A bag of sugar weighs 6.00 lb on Earth. What would it weigh in newtons on the Moon, where the free-fall acceleration is one-sixth that on Earth?
To determine the weight of the bag of sugar on the Moon, we need to first calculate the weight in newtons on Earth and then adjust it based on the moon's gravitational pull.
Step 1: Calculate the weight on Earth.
Weight is a measure of the force exerted on an object due to gravity. On Earth, the weight of an object can be calculated using the formula:
Weight = mass * gravity
Assuming the gravitational acceleration on Earth is 9.8 m/s^2, we can convert the weight of the bag of sugar from pounds to kg as follows:
1 lb ≈ 0.4536 kg
Weight on Earth = 6.00 lb * 0.4536 kg/lb * 9.8 m/s^2
Step 2: Adjust for the Moon's gravitational pull.
The gravitational acceleration on the Moon is one-sixth that of Earth (i.e., 1/6 * 9.8 m/s^2).
Weight on the Moon = Weight on Earth * (1/6 * 9.8 m/s^2)
Once we plug in the values, we can calculate the weight of the bag of sugar on the Moon.
To find the weight of the bag of sugar on the Moon, we need to first understand the concept of weight and how it differs from mass.
Weight is the force exerted on an object due to gravity. It depends on the mass of the object and the acceleration due to gravity. On Earth, the acceleration due to gravity is approximately 9.8 m/s^2.
Mass, on the other hand, is a measure of the amount of matter in an object and is a constant property. The mass of the bag of sugar remains the same regardless of where it is.
Now, to calculate the weight of the bag of sugar on the Moon, where the acceleration due to gravity is one-sixth of that on Earth, we can use the following formula:
Weight = mass * acceleration due to gravity
Let's calculate it step by step.
Step 1: Convert the weight of the bag of sugar on Earth from pounds to kilograms. We can use the conversion factor that 1 lb is equal to 0.4536 kg.
Weight on Earth = 6.00 lb * 0.4536 kg/lb = 2.7216 kg
Step 2: Calculate the weight of the bag of sugar on the Moon.
Weight on Moon = Weight on Earth * (Acceleration due to gravity on Moon / Acceleration due to gravity on Earth)
Acceleration due to gravity on Moon = 1/6 * Acceleration due to gravity on Earth = 1/6 * 9.8 m/s^2
Weight on Moon = 2.7216 kg * (1/6 * 9.8 m/s^2 / 9.8 m/s^2)
Simplifying the equation, we get:
Weight on Moon = 2.7216 kg * (1/6)
Weight on Moon = 0.4536 kg
So, the bag of sugar would weigh approximately 0.45 kg or 0.45 N (Newtons) on the Moon.
6.00 lb weight on earth means its mass (anywhere) is M = 6/2.2 = 2.73 kg.
On the moon, its weight is
W' = M g' where g' = 9.81/6 = 1.63 m/s^2
W' = 4.46 Newtons
You could also have use the pounds-force (lbf) to Newtons conversion factor directly, if you happened to know it.
1 lbf = (1/2.205 kg)*9.81 m/s^2 = 4.45 N
The bag weighs 1.00 lb on the Moon, hence 4.45 N