1.) The earth's radius is about 3956.52 mi. An object that has a mass of 20 kg is taken to a height of 160 km above the earth's surface.

a. What is the mass of the object at this height?
b. How much does the object weigh at this height?

a. mass remains constant.

b. weight=mass(r/(r+h))^2

40kg

a. To find the mass of the object at a height of 160 km above the earth's surface, we first need to understand how gravity affects the object's mass. Mass remains constant regardless of the distance from the Earth's surface. Therefore, the mass of the object will still be 20 kg at this height.

b. Weight, on the other hand, is the force exerted on an object due to gravity. To calculate the weight of the object at this height, we can use the formula:

Weight = mass * gravitational acceleration

At the Earth's surface, the standard gravitational acceleration is approximately 9.8 m/s^2. However, as we move away from the Earth's surface, the acceleration due to gravity decreases. To account for this, we'll need to calculate the gravitational acceleration at a height of 160 km above the Earth's surface using the formula:

gravitational acceleration = (earth's radius / (earth's radius + height))^2 * standard gravitational acceleration

Substituting the values, we get:

gravitational acceleration = (3956.52 mi / (3956.52 mi + 160 km))^2 * 9.8 m/s^2

Note that we need to convert 160 km to miles: 160 km = 99.419 miles

Substituting the converted value, we get:

gravitational acceleration = (3956.52 mi / (3956.52 mi + 99.419 mi))^2 * 9.8 m/s^2

Calculating this gives us:

gravitational acceleration = (3956.52 mi / 4055.939 mi)^2 * 9.8 m/s^2

gravitational acceleration ≈ (0.97411)^2 * 9.8 m/s^2

Now we can calculate the weight of the object:

Weight = mass * gravitational acceleration
Weight = 20 kg * [(0.97411)^2 * 9.8 m/s^2]

Calculating this gives us:

Weight ≈ 20 kg * (0.9484) * (9.8 m/s^2)

Weight ≈ 185.92 N

Therefore, the object weighs approximately 185.92 N at a height of 160 km above the Earth's surface.

To find the answers to these questions, we need to understand the concept of gravitational force and how it depends on mass and distance.

1. a) To calculate the mass of the object at a height of 160 km above the Earth's surface, we need to know that the mass of an object remains constant regardless of its position. So, the mass of the object is still 20 kg at this height.

1. b) To calculate the weight of an object, we need to consider the gravitational force acting on it. The weight of an object is given by the equation:

Weight = mass * acceleration due to gravity

The acceleration due to gravity varies with the distance from the center of the Earth. At the Earth's surface, the acceleration due to gravity is approximately 9.8 m/s^2. However, as we move further away from the Earth's surface, the gravitational force weakens.

To calculate the weight at a height of 160 km above the Earth's surface, we need to determine the new value of the acceleration due to gravity at that height.

The equation for the acceleration due to gravity as a function of distance from the Earth's center is:

acceleration due to gravity = (gravitational constant * mass of Earth) / (radius of Earth + height)^2

Plugging in the values, we get:

acceleration due to gravity = (6.674 x 10^-11 m^3/kg/s^2 * 5.972 x 10^24 kg) / (6371000 + 160000)^2

Solving this equation will give us the new value of the acceleration due to gravity at a height of 160 km above the Earth's surface.

Once we have the new value of the acceleration due to gravity, we can use it to calculate the weight of the object:

Weight = mass * acceleration due to gravity

Substituting the mass of the object (20 kg) and the new value of the acceleration due to gravity into the equation will give us the weight of the object at a height of 160 km above the Earth's surface.