Sage-Tips

How is gravitational potential formula derived?

Since the force required to lift it is equal to its weight, it follows that the gravitational potential energy is equal to its weight times the height to which it is lifted. PE = kg x 9.8 m/s2 x m = joules. PE = lbs x ft = ft lb.

What is r in GmM R?

1. F = GmM/r2 = ma, where F is the gravitational force, G is the gravitational constant, M is the mass of the Earth, r is the radius of the Earth, and m is the mass of another object (near the surface of the Earth).

What is potential energy derive its expression?

Energy possessed by a body by virtue of its position is called potential energy. But, F = mg, the weight of the body.

What is gravitational potential energy derive an expression for gravitational potential energy and gravitational potential?

The change in gravitational potential energy, ΔPEg, is ΔPEg = mgh, with h being the increase in height and g the acceleration due to gravity. The gravitational potential energy of an object near Earth’s surface is due to its position in the mass-Earth system.

What is the G in GmM R?

g = GM/r2, Where M is the mass of the Earth, r the radius of the Earth (or distance between the center of the Earth and you, standing on its surface), and G is the gravitational constant.

What is G in F GmM r2?

F = GmM/r2 = ma, where F is the gravitational force, G is the gravitational constant, M is the mass of the Earth, r is the radius of the Earth, and m is the mass of another object (near the surface of the Earth).

What is the potential energy derive an equation for gravitational potential energy of a body of mass m at a height h?

POTENTIAL ENERGY: The energy possessed by the body because of it position or shape is called potential energy. Therefore, the equation for gravitational potential energy of a body of mass m at a height h is mgh.

What is the potential energy derive an expression for the gravitational potential energy?

Gravitational Potential Energy ΔU = mgh.

What is r in gravitational force?

F=Gm1m2r2. where F is the force between the masses, G is the gravitational constant, m1 is the first mass, m2 is the second mass and r is the distance between the centers of the masses.

How do you derive the gravitational potential energy equation?

The derivation of the gravitational potential energy equation starts with the Universal Gravitation Equation: F = GMm/R2

How to calculate U = -GMm/r?

U = mgh applies only for a uniform field, so it does not apply here where the field goes as 1/r2. F = -dU/dr ΔU = – ∫F dr This gives U = -GmM/r, if we define the potential energy to be zero at r = infinity. This is what we do – you are NOTfree to define the zero anywhere you want – it is pre-defined to be zero at infinity.

How do you find the magnitude of the gravitational force?

We know that the magnitude of the gravitational force is given by: F = -GmM/r2 Use the connection between force and potential energy to determine the general form of gravitational potential energy. U = mgh applies only for a uniform field, so it does not apply here where the field goes as 1/r2.

How can the potential energy of a test mass be negative?

If a test mass moves from a point inside the gravitational field to the other point inside the same gravitational field of source mass, then the change in potential energy of the test mass is given by; > r f then ΔU is negative.