Calculate the force on a mass of 10kg placed on the earth's surface ( radius of earth = 6.4*10^6m and mass of earth =6.0*10^24kg and G=6.7*10^-11?
F =6.67*10*6*10/4.096=977.05
f=GM1M2/r2
given; MI=10KG
M2=6.0*10^24
r2=6.4*10^6
G=6.7*10^-11
sol;
6.7*10^*10kg*6.0*10% 6.4*10^2
=98N
NOTE; laws of indices applied
come on, this is calculator work.
F= 6.67e-11 * 6.0e24 / (6.4e6)^2 =...
Paste this into your google search engine:
6.67e-11 * 6.0e24 / (6.4e6)^2 =
6.67*10*6*10/40.9'2
Well, let's crunch some numbers here. According to Newton's law of universal gravitation, the force between two masses is given by the equation F = (G * m1 * m2) / r^2, where G is the gravitational constant, m1 and m2 are the masses, and r is the distance between them.
In this case, the mass of the Earth is 6.0*10^24 kg and the mass you've given is 10 kg. The radius of the Earth is 6.4*10^6 m. Plugging these values into the equation, we get:
F = (6.7*10^-11 * (10 kg) * (6.0*10^24 kg)) / (6.4*10^6 m)^2
Now, let me simplify this for you. Obviously, I can't do math in my head, but I can tell you that the force you're asking about is quite small compared to your mass. The Earth's mass is almost 24 orders of magnitude larger than yours! So, it's safe to say that you would hardly feel the force. You won't be pushed around by Earth's gravity, buddy.
To calculate the force on a mass on the earth's surface, we can use Newton's law of universal gravitation. The formula is given by:
F = (G * m1 * m2) / r^2
Where:
F is the force of gravitation,
G is the gravitational constant (6.7 * 10^-11 Nm^2/kg^2),
m1 and m2 are the masses of the two objects involved (in this case, the mass of the Earth and the mass of the object),
r is the distance between the centers of the two objects.
In this case, the mass of the Earth (m1) is 6.0 * 10^24 kg, and the mass of the object (m2) is 10 kg. The distance between the object and the center of the Earth is equal to the radius of the Earth, which is 6.4 * 10^6 m.
Plugging in these values into the formula:
F = (6.7 * 10^-11 Nm^2/kg^2 * 6.0 * 10^24 kg * 10 kg) / (6.4 * 10^6 m)^2
Simplifying the equation:
F = (6.7 * 6.0 * 10^13 * 10) / (6.4 * 6.4 * 10^12)
F = (4.02 * 10^14) / (40.96 * 10^12)
F ≈ 9.82 N
Therefore, the force acting on a mass of 10 kg on the Earth's surface is approximately 9.82 Newtons.