Find the Gravitational potential at a point on the earth's surface. Take mass of earth as 5.98*10^24kg, it's radius as 6.38*10^6m and G=6.67*10^-11Nm^2kg^-2.
Plz i need sir damon and steve including reiny to show me step and solution plz
This should help.
http://hyperphysics.phy-astr.gsu.edu/hbase/gpot.html
To find the gravitational potential at a point on the Earth's surface, we can use the formula:
Potential = (G * Mass of Earth) / Radius of Earth
Given:
Mass of Earth (m) = 5.98 * 10^24 kg
Radius of Earth (r) = 6.38 * 10^6 m
Gravitational constant (G) = 6.67 * 10^-11 Nm^2kg^-2
Substituting the values into the formula, we have:
Potential = (6.67 * 10^-11 Nm^2kg^-2 * 5.98 * 10^24 kg) / (6.38 * 10^6 m)
To simplify the calculation, we can cancel out the units in the numerator and denominator:
Potential = (6.67 * 5.98 * 10^-11 * 10^24) / (6.38 * 10^6) N
Now, let's evaluate the expression step by step:
Step 1: Calculate the numerator.
Numerator = (6.67 * 5.98 * 10^-11 * 10^24) N
Using the rules of exponents, multiply the numbers and add the exponents:
Numerator = (6.67 * 5.98) * (10^-11 * 10^24) N
Multiply the decimal numbers without exponents:
Numerator = 39.8266 * (10^-11 * 10^24) N
Add the exponents of 10:
Numerator = 39.8266 * 10^(24 - 11) N
Numerator = 39.8266 * 10^13 N
Step 2: Calculate the denominator.
Denominator = 6.38 * 10^6 m
Step 3: Divide the numerator by the denominator.
Potential = (39.8266 * 10^13 N) / (6.38 * 10^6 m)
Dividing the numbers will give us:
Potential = 6.23723 * 10^7 N/m
So, the gravitational potential at a point on the Earth's surface is approximately 6.23723 * 10^7 N/m.