Fields Flashcards

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1
Q

What is gravitational potential energy? What is the implication of this definition?

A
  • the GPE of two bodies is the work that was done in bringing the bodies to their present position from when they were infinitely far apart.
  • All GPE values are negative as work is done by as mass as it moves closer to another mass.
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2
Q

What are two formulas for gravitational field strength?

A
  • g = F/m DB

- g = -GM/r² DB

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3
Q

What is a formula for GPE, and how is it derived?

A
  • Work done = GPE = integral between r and infinity of the force on a small test mass dr.
    W = Ep = -GMm/r DB
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4
Q

What is gravitational potential? How can it be calculated?

A

(Vg) at a point P in a gravitational field is the work done per unit mass in bringing a small point mass m from infinity to point P.
Vg = W/m
Vg = -GM/r (Jkg-1) DB

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5
Q

How can you calculate the work done in moving a mass, m, from P to Q in a gravitational field?

A

W = change in Ep = m∆V not in DB

When an external agent does work to move the mass at a constant small speed (so KE of mass is negligible).

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6
Q

What does a graph of distance against gravitational potential (y axis) look like?

A
  • A declining negative curve with an asymptote at both axis. As Vg → 0, r → ∞
  • Called a ‘potential well’.
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7
Q

How can you find the electric field created by an arrangement of point charges?

A

Add the vectors of the electric fields created by each of the individual charges. Often some will cancel out.

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8
Q

What is electric potential? How can you calculate it?

A

(Ve) at point P is the amount of work done per unit charge as a small positive test charge q is moved from infinity to the point P.
Ve = W/q = kQ/r (JC-1)

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9
Q

What is electric potential energy?

A
  • the GPE of two charges is the work that was done in bringing the charges to their present position from when they were infinitely far apart.
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10
Q

What are two formulas for electric potential energy, Ep?

A

Ep = qVe = kq₁q₂/r

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11
Q

How can you calculate the work done in moving a charge from A to B in an electric field?

A

W = change in Ep = q∆V not in DB

When an external agent does work to move the mass at a constant small speed (so KE of mass is negligible).

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12
Q

How can you find the potential at point P of an electric field created by an arrangement of point charges?

A
  • Potential is a scalar quantity, it is the sum of the individual electric potentials.
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13
Q

What does the graph of distance against electric potential (y axis) of a positively charged spherical object radius R look like?

A
  • Potential is constant everywhere inside the sphere (when r is less than R),
  • Outside, the potential declined as 1/r
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14
Q

What is an equipotential surface?

A

A surface that connects all points around a mass or charge that have the same potential. Often spherical ‘shells’. Perpendicular to field lines.

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15
Q

What is special about a graph of distance against potential? How is it derived?

A

The gradient of the graph is the same as the magnitude of the field strength (either gravitational or electric)
Found by equating two equations m∆V and Fdistmoved for work done moving a (mass) from one equipotential surface to a neighbor.

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16
Q

How can you derive an equation for the kinetic energy of an object orbiting a planet? (need to know how to do)

A

The gravitational force provides the centripetal force,
∴ GMm/r² = mv²/r
so v² = GM/r
Multiply both sides by m/2 to get Ek = GMm/2r

17
Q

How can you derive the total energy of an object orbiting a planet?

A
Et = Ek + Ep
Et = GMm/2r - GMm/r
Et = -GMm/2r
18
Q

How can you find the velocity of an object orbiting a planet?

A

v =sqrt(GM/r) DB

19
Q

What does the graph of energy against orbital radius look like for Et, Ek and Ep?

A

All are curves beginning at R radius of the planet that tend towards the x axis.

  • Et is a reflection of Ek in the x axis(-ve)
  • Ep = 2Et, also negative.
20
Q

What will happen if an object is launched from the surface of a planet with a total energy…
< 0
= 0
> 0

A
  • It will go into an elliptical or circular orbit
  • It will follow a parabolic path and never return
  • It will follow a hyperbolic path to infinity.
21
Q

What will happen if a spaceship in orbit fires its rockets

  • opposite the direction of travel
  • in the same direction as travel.
A
  • The total energy will increase, the radius of the orbit will increase, Ek decreases, Ep increases.
  • The radius of the orbit decreases, Ek increases, Ep decreases.
    COUNTERINTUITIVE! Imagine climbing up or down the potential well of the energy graphs.
22
Q

What is escape velocity?

A

The minimum speed that a mass must have in order to escape a gravitational field ie. reach infinity. Applies to ballistic motion only.

23
Q

How can you derive escape velocity?

A

Note that the total energy of the system must be 0 at launch (conservation - when it reaches infinity it will have no energy left)
Ek + Ep = 0
1/2 mvesc² - GMm/R = 0
rearrange. DB

24
Q

Why does an astronaut feel weightless?

A

The astronaut and spacecraft are both falling freely - they have the same acceleration.