Three masses are arranged in the (x, y)
plane.
3kg (0,0)
7kg (10,0)
6kg (0,3)
What is the magnitude of the resulting
force on the 3 kg mass at the origin? The value of the universal gravitational constant is 6.6726 × 10^−11 N · m^2/kg^2.
Answer in units of N
what ive done
G*(7)*(3)/10^2 = 1.401246*10^-11
G*(3)*(6)/3^2 = 1.33452*10^-10
sqrt((1.401246*10^-11)^2 + (1.33452*10^-10)^2)
= 1.341856376*10^-10
my program tells me im wrong. im getting frustrated. please help?
I figured it out......i don't understand why no one has helped me yet in the past week
did you ever figure it out?
I understand that you're having trouble finding the correct answer to the magnitude of the resulting force on the 3 kg mass at the origin. Let me guide you through the correct calculation.
To find the magnitude of the resulting force, we need to calculate the gravitational force between the 3 kg mass and both the 7 kg and 6 kg masses. Then, we can use vector addition to find the resultant force.
Here's how you can calculate it step by step:
1. Calculate the gravitational force between the 3 kg mass and the 7 kg mass:
F₁ = (G * (m₁ * m₂)) / r₁²
where:
G is the universal gravitational constant (6.6726 × 10^−11 N · m^2/kg^2)
m₁ is the mass of the 3 kg mass
m₂ is the mass of the 7 kg mass
r₁ is the distance between the masses (which is the x-coordinate of the 7 kg mass)
Plugging in the values:
F₁ = (6.6726 × 10^−11 N · m^2/kg^2 * 3 kg * 7 kg) / (10 m)²
F₁ = 1.4024 × 10^−10 N
2. Calculate the gravitational force between the 3 kg mass and the 6 kg mass:
F₂ = (G * (m₁ * m₃)) / r₂²
where:
m₃ is the mass of the 6 kg mass
r₂ is the distance between the masses (which is the y-coordinate of the 6 kg mass)
Plugging in the values:
F₂ = (6.6726 × 10^−11 N · m^2/kg^2 * 3 kg * 6 kg) / (3 m)²
F₂ = 1.3345 × 10^−10 N
3. Use vector addition to find the resultant force:
Resultant force = √(F₁² + F₂²)
Resultant force = √((1.4024 × 10^−10 N)² + (1.3345 × 10^−10 N)²)
Resultant force ≈ 1.8989 × 10^−10 N
Therefore, the correct magnitude of the resulting force on the 3 kg mass at the origin is approximately 1.8989 × 10^−10 N.