Answer:
83%
Explanation:
On the surface, the weight is:
W = GMm / R²
where G is the gravitational constant, M is the mass of the Earth, m is the mass of the shuttle, and R is the radius of the Earth.
In orbit, the weight is:
w = GMm / (R+h)²
where h is the height of the shuttle above the surface of the Earth.
The ratio is:
w/W = R² / (R+h)²
w/W = (R / (R+h))²
Given that R = 6.4×10⁶ m and h = 6.3×10⁵ m:
w/W = (6.4×10⁶ / 7.03×10⁶)²
w/W = 0.83
The shuttle in orbit retains 83% of its weight on Earth.
Answer:
d = 2021.6 km
Explanation:
We can solve this distance exercise with vectors, the easiest method s to find the components of the position of each plane and then use the Pythagorean theorem to find distance between them
Airplane 1
Height y₁ = 800m
Angle θ = 25°
cos 25 = x / r
sin 25 = z / r
x₁ = r cos 20
z₁ = r sin 25
x₁ = 18 103 cos 25 = 16,314 103 m
= 16314 m
z₁ = 18 103 sin 25 = 7,607 103 m= 7607 m
2 plane
Height y₂ = 1100 m
Angle θ = 20°
x₂ = 20 103 cos 25 = 18.126 103 m = 18126 m
z₂ = 20 103 without 25 = 8.452 103 m = 8452 m
The distance between the planes using the Pythagorean Theorem is
d² = (x₂-x₁)² + (y₂-y₁)² + (z₂-z₁)²2
Let's calculate
d² = (18126-16314)² + (1100-800)² + (8452-7607)²
d² = 3,283 106 +9 104 + 7,140 105
d² = (328.3 + 9 + 71.40) 10⁴
d = √(408.7 10⁴)
d = 20,216 10² m
d = 2021.6 km
Answer:
The change in gravitational potential energy of the hiker = 2869685 J
Explanation:
Potential Energy: This is the energy possessed by a body, due to its change in position in the gravitational field. The unit of potential energy is Joules (J)
From the question,
Change in gravitational potential energy = Energy of the hiker at the top of Mt. Whitney - Energy of the hiker at the floor of Death valley.
ΔEp = mgh₂ - mgh₁
ΔEp = mg(h₂-h₁)........................... Equation 1
Where ΔEp = change in Potential Energy of the hiker, m = mass of the hiker, g = acceleration due to gravity, h₁ = lowest point in Death valley, h₂ = Elevation of Mt. Whitney.
Given: m = 65.0 kg, h₁ = -85 m ( because is a valley), h₂ = 4420 m,
Constant: g = 9.8 m/s²
Note: The h₁ is negative because is below sea level.
Substituting into equation 1
ΔEp = 65×9.8×[4420-(-85)]
ΔEp = 637(4420+85)
ΔEp = 637(4505)
ΔEp = 2869685
ΔEp = 2869685 J.
Thus the change in gravitational potential energy of the hiker = 2869685 J
Answer:
The options are approximations of the exact answers:
A) 
B) 
C) 
D) Toward the inner wall
E) 
Explanation:
A) The electric field in a parallel plate capacitor is given by the formula 
, where 
and in our case 
and, for air,
, so we have:
B) The K+ ion has one elemental charge excess, so its charge is 
, and the force a charge experiments under an electric field E is given by F=qE, so we have:
C) The potential difference between two points separated a distance d under an uniform electric potential E is given by 
, so we have:
D) The electic field goes from positive to negative charges, so it goes towards the inner wall.
E) The work done by an electric field through a potential difference 
on a charge Q is 
, and is equal to the kinetic energy imparted on it, so we have:
Answer:
ω = 4.07 rad/s
Explanation:
By conservation of the energy:
W = ΔK
where 
Solving for ω:
