A bag of sugar weighs 3.00 lb on Earth. What would it weigh in newtons on the Moon, where the free-fall acceleration is one-sixth that on Earth?
N
Repeat for Jupiter, where g is 2.64 times that on Earth.
N
Find the mass of the bag of sugar in kilograms at each of the three locations.
Earth
?kg
Moon
?kg
Jupiter
?kg
a) 3/6
b) 3*2.64
c)a kg is about 2.2 lbs.
To find the weight of the bag of sugar on the Moon and Jupiter, we need to use the formula:
Weight = mass * acceleration due to gravity
First, let's find the weight of the bag of sugar on the Moon.
Given:
Weight on Earth = 3.00 lb
Acceleration due to gravity on the Moon = 1/6 that on Earth
To convert pounds to newtons, we need to know the acceleration due to gravity in newtons on Earth.
The acceleration due to gravity on Earth is approximately 9.8 m/s^2. We will use this value in our calculations.
1. Convert the weight on Earth from pounds to newtons:
Weight on Earth = 3.00 lb * 4.448 N/lb (approximately) = 13.344 N
2. Calculate the weight on the Moon using the formula:
Weight on Moon = Weight on Earth * (Acceleration due to gravity on the Moon / Acceleration due to gravity on Earth)
Weight on Moon = 13.344 N * (1/6) = 2.224 N
So, the weight of the bag of sugar on the Moon is approximately 2.224 newtons (N).
Next, let's find the weight of the bag of sugar on Jupiter.
Given:
Acceleration due to gravity on Jupiter = 2.64 times that on Earth
3. Calculate the weight on Jupiter using the formula:
Weight on Jupiter = Weight on Earth * (Acceleration due to gravity on Jupiter / Acceleration due to gravity on Earth)
Weight on Jupiter = 13.344 N * 2.64 = 35.161 N
So, the weight of the bag of sugar on Jupiter is approximately 35.161 newtons (N).
Now, let's find the mass of the bag of sugar at each of the three locations.
To find the mass, we can rearrange the formula:
Weight = mass * acceleration due to gravity
To solve for mass, we divide both sides by the acceleration due to gravity:
Mass = Weight / acceleration due to gravity
For Earth, the acceleration due to gravity is approximately 9.8 m/s^2.
4. Calculate the mass on Earth:
Mass on Earth = Weight on Earth / Acceleration due to gravity on Earth
Mass on Earth = 13.344 N / 9.8 m/s^2 ≈ 1.362 kg
So, the mass of the bag of sugar on Earth is approximately 1.362 kilograms (kg).
To find the mass on the Moon, we use the weight on the Moon and the acceleration due to gravity on the Moon (1/6 that on Earth).
5. Calculate the mass on the Moon:
Mass on Moon = Weight on Moon / Acceleration due to gravity on Moon
Mass on Moon = 2.224 N / (9.8 m/s^2 * 1/6) ≈ 0.238 kg
So, the mass of the bag of sugar on the Moon is approximately 0.238 kilograms (kg).
To find the mass on Jupiter, we use the weight on Jupiter and the acceleration due to gravity on Jupiter (2.64 times that on Earth).
6. Calculate the mass on Jupiter:
Mass on Jupiter = Weight on Jupiter / Acceleration due to gravity on Jupiter
Mass on Jupiter = 35.161 N / (9.8 m/s^2 * 2.64) ≈ 1.438 kg
So, the mass of the bag of sugar on Jupiter is approximately 1.438 kilograms (kg).
In summary:
Weight on the Moon: 2.224 N
Mass on the Moon: 0.238 kg
Weight on Jupiter: 35.161 N
Mass on Jupiter: 1.438 kg