Determine the mass of a person on the moon whose mass on Earth is 70 kg
Determine the weight of a person on the moon whose weight on Earth is 148 lbs.
How is the mutual gravitational force affected by changing the separation distance between two 1.0 kg masses if the distance between them is
(a) decreased to two-thirds.
(b) increased to 2.7 times.
To determine the mass of a person on the moon, you need to understand that mass is a fundamental property of matter which remains constant regardless of the location. So, the mass of the person on the moon will be the same as their mass on Earth, which is 70 kg.
To determine the weight of a person on the moon, you need to know that weight is the force of gravity acting on an object. The gravitational force depends on the mass of the object and the acceleration due to gravity. On Earth, the acceleration due to gravity is roughly 9.8 m/s^2, while on the moon it is about 1/6th of that, approximately 1.6 m/s^2.
To calculate the weight of the person on the moon, you can use the formula:
Weight = Mass x Acceleration due to gravity
First, convert the weight of the person on Earth from pounds to kilograms. 1 pound is approximately 0.4536 kilograms. So, the weight of the person on Earth is 148 lbs x 0.4536 kg/lb = 67.13 kg.
Now, calculate the weight on the moon using the formula:
Weight on the moon = Mass x Acceleration due to gravity on the moon
Weight on the moon = 67.13 kg x 1.6 m/s^2 = 107.41 N
Therefore, the weight of the person on the moon is approximately 107.41 Newtons.
Regarding the mutual gravitational force between two masses, it is affected by the distance between them. The gravitational force between two masses is inversely proportional to the square of the distance between them. In other words, as the separation distance decreases, the gravitational force increases, and as the separation distance increases, the gravitational force decreases.
(a) If the distance between the two 1.0 kg masses is decreased to two-thirds of the original distance, the new gravitational force will be:
New force = (Original force) x (Original distance / New distance)^2
New force = (Original force) x (3/2)^2
New force = (Original force) x (9/4)
So, the new force is 9/4 times the original force.
(b) If the distance between the two 1.0 kg masses is increased to 2.7 times the original distance, the new gravitational force will be:
New force = (Original force) x (Original distance / New distance)^2
New force = (Original force) x (1/2.7)^2
New force = (Original force) x (1/7.29)
So, the new force is 1/7.29 times the original force.