F = G mM / r^2, where
<span>F = gravitational force between the earth and the moon, </span>
<span>G = Universal gravitational constant = 6.67 x 10^(-11) Nm^2/(kg)^2, </span>
<span>m = mass of the moon = 7.36 × 10^(22) kg </span>
<span>M = mass of the earth = 5.9742 × 10^(24) and </span>
<span>r = distance between the earth and the moon = 384,402 km </span>
<span>F </span>
<span>= 6.67 x 10^(-11) * (7.36 × 10^(22) * 5.9742 × 10^(24) / (384,402 )^2 </span>
<span>= 1.985 x 10^(26) N</span>
D. There is a known constant concentration of C14 in Nature. As we consume living things to survive our bodies (made of carbon) stop replenishing our body's carbon (we stop eating) and start to decay. Since we know the 1/2 life of C14 and the ratio of C14 to normal C12 we can determine fairly accurately how long ago a thing stopped consuming carbon (e.g. when it died)
Answer:
-20.0 m/s and 30.0 m/s
Explanation:
Momentum is conserved:
m (30.0) + m (-20.0) = m v₁ + m v₂
30.0 − 20.0 = v₁ + v₂
10.0 = v₁ + v₂
Since the collision is perfectly elastic, energy is also conserved. Since there's no rotational energy or work done by friction, the initial kinetic energy equals the final kinetic energy.
½ m (30.0)² + ½ m (-20.0)² = ½ mv₁² + ½ mv₂²
(30.0)² + (-20.0)² = v₁² + v₂²
1300 = v₁² + v₂²
We now have two equations and two variables. Solve the system of equations using substitution:
1300 = v₁² + (10 − v₁)²
1300 = v₁² + 100 − 20v₁ + v₁²
0 = 2v₁² − 20v₁ − 1200
0 = v₁² − 10v₁ − 600
0 = (v₁ + 20) (v₁ − 30)
v₁ = -20, 30
If v₁ = -20, v₂ = 30.
If v₁ = 30, v₂ = -20.
So either way, the final velocities are -20.0 m/s and 30.0 m/s.
