the gravitional force exerted on objects on the moon is about 1/6 that of earth. if an object weighs 240 newtons on the moon, on earth it would weigh _________.show work
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To determine how much an object would weigh on Earth if it weighs 240 Newtons on the Moon, we need to use the fact that the gravitational force on the Moon is about 1/6 that of Earth.
Let's use the formula for weight: Weight = Mass × Gravitational Acceleration.
On Earth, the acceleration due to gravity is approximately 9.8 m/s^2, while on the Moon it is one-sixth of that, which is about 1.63 m/s^2.
Let's assume the mass of the object is 'm' kg.
On the Moon:
Weight = Mass × Gravitational Acceleration (Moon)
240 Newtons = m kg × 1.63 m/s^2
Now we can solve for 'm':
m kg = 240 N / 1.63 m/s^2
m ≈ 147.4 kg
Now that we have the mass, we can calculate the weight on Earth:
Weight = Mass × Gravitational Acceleration (Earth)
Weight = 147.4 kg × 9.8 m/s^2
Calculating the weight on Earth:
Weight ≈ 1442.52 Newtons
Therefore, an object that weighs 240 Newtons on the Moon would weigh approximately 1442.52 Newtons on Earth.