To solve this problem it is necessary to apply the concepts related to the conservation of the Gravitational Force and the centripetal force by equilibrium,
![F_g = F_c](https://tex.z-dn.net/?f=F_g%20%3D%20F_c)
![\frac{GmM}{r^2} = \frac{mv^2}{r}](https://tex.z-dn.net/?f=%5Cfrac%7BGmM%7D%7Br%5E2%7D%20%3D%20%5Cfrac%7Bmv%5E2%7D%7Br%7D)
Where,
m = Mass of spacecraft
M = Mass of Earth
r = Radius (Orbit)
G = Gravitational Universal Music
v = Velocity
Re-arrange to find the velocity
![\frac{GM}{r^2} = \frac{v^2}{r}](https://tex.z-dn.net/?f=%5Cfrac%7BGM%7D%7Br%5E2%7D%20%3D%20%5Cfrac%7Bv%5E2%7D%7Br%7D)
![\frac{GM}{r} = v^2](https://tex.z-dn.net/?f=%5Cfrac%7BGM%7D%7Br%7D%20%3D%20v%5E2)
![v = \sqrt{\frac{GM}{r}}](https://tex.z-dn.net/?f=v%20%3D%20%5Csqrt%7B%5Cfrac%7BGM%7D%7Br%7D%7D)
PART A ) The radius of the spacecraft's orbit is 2 times the radius of the earth, that is, considering the center of the earth, the spacecraft is 3 times at that distance. Replacing then,
![v = \sqrt{\frac{(6.67*10^{-11})(5.97*10^{24})}{3*(6.371*10^6)}}](https://tex.z-dn.net/?f=v%20%3D%20%5Csqrt%7B%5Cfrac%7B%286.67%2A10%5E%7B-11%7D%29%285.97%2A10%5E%7B24%7D%29%7D%7B3%2A%286.371%2A10%5E6%29%7D%7D)
![v = 4564.42m/s](https://tex.z-dn.net/?f=v%20%3D%204564.42m%2Fs)
From the speed it is possible to use find the formula, so
![T = \frac{2\pi r}{v}](https://tex.z-dn.net/?f=T%20%3D%20%5Cfrac%7B2%5Cpi%20r%7D%7Bv%7D)
![T = \frac{2\pi (6.371*10^6)}{4564.42}](https://tex.z-dn.net/?f=T%20%3D%20%5Cfrac%7B2%5Cpi%20%286.371%2A10%5E6%29%7D%7B4564.42%7D)
![T = 8770.05s\approx 146min\approx 2.4hour](https://tex.z-dn.net/?f=T%20%3D%208770.05s%5Capprox%20146min%5Capprox%202.4hour)
Therefore the orbital period of the spacecraft is 2 hours and 24 minutes.
PART B) To find the kinetic energy we simply apply the definition of kinetic energy on the ship, which is
![KE = \frac{1}{2} mv^2](https://tex.z-dn.net/?f=KE%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20mv%5E2)
![KE = \frac{1}{2} (100)(4564.42)^2](https://tex.z-dn.net/?f=KE%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%28100%29%284564.42%29%5E2)
![KE = 1.0416*10^9J](https://tex.z-dn.net/?f=KE%20%3D%201.0416%2A10%5E9J)
Therefore the kinetic energy of the Spacecraft is 1.04 Gigajules.
Answer:
2.5 m/s
Explanation:
Mechanical energy is the sum of the potential and kinetic energy.
E = PE + KE
E = mgh + ½mv²
172.1 J = (7.26 kg) (9.8 m/s²) (2.1 m) + ½ (7.26 kg) v²
v = 2.5 m/s
The density is determined on the steepness of the slope. The greater the density is bases upon the steepest slope. To conclude, I'd say Line A has the steepest slope therefore has the greatest density.
Hi there!
We know that:
Force due to gravity = Mgsinθ
Force due to friction = μMgcosθ
Let the positive direction be directed in the direction of the block's acceleration, which is downward.
Thus:
ΣF = Mgsinθ - μMgcosθ
Solving for acceleration requires diving all terms by the mass, so:
a = gsinθ - μgcosθ
Substitute in given values. (g = 9.8 m/s²)
a = 9.8sin(30) - 0.3(9.8)cos(30) = 2.354 m/s²
Answer:
4.8 mph
Explanation:
From the question,
Average speed = total distance/total time
V = d/t....................... Equation 1
Where d = distance, t = time
Given: d = 26.2 miles, t = 5.5 hours.
Substitute these values into equation 1
V = 26.2/5.5
V = 4.76 mph
V ≈ 4.8 mph