By the law of universal gravitation, the gravitational force <em>F</em> between the satellite (mass <em>m</em>) and planet (mass <em>M</em>) is
<em>F</em> = <em>G</em> <em>M</em> <em>m</em> / <em>R </em>²
where
<em>• G</em> = 6.67 × 10⁻¹¹ m³/(kg•s²) is the universal gravitation constant
• <em>R</em> = 2500 km + 5000 km = 7500 km is the distance between the satellite and the center of the planet
Solve for <em>M</em> :
<em>M</em> = <em>F R</em> ² / (<em>G</em> <em>m</em>)
<em>M</em> = ((3 × 10⁴ N) (75 × 10⁵ m)²) / (<em>G</em> (6 × 10³ kg))
<em>M</em> ≈ 2.8 × 10¹⁴ kg
Answers:
a) 10 m
b) time=1.6 s, frquency=0.625 Hz
c) 6.25 m/s
Explanation:
a) If there is a crest at each dock and another three crests between the two docks, and the wavelength is the distance between to crests; this means we have in :
Clearing :
b) This part can be solved by a Rule of Three:
If 10 waves ---- 16 s
1 wave -----
Then:
This is the period of the wave
On the other hand, the frequency of the wave has an inverse relation with its period :
This is the frequency of the wave
c) The speed of a wave is given by the following equation:
Finally:
Answer:
Part A) the angular acceleration is α= 44.347 rad/s²
Part B) the angular velocity is 195.13 rad/s
Part C) the angular velocity is 345.913 rad/s
Part D ) the time is t= 7.652 s
Explanation:
Part A) since angular acceleration is related with angular acceleration through:
α = a/R = 10.2 m/s² / 0.23 m = 44.347 rad/s²
Part B) since angular acceleration is related
since
v = v0 + a*(t-t0) = 51.0 m/s + (-10.2 m/s²)*(3.4 s - 2.8 s) = 44.88 m/s
since
ω = v/R = 44.88 m/s/ 0.230 m = 195.13 rad/s
Part C) at t=0
v = v0 + a*(t-t0) = 51.0 m/s + (-10.2 m/s²)*(0 s - 2.8 s) = 79.56 m/s
ω = v/R = 79.56 m/s/ 0.230 m = 345.913 rad/s
Part D ) since the radial acceleration is related with the velocity through
ar = v² / R → v= √(R * ar) = √(0.23 m * 9.81 m/s²)= 1.5 m/s
therefore
v = v0 + a*(t-t0) → t =(v - v0) /a + t0 = ( 1.5 m/s - 51.0 m/s) / (-10.2 m/s²) + 2.8 s = 7.652 s
t= 7.652 s
Answer:
40 N/m
Explanation:
F = -kx (This is the Hooke's Law equation)
F is the force the spring exerts = 8 N
-k = spring constant
x = displacement (The distance stretched past it's natural length) = 20cm
x needs to be in meters, and 20 cm is = to 0.2 meters
Finally:
8N = -k (0.2m)
-k = 8N / 0.2 m
k = -40 N/m
Anything less dense than water will float, like oil. Anything more dense than water will sink, like rock.