Suppose planet earth suddenly grew in size, so that its radius was twice as large as before. Also suppose that at the same time, its mass also doubled to twice its former mass. If you weight used to be 700 N, what is it on this "new" Earth. Describe why this is the answer using appropriate formulas.
F = G m M/r^2
F' = G m 2M/(2r)^2
F'/F = 2/4 =1/2
700* 1/2 = 350 N
force= M/d^2
M is doubled, d is x2, so you have
a factor 2/4 or weight is 1/2 , or 350N
To find your weight on the "new" Earth, we need to understand the relationship between weight and mass, as well as the impact of the changes to the Earth's radius and mass.
Weight is the force exerted on an object due to gravity, while mass is the amount of matter contained in the object. The relationship between weight (W), mass (m), and the acceleration due to gravity (g) can be described by the formula:
W = m * g
where g is approximately 9.8 m/s^2 on Earth.
First, let's analyze the impact of the Earth's radius doubling. The gravitational force acting on an object is inversely proportional to the square of the distance between the object and the center of the Earth. Doubling the radius would result in a four-fold decrease in gravitational force.
However, we also need to consider that the mass of the Earth has doubled. According to Newton's law of universal gravitation, the gravitational force is directly proportional to the mass of the attracting objects. Thus, the doubled mass of the Earth will result in a doubling of the gravitational force.
Combining these factors, the new weight (W') can be calculated as follows:
W' = (m * g') = (m * (g * (1/4))) = (m * (g/4)) = (W/4)
Therefore, your weight on the "new" Earth would be one-fourth (1/4) of your previous weight. Given that your former weight was 700 N, your weight on the "new" Earth would be:
W' = 700 N * (1/4) = 175 N
In summary, doubling the radius of the Earth led to a quarter (1/4) of the previous gravitational force, while doubling the mass contributed to doubling the gravitational force. This combination led to your weight on the "new" Earth being one-fourth (1/4) of your previous weight.