Gravitational potential Flashcards
1
Q
What is gravitational potential energy?
A
- the energy of an object due to its position in a gravitational field
- gets weaker as distance increases
- the position for zero gpe is at inifnity - the object would be so far away that the gravitational force on it is negligible
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2
Q
What is gravitational potential at a point in a gravitational field?
A
- work done/energy change (against the field) per unit mass (1) when moved from infinity to the point (1)
- the GPE that a unit mass would have in simple terms
3
Q
What is teh equation for the work needed to enable it to escape completely?
A
W = mV
4
Q
What is the unit of gravitational potential?
A
J kg-1
5
Q
Derive the equation to show that the speed of a satellite is inversely propotional to the square root of its radius
A
- F = mv2 / r
- F = Gm1m2 / r2
- therefore
- V2 = Gm1m2r / r2m
- V = √ (GM / r)
- so v ∝ 1 / √r as GM is a constant
6
Q
Rearrange the equation for the T2 equation
draw it using equation sheet
also using the derived speed equation
what relationship does this show?
A
- v = 2πr / T therefore T = 2π / v
- T = 2πr / √(GM / r) = 2πr√r / √GM
- square both sides to make it easier to deal with
- T2 = 22π2r2r / GM
- = 4π2r3 / GM
- shows T2 ∝ r3 (rest are cosntants)
7
Q
Why is v ∝ 1 / √r
no need for equation
A
potential energy transferred to kinetic energy
8
Q
Why is gravitational potential negative?
A
- work has to be done against the field to move an object out of it
- potential energy becomes less negative as the object moves upwarsd
9
Q
What is escape velocity? how is it derived
A
- escape velocity is defined as the velocity at which an object KE is equal to minus its GPE
- this means total energy is zero
- multiply V by mass, m, to get the GPE
- total energy = 0 = 1/2 mv2 - GMm / r
- so 1/2mv2 = GMm / r
- cancel m >> 1/2 v2 = GM / r
- v =√(2GM / r )
