A kettle transfers \(180\,000\,\mathrm{J}\) of energy in \(150\,\mathrm{s}\). Calculate the power of the kettle.
\(P = E/t = 180000/150 = 1200\,\mathrm{W}\) (\(1.2\,\mathrm{kW}\)).
Energy
10 exam-style questions on energy stores, transfers, efficiency, power and specific heat capacity. Tap Show answer for full working.
3 Easy 4 Medium 3 Hard
A machine does \(2400\,\mathrm{J}\) of useful work when \(3000\,\mathrm{J}\) of energy is supplied. Calculate its efficiency as a percentage.
Efficiency \(= (2400/3000)\times100 = 80\%\).
State four energy stores. Give one example of a transfer of energy from the kinetic store to the thermal store.
Examples: kinetic, gravitational potential, elastic potential, chemical, thermal, nuclear, electrostatic, magnetic.
Example transfer: a moving car braking — kinetic store decreases, thermal store of brakes/road increases (via friction/work).
A \(2.0\,\mathrm{kg}\) mass is lifted through a height of \(1.5\,\mathrm{m}\). Calculate the increase in gravitational potential energy. (\(g = 9.8\,\mathrm{N\,kg}^{-1}\).)
\(\Delta E_p = mgh = 2.0\times9.8\times1.5 = 29.4\,\mathrm{J}\).
A car of mass \(1200\,\mathrm{kg}\) travels at \(20\,\mathrm{m\,s}^{-1}\). Calculate its kinetic energy. If the car comes to rest, state what happens to this energy.
\(E_k = \frac12 mv^{2} = 0.5\times1200\times400 = 240\,000\,\mathrm{J}\).
Transferred mainly to the thermal store of the brakes (and surroundings) by work done against friction.
How much energy is needed to raise the temperature of \(0.50\,\mathrm{kg}\) of water by \(30^\circ\mathrm{C}\)? (Specific heat capacity of water \(= 4200\,\mathrm{J\,kg}^{-1}{}^\circ\mathrm{C}^{-1}\).)
\(\Delta E = mc\Delta\theta = 0.50\times4200\times30 = 63\,000\,\mathrm{J}\).
A spring is stretched by \(0.12\,\mathrm{m}\). The spring constant is \(250\,\mathrm{N\,m}^{-1}\). Calculate the elastic potential energy stored.
\(E_e = \frac12 ke^{2} = 0.5\times250\times0.0144 = 1.8\,\mathrm{J}\).
A \(1.5\,\mathrm{kW}\) heater is used to heat \(2.0\,\mathrm{kg}\) of water from \(20^\circ\mathrm{C}\) to \(80^\circ\mathrm{C}\). Calculate the minimum time this would take, assuming no energy losses. (Specific heat capacity of water \(= 4200\,\mathrm{J\,kg}^{-1}{}^\circ\mathrm{C}^{-1}\).)
\(\Delta E = mc\Delta\theta = 2.0\times4200\times60 = 504\,000\,\mathrm{J}\).
\(t = E/P = 504000/1500 = 336\,\mathrm{s}\) (\(5.6\) minutes).
A ball of mass \(0.20\,\mathrm{kg}\) is dropped from a height of \(5.0\,\mathrm{m}\). Calculate its speed just before it hits the ground, assuming no air resistance. (\(g = 9.8\,\mathrm{N\,kg}^{-1}\).)
Loss in \(E_p\) = gain in \(E_k\): \(mgh = \frac12 mv^{2} \Rightarrow v = \sqrt{2gh} = \sqrt{2\times9.8\times5.0} = 9.9\,\mathrm{m\,s}^{-1}\).
An electric motor lifts a \(40\,\mathrm{kg}\) load through \(3.0\,\mathrm{m}\) in \(8.0\,\mathrm{s}\). The motor is supplied with \(200\,\mathrm{W}\) of electrical power. Calculate the efficiency of the motor. (\(g = 9.8\,\mathrm{N\,kg}^{-1}\).)
Useful energy \(= mgh = 40\times9.8\times3.0 = 1176\,\mathrm{J}\).
Useful power \(= 1176/8.0 = 147\,\mathrm{W}\).
Efficiency \(= (147/200)\times100 = 73.5\%\).