A 125 object is taken to a height of 210 above the Earth's surface.

Part A

What is the object's mass at this height?
Part B

What is the object's weight at this height?

To answer Part A and Part B of the question, we need to understand the concepts of mass and weight in relation to height.

Part A - What is the object's mass at this height?

The mass of an object does not change with height. Mass is a property of matter and represents the amount of material the object contains. It is measured in kilograms (kg). Therefore, the mass of the object remains constant at 125 kg irrespective of the height above the Earth's surface.

Part B - What is the object's weight at this height?

Weight, on the other hand, is a measure of the force of gravity acting on an object. It depends on two factors: the mass of the object and the gravitational acceleration at that location.

The formula to calculate weight is:

Weight = mass × gravitational acceleration

However, the value of gravitational acceleration changes with height. Near the Earth's surface, the standard value for gravitational acceleration is approximately 9.8 meters per second squared (m/s²). As we go higher above the Earth's surface, the gravitational acceleration decreases gradually.

To calculate the object's weight at a height of 210 meters above the Earth's surface, we need to determine the gravitational acceleration at that height. This can be done using the equation for the variation of gravitational acceleration with height:

g(h) = g₀ / (1 + h/r)²

Where:
g(h) is the gravitational acceleration at height h,
g₀ is the standard gravitational acceleration near the Earth's surface (9.8 m/s²),
h is the height above the Earth's surface, and
r is the radius of the Earth (approximately 6,371 km or 6,371,000 meters).

Let's calculate the gravitational acceleration at a height of 210 meters:

g(210) = 9.8 / (1 + 210/6,371,000)²

g(210) ≈ 9.794 m/s² (rounded to three decimal places)

Now we can calculate the object's weight at this height using the formula:

Weight = mass × gravitational acceleration

Weight = 125 kg × 9.794 m/s²

Weight ≈ 1,224.25 Newtons (N) (rounded to two decimal places)

Therefore, the object's weight at a height of 210 meters above the Earth's surface is approximately 1,224.25 Newtons.