A physicist models gravity on a planet in another galaxy. Compared with its value on Earth, G there is…
How strongly does Earth attract the Moon? 'Very strongly' is not an answer. This lesson gets the number, in newtons.
Newton's law gives it. The routine is the same three steps you have used all course.
Step 1: write down what we know, and mark what we need to find.
Step 2: select the correct equation. Here it is Newton's law: F = G m₁m₂ / r². Step 3: substitute in the values, and calculate.
The one new wrinkle is scientific notation: planet masses arrive as powers of ten. Keep each value as its number times its power of ten, substitute the whole thing, and let the calculator carry the powers.
Earth (mass 6.0 × 10²⁴ kg) and the Moon (mass 7.3 × 10²² kg) have centers 3.8 × 10⁸ m apart. Calculate the gravitational force between them.
Write down the values in the question:
m₁ = 6.0 × 10²⁴ kg
m₂ = 7.3 × 10²² kg
r = 3.8 × 10⁸ m
G = 6.67 × 10⁻¹¹ N·m²/kg²
F = ?
Write down the equation:
F = G m₁m₂ / r²
Substitute in the values:
F = (6.67 × 10⁻¹¹)(6.0 × 10²⁴)(7.3 × 10²²) / (3.8 × 10⁸)²
Simplify:
F = 2.0 × 10²⁰ N (2 significant figures)
An 800 kg satellite's center sits 8.0 × 10⁶ m from Earth's center (Earth: 6.0 × 10²⁴ kg). Which substitution is correct?
Carry out that calculation: enter the force on the 800 kg satellite, in newtons.
The Moon (mass 7.3 × 10²² kg) and a 2,400 kg orbiter have centers 2.0 × 10⁶ m apart. Calculate the force between them.
Write down the values in the question:
m₁ = 7.3 × 10²² kg
m₂ = 2,400 kg
r = 2.0 × 10⁶ m
G = 6.67 × 10⁻¹¹ N·m²/kg²
F = ?
Write down the equation:
F = G m₁m₂ / r²
Substitute in the values:
F = (6.67 × 10⁻¹¹)(7.3 × 10²²)(2400) / (2.0 × 10⁶)²
Simplify:
F = 2.9 × 10³ N (2 significant figures)
Planet W (4.0 × 10²⁴ kg) and its moon (2.0 × 10²² kg) have centers 4.0 × 10⁸ m apart. Enter the force between them, in newtons.
A student computes the pull between Earth and a satellite but divides by r instead of r². Compared with the true force, the computed value is…
Two loaded 5.0 × 10⁴ kg train cars sit on parallel tracks, each car 15 m long, their centers 20 m apart. Enter the gravitational force between them, in newtons.