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
To find the weight of the sugar bag in newtons on the Moon and Jupiter, we first need to understand the concept of weight and how it is related to the mass and gravitational acceleration.
Weight is the force exerted on an object due to gravity. It is given by the equation:
Weight = mass * acceleration due to gravity
On Earth, the acceleration due to gravity is approximately 9.8 m/s^2. Given that the weight of the sugar bag on Earth is 3.00 lb (pound), we need to convert it to kilograms (kg) for further calculations.
1 lb is approximately equal to 0.453592 kg. Therefore, 3.00 lb is equal to 3.00 * 0.453592 = 1.360776 kg (approximately).
Now, let's calculate the weight of the sugar bag on the Moon and Jupiter.
On the Moon:
The free-fall acceleration on the Moon is one-sixth that on Earth, so the acceleration due to gravity on the Moon is 9.8 m/s^2 / 6 = 1.6333... m/s^2.
Weight on the Moon = mass * acceleration due to gravity on the Moon
Weight on the Moon = 1.360776 kg * 1.6333... m/s^2
Weight on the Moon ≈ 2.220012... N (newtons)
Therefore, the weight of the sugar bag on the Moon would be approximately 2.220012 newtons.
On Jupiter:
The gravitational acceleration on Jupiter is 2.64 times that on Earth, so the acceleration due to gravity on Jupiter is 2.64 * 9.8 m/s^2 = 25.872 m/s^2.
Weight on Jupiter = mass * acceleration due to gravity on Jupiter
Weight on Jupiter = 1.360776 kg * 25.872 m/s^2
Weight on Jupiter ≈ 35.2204... N (newtons)
Therefore, the weight of the sugar bag on Jupiter would be approximately 35.2204 newtons.
Now, let's calculate the mass of the sugar bag in kilograms for each of the three locations.
On Earth, the mass of the sugar bag is already given as 1.360776 kg.
On the Moon, the mass is the same as on Earth since mass is an inherent property of an object and remains constant regardless of the location.
On Jupiter, we can calculate the mass using the equation:
Weight = mass * acceleration due to gravity on Jupiter
Rearranging the equation:
Mass = Weight / acceleration due to gravity on Jupiter
Mass = 35.2204 N / 25.872 m/s^2
Mass ≈ 1.361890... kg
Therefore, the mass of the sugar bag on Jupiter would be approximately 1.361890 kilograms.