In order to calculate the weight of an object sitting on the Earth’s surface, one would use the following formula: FG = GMEm r 2 where G = 6.674 × 10−11 m3 kg s2 is the universal gravitational constant, ME = 5.97 × 1024 kg is the mass of the Earth (also a constant), r is the radius of the Earth at the object’s location (measured in m), and m = the mass of the object (measured in kg). Calculate your weight (to the correct number of significant figures) using this formula if your mass is 9.01 × 104 g and the radius of the Earth at the object’s location is 6.382 × 106 m. Use unit algebra to express the unit for weight as some combination of the metric system’s standard units for mass, length, and time.

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orianapineiro orianapineiro · Answer 1 · 2019-10-13T19:27:26+02:00

Answer:

The weight is 881.397 N

Explanation:

You have to replace the values of G, ME, r and m in the given formula to calculate the weight

[tex]FG=\frac{GMEm}{r^{2} }[/tex]

The mass of the object (in this case, your mass) should be replaced in kg, so you have to covert it to kg

Is known that 1000g=1kg, so dividing the mass by 1000 you will obtain the mass is kg:

m = [tex]\frac{(9.01)(10^{4}) }{1000} = 90.1 kg[/tex]

Replacing the values in the formula:

[tex]FG= \frac{(6.674)(10^{-11})(5.97)(10^{24})(90.1) }{[(6.382)(10^{6} )]^{2} }[/tex]

Calculating the value of FG:

FG= 881.397

Now you have to use unit algebra to find the unit for weight. You have to replace just the units in the given formula:

FG= [tex]\frac{(m^{3}/kgs^{2})(kg)(kg)}{m^{2}} = \frac{(m^{3}/kgs^{2})(kg^{2})}{m^{2} }[/tex]

Applying properties of exponential numbers and rational numbers:

[tex]\frac{m^{3}kg^{2}}{kgs^{2}m^{2}} = \frac{kg m}{s^{2} } = N[/tex]

where N is newton, the unit for force.

So, the weight (given by FG) is: 881.397 N