Potential energy and potential
Work done is stored energy. Divide by the mass or charge and you get potential.
Lifting a box, stretching a spring and pushing two like charges together all store energy. Is there one idea that covers all three?
A spring (k = 40 N m⁻¹) is stretched from rest by 0.10 m. The elastic energy stored is…
The area under a force–displacement graph represents…
The gravitational potential at a point is −6.0 × 10⁷ J kg⁻¹. The work needed to take a 2.0 kg mass from there to infinity is…
The electric potential a distance r from a point charge +Q is V. At a distance 2r it is…
Gravitational potential V_g = −GM / r is negative everywhere because…
A charge of 3.0 C is moved from a point at 4.0 V to a point at 10 V. The work done by an external agent is…
Explain the difference between gravitational potential energy and gravitational potential. Give the unit of each.
At a height equal to the Earth’s radius above its surface, g is about…
The tesla is equivalent to…
Key points
- • Work done = area under the force–displacement graph = energy change. For a spring EPE = ½kx².
- • Potential is energy per unit mass or charge, zero at infinity.
- • V_g = −GM / r (always negative). V = kQ / r (sign of Q).
- • Energy = mass × V_g, or charge × V. A potential difference of 1 V means 1 J per coulomb.
Formulas
- EPE = ½kx²
- Vg = −GM / r
- V = kQ / r
- WD = q ΔV
Key terms
- Gravitational potential :
- energy per unit mass, zero at infinity, always negative
- Electric potential :
- energy per unit charge, V = kQ / r
- Volt :
- one joule per coulomb
Common errors
- • Using force × distance when the force is not constant.
- • Giving gravitational potential a positive sign.
- • Treating potential (per unit) as if it were the energy of the object.