be expressed by:
W = F.d.cosθ
F is the force applied to the object, d is the displacement and θ is the angle formed between the force and the displacement.
For the ice block, the angle is 0, i.e., force and distance are at the same direction, so:
W = F.d.cos(0)
W = F.d
To determine d:
d =
d =
d = 0.33 m
The distance d the block ice moved is 33 cm.
Answer:
7.9060 m²
8.57 Volts
5.142×10⁻⁶ Joule
1.2×10⁻⁶ Coulomb
Explanation:
C = Capacitance between plates = 0.14 μF = 0.14×10⁻⁶ F
d = Distance between plates = 0.5 mm = 0.5×10⁻³ m
Q = Charge = 1.2 μC = 1.2×10⁻⁶ C
ε₀ = Permittivity = 8.854×10⁻¹² F/m
Capacitance
∴ Area of each plate is 7.9060 m²
Voltage
∴ Potential difference between the plates if the capacitor is charged to 1.2 μC is 8.57 Volts.
Energy stored
E=0.5CV²
⇒E = 0.5×0.14×10⁻⁶×8.57²
⇒E = 5.142×10⁻⁶ Joule
∴ Stored energy is 5.142×10⁻⁶ Joule
Charge
Q = CV
⇒Q = 0.14×10⁻⁶×8.57
⇒Q = 1.2×10⁻⁶ C
∴ Charge the capacitor carries before a spark occurs between the two plates is 1.2×10⁻⁶ Coulomb