For this question, we're told that a person is accelerating upward while in an elevator, and we're asked to find how this person's weight changes as a result.

To begin, it's most useful to solve this problem by considering the forces acting in the vertical direction. Downward, we have the mass of the person. Upward, we have the tension in the cord that is pulling the elevator up. We can use this information to set up the following expression.

Also, note that the tension in the elevator is what is providing all the upward force. Thus, the elevator floor will be exerting this same amount of force on the person (normal force) and, as a result, the person will exert the same force (weight) on the elevator floor. Hence, tension is a measurement of the person's weight.

Now, we'll need to take the ratio of the person's weight while accelerating in the elevator to the person's weight while at rest. This will give us the factor by which his weight changes.

Normal force is independent of surface area, and only dependent on the opposite force being applied, in this case gravity. While the pressure on her foot may change, the force of gravity pushing her down stays the same.

The ground exerts an equal force as the person exerts on it, which is the normal force. This is simply the mass of the person times the acceleration due to gravity which is . This ends with the normal force and the force exerted by the ground on the person being .

This question tests your understanding of the concept of normal force. In a block that remains stationary, in which the only two forces acting upon it are the force of gravity, and normal force, you therefore know that the normal force must be equal to the force of gravity, since the block is not accelerating or decelerating (i.e. the sum of the forces is equal to zero). 

Thus, we can set the normal force equal to the force of gravity, and solve as follows:

Therefore, the normal force exerted on the block by the ground is .

The acceleration of gravity is given by the equation , where G is constant.

For Earth, .

For the new planet, 

.

So, the acceleration is the same in both cases.

The equation to calculate the escape velocity from a planet is

The diameter of the planet is given and can be divided by two to determine the radius of the planet. By plugging in the given values, the escape velocity threshold can be determined:

We need to know Newton's law of universal gravitation to solve this problem:

It is important to note that both suns will feel the same gravitational force. However, since they have different masses, they will accelerate at different rates.

Plugging in the variables we have, we get:

To solve this problem, use Newton's law of universal gravitation:

We are given the constant, as well as the satellite masses and distance (radius). Using these values we can solve for the force.

To solve this problem, use Newton's law of universal gravitation:

We are given the constant, as well as the satellite masses and distance (radius). Using these values we can solve for the force.

To solve this problem, use Newton's law of universal gravitation:

We are given the value of the force, the distance (radius), and the gravitational constant. We are also told that the masses of the two satellites are equal. Since the masses are equal, we can reduce the numerator of the law of gravitation to a single variable.

Now we can use our give values to solve for the mass.