a bag of sugar weighs 5.00 lb on earth. What would it weigh in newton on the moon, where the free fall is one-sixth that of the earth?
To determine the weight of the bag of sugar on the moon in Newtons, we need to know the formula for weight:
Weight = mass × gravitational acceleration
Given that the mass of the sugar bag remains the same on both the earth and the moon, we only need to factor in the different gravitational accelerations.
On earth, the gravitational acceleration is approximately 9.8 m/s², while on the moon it is one-sixth that of the earth, so it would be:
Gravitational acceleration on the moon = 1/6 × 9.8 m/s² = 1.6333 m/s²
Now, let's calculate the weight of the sugar bag on the moon in Newtons:
Weight on the moon = mass × gravitational acceleration on the moon
Weight on the moon = 5.00 lb × 1.6333 m/s²
However, we need to convert the weight from pounds to kilograms since the unit of mass in the formula is kilograms:
1 lb ≈ 0.4536 kg
Weight on the moon = 5.00 lb × 0.4536 kg/lb × 1.6333 m/s²
Weight on the moon ≈ 3.7132 kg × 1.6333 m/s²
Weight on the moon ≈ 6.0557 N
Therefore, the bag of sugar would weigh approximately 6.06 Newtons on the moon.
To find the weight of the bag of sugar on the moon, we first need to understand the concept of weight and the influence of gravity on an object.
Weight is the force exerted on an object due to gravity. It is measured in Newtons (N). On Earth, the standard acceleration due to gravity is approximately 9.8 m/s².
On the moon, the gravitational acceleration is one-sixth that of Earth's, making it approximately 1.63 m/s² (9.8 m/s² ÷ 6).
To find the weight of the bag of sugar on the moon, we can use the following formula:
Weight = Mass x Acceleration due to gravity
In this case, we know the weight on Earth is 5.00 lb. However, in order to calculate the weight on the moon, we need to convert this mass from pounds (lb) to kilograms (kg) since the SI unit (International System of Units) for mass is kilograms.
1 lb is approximately equal to 0.4536 kg.
Therefore, the mass of the bag of sugar on Earth can be calculated as follows:
Mass = Weight on Earth ÷ Acceleration due to Earth's gravity
Mass = 5.00 lb ÷ 0.4536 kg/lb
After calculating the mass of the bag of sugar in kilograms, we can find the weight on the moon by using the formula mentioned above:
Weight on the Moon = Mass on Earth x Acceleration due to the Moon's gravity
Weight on the Moon = Mass in kg x 1.63 m/s²
By plugging in the values, you can determine the weight of the bag of sugar on the moon in Newtons.