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
Answe
To solve these questions, we need to understand the relationship between weight, mass, and gravity.
On Earth, weight can be calculated using the formula:
weight = mass * gravitational acceleration on Earth (approximately 9.8 m/s^2)
Now, let's calculate the weight of the bag of sugar on the Moon:
Since the free-fall acceleration on the Moon is one-sixth that on Earth, we can say the gravitational acceleration on the Moon (g_moon) is:
g_moon = (1/6) * g_earth
Therefore, the weight of the bag of sugar on the Moon (weight_moon) can be calculated as:
weight_moon = mass * g_moon
To calculate the weight on Jupiter, we can use a similar approach. Since the gravitational acceleration on Jupiter (g_jupiter) is 2.64 times that on Earth, we have:
g_jupiter = 2.64 * g_earth
Therefore, the weight of the bag of sugar on Jupiter (weight_jupiter) can be calculated as:
weight_jupiter = mass * g_jupiter
Now, let's calculate the mass of the bag of sugar at each of the three locations:
On Earth, the weight is 3.00 lbs. To convert this weight to mass, we can use the formula:
mass = weight_earth / g_earth
Substituting the values, we have:
mass_earth = 3.00 lbs / 9.8 m/s^2
To convert this mass to kilograms, we need to multiply it by the conversion factor of 0.453592 kg/lb:
mass_earth = mass_earth * 0.453592 kg/lb
Repeat the same process for the Moon and Jupiter using the respective values for weight_moon, weight_jupiter, and the corresponding values of g_moon and g_jupiter.
Calculating the mass on the Moon:
mass_moon = weight_moon / g_moon
mass_moon = mass_moon * 0.453592 kg/lb
Calculating the mass on Jupiter:
mass_jupiter = weight_jupiter / g_jupiter
mass_jupiter = mass_jupiter * 0.453592 kg/lb
Now that we have explained the process, let's calculate the answers.
Weight on the Moon:
weight_moon = 3.00 lbs * (1/6) * 9.8 m/s^2
Mass on the Moon:
mass_moon = weight_moon / (1/6) * 9.8 m/s^2 * 0.453592 kg/lb
Weight on Jupiter:
weight_jupiter = 3.00 lbs * 2.64 * 9.8 m/s^2
Mass on Jupiter:
mass_jupiter = weight_jupiter / (2.64 * 9.8 m/s^2) * 0.453592 kg/lb
moon weight=1/6 * earthweight
Jupiterweight=2.64* earthweight
earth mass=earthweight/2.2
Moon mass=earthmass
jupitermass=earthmass