Answer:
3.64×10⁸ m
3.34×10⁻³ m/s²
Explanation:
Let's define some variables:
M₁ = mass of the Earth
r₁ = r = distance from the Earth's center
M₂ = mass of the moon
r₂ = d − r = distance from the moon's center
d = distance between the Earth and the moon
When the gravitational fields become equal:
GM₁m / r₁² = GM₂m / r₂²
M₁ / r₁² = M₂ / r₂²
M₁ / r² = M₂ / (d − r)²
M₁ / r² = M₂ / (d² − 2dr + r²)
M₁ (d² − 2dr + r²) = M₂ r²
M₁d² − 2dM₁ r + M₁ r² = M₂ r²
M₁d² − 2dM₁ r + (M₁ − M₂) r² = 0
d² − 2d r + (1 − M₂/M₁) r² = 0
Solving with quadratic formula:
r = [ 2d ± √(4d² − 4 (1 − M₂/M₁) d²) ] / 2 (1 − M₂/M₁)
r = [ 2d ± 2d√(1 − (1 − M₂/M₁)) ] / 2 (1 − M₂/M₁)
r = [ 2d ± 2d√(1 − 1 + M₂/M₁) ] / 2 (1 − M₂/M₁)
r = [ 2d ± 2d√(M₂/M₁) ] / 2 (1 − M₂/M₁)
When we plug in the values, we get:
r = 3.64×10⁸ m
If the moon wasn't there, the acceleration due to Earth's gravity would be:
g = GM / r²
g = (6.672×10⁻¹¹ N m²/kg²) (5.98×10²⁴ kg) / (3.64×10⁸ m)²
g = 3.34×10⁻³ m/s²
We are given that the maximum mass capacity is 1 metric
ton or 1000 kg. Therefore the amount of people this can hold is simply the
ratio of the maximum mass capacity over the mass of the person, that is:
people = 1000 kg / 91 kg
people = 10.98
So the elevator can safely occupy 10 people. We will not exceed to 11.
B
Think of inertia of getting into a car accident without a seat belt although the car stops you will not you would likely fly out the window
Answer: 6s
Explanation:
Vs=32m/s speed at beginning of slowing down
Vf=0m/s stop speed
a= -6 m/s² acceleration
----------------
Use equation for acceleration :
a=(Vf-Vs)/t
a*t=Vf-Vs
t=(Vf-Vs)/a
t=(0-36)/-6
t=-36/-6
t=6 s
Answer:
Explanation:
a) ωp = 2π radians / 1.7 s = <u>3.7 rad/s</u>
b) ωs = 3.7 rad/s(9.5 cm / 4.5 cm) = 7.8 rad/s
v = (ωs)R = 7.8(65) = 507 cm/s or <u>5.1 m/s</u>
c) ωs = 3.5 m/s / 0.65 m = 5.38 rad/s
ωp = 5.38(4.5 cm / 9.5 cm) = 2.55 rad/s
t = θ/ω = 2π / 2.55 = 2.463... <u>2.5 s</u>
