How I mark these
A correct number with no equation is one mark at most. Write the substitution line so I can give error-carried-forward if you slip the arithmetic.
1 · Efficiency and Sankey
A lamp’s Sankey diagram
A lamp is supplied with $60\,\text{J}$ of energy. $12\,\text{J}$ is transferred usefully as light. The rest is wasted as thermal energy.
Quantities
Input $=60\,\text{J}$. Useful $=12\,\text{J}$. Wasted $=60-12=48\,\text{J}$.
Equation and substitute
$$\text{efficiency} = \frac{12}{60}\times 100\% = 20\%$$On a Sankey diagram the input arrow is five times as wide as the useful (light) arrow, and the wasted (thermal) arrow is four times the useful width. Input = useful + wasted.
Sense-check: a filament lamp should be inefficient. $20\%$ is typical; $80\%$ would be a kettle, not a lamp.
2 · $W=Fd$
Pushing a crate
A warehouse worker pushes a crate with a horizontal force of $90\,\text{N}$ for $4.0\,\text{m}$ along the floor.
Quantities
$F=90\,\text{N}$, $d=4.0\,\text{m}$ (already along the force).
$$W = F \times d = 90 \times 4.0 = 360\,\text{J}$$Work done = energy transferred (4.12). If speed is constant, the $360\,\text{J}$ has gone to the thermal store (friction).
3 · $mgh$
Lifting a box onto a shelf
A box of mass $8.0\,\text{kg}$ is lifted through a vertical height of $1.5\,\text{m}$. $g=10\,\text{N/kg}$.
Quantities
$m=8.0\,\text{kg}$, $g=10\,\text{N/kg}$, $h=1.5\,\text{m}$.
$$\Delta GPE = m g h = 8.0 \times 10 \times 1.5 = 120\,\text{J}$$Sense-check: weight is $80\,\text{N}$; lifting $80\,\text{N}$ through $1.5\,\text{m}$ is $120\,\text{J}$. Same number from $W=Fd$.
4 · $\tfrac{1}{2}mv^2$
A trolley on the bench
A trolley of mass $1.2\,\text{kg}$ moves at $5.0\,\text{m/s}$. Calculate its kinetic energy.
Quantities — square $v$ first
$m=1.2\,\text{kg}$, $v=5.0\,\text{m/s}$, $v^2=25$.
$$KE = \tfrac{1}{2} \times 1.2 \times 25 = 15\,\text{J}$$Wrong: $\tfrac{1}{2}\times 1.2\times 5.0=3.0$, then forget to square. That is the mark I take off most often.
5 · $GPE\rightarrow KE$ without friction
Brick dropped from a wall
A brick of mass $2.0\,\text{kg}$ is dropped from rest from a height of $5.0\,\text{m}$. Air resistance is negligible.
Step 1 — gravitational store
$$\Delta GPE = 2.0 \times 10 \times 5.0 = 100\,\text{J}$$Step 2 — conservation (no drag)
$$KE = 100\,\text{J}$$Step 3 — speed
$$v^2 = \frac{2\times 100}{2.0} = 100 \qquad v = 10\,\text{m/s}$$Or $v=\sqrt{2gh}=\sqrt{2\times 10\times 5.0}=\sqrt{100}=10\,\text{m/s}$. The mass cancelled — a heavier brick hits at the same speed if there is no drag.
6 · $GPE\rightarrow KE$ with friction
Skateboard down a ramp
A skateboarder of mass $50\,\text{kg}$ starts from rest at a height of $3.2\,\text{m}$. On the way down, $400\,\text{J}$ is transferred to the thermal store by friction. Find the kinetic energy and the speed at the bottom.
Quantities
$m=50\,\text{kg}$, $h=3.2\,\text{m}$, $g=10\,\text{N/kg}$, $W_f=400\,\text{J}$.
$$\Delta GPE = 50 \times 10 \times 3.2 = 1600\,\text{J}$$ $$KE = 1600 - 400 = 1200\,\text{J}$$ $$v = \sqrt{\frac{2\times 1200}{50}} = \sqrt{48} \approx 6.9\,\text{m/s}$$Without friction the speed would have been $\sqrt{2gh}=\sqrt{64}=8.0\,\text{m/s}$. Friction has taken $400\,\text{J}$, so she is slower — that is the sense-check.
7 · $P=W/t$
A motor lifting a load
A motor lifts an $80\,\text{kg}$ load through $12\,\text{m}$ in $16\,\text{s}$ at constant speed. Calculate the work done against gravity and the useful power of the motor.
Work first (energy transferred to the gravitational store)
$$W = m g h = 80 \times 10 \times 12 = 9600\,\text{J}$$Then power
$$P = \frac{W}{t} = \frac{9600}{16} = 600\,\text{W}$$If the motor is only $75\%$ efficient, the electrical input power is $600/0.75=800\,\text{W}$. The extra $200\,\text{W}$ fills the thermal store of the motor and air.
8 · Explain (4 marks) · insulation
Why double glazing and cavity-wall foam reduce wasted energy
A house has cavity walls filled with foam and double-glazed windows. Explain how these features reduce the rate of thermal energy transfer to the outside.
Air (or the gas between the panes) is a poor conductor, so conduction through the window is reduced [1]. The trapped layer is thin / the foam fills the cavity, so convection currents cannot be set up in the gap [1]. Foam traps many pockets of air, which is a thermal insulator, so conduction through the wall is reduced [1]. Less energy leaves the thermal store of the room in a given time, so the house cools more slowly [1].
“They keep the heat in” with no mention of trapped air, conduction or convection is 1 mark at most. “Convection in the glass” is wrong — glass is a solid.
Then sit the five quizzes and the three papers.