It is a fundamental law of Physics that the force the Earth exerts on an object varies inversely as the square of its' distance from the Earth's center. Thus, an object's weight F(x) is related to its' distance x from the Earth's center by a formula of the form k F(x) = x? k is a constant of proportionality whose value depends on the mass of the object and the units of force and distance. Of course, to move an object AWAY from Earth, the Force required is at least its' weight at a given distance x..hence F(x) can also be used 5) as a Force function. SpaceX's retired Dragon spacecraft, which was used to help supply the International Space Station (ISS), weighs approximately 4.65 tons "dry" (unloaded) on the surface of the Earth. a) Assuming that the Earth is a sphere of radius 4000 miles, solve the equation k 5 to discover the constant k in the Force formula mentioned 4.65 = 4000 above. Then, write F(x) out with that specifick value installed. This will be the Force model that pertains to the Dragon specifically. Evaluate the force model from part a to find the amount of force necessary to b) move the Dragon a small distance away from Earth when it is already located at an altitude of 150 miles above Earth's surface (x = 4150 miles). c) Use integration to find the amount of Work necessary to move the Dragon from the Earth's surface to the orbital altitude of the ISS, which is about 250 miles above Earth's surface.
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
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