A strong planning answer gives each sentence a clear job. 1. State what changes and what stays constant. 2. Name what you will measure, the apparatus and timing. 3. Give the exact quantities to use. 4. Define the observable endpoint. 5. Explain how you will process the results. 6. Match eac

10.19 cm, 10.20 cm and 10.21 cm are tightly grouped, but all can still be biased in the same direction. A zero check reveals a +0.20 cm systematic offset. After subtracting it, the mean changes from 10.20 cm to 10.00 cm while the 0.02 cm spread remains. Extra displayed decimal places do no

When one oscillation is too short to time well by hand, time several complete oscillations instead. The same start-stop error is a larger fraction of a short interval. Choose N so the total time is long enough to measure well. Repeat the total time and keep both raw readings. Then calculat

Two neighbouring nodes are half a wavelength apart, not one full wavelength. A node stays still, while an antinode has the largest displacement amplitude. The solid and dashed curves show the same string at opposite extremes. A node and its nearest antinode are a quarter wavelength apart.

Squaring takes both −2 and 2 to 4. An inverse function must take each output back to just one input. Restrict the original domain to x ≥ 0, and the inverse is f⁻¹(x) = √x, defined for x ≥ 0. What changes if we keep x ≤ 0 instead? Choose the inverse on the last slide and state its domain

In this example, some bacteria are resistant before the antibiotic is added. The antibiotic kills susceptible bacteria, while resistant survivors reproduce. They pass on resistance, so it becomes more common in the population. This is natural selection, not bacteria changing because they n

Before mitosis, DNA replicates during S phase of interphase. The DNA doubles, but the chromosome number stays the same. Each replicated chromosome has two sister chromatids, each containing one DNA molecule. The sisters count as separate chromosomes when they separate at anaphase. DNA a

At low substrate concentrations, adding more substrate increases the initial reaction rate. Near saturation, most enzyme active sites are occupied, so extra substrate has little effect. Adding more enzyme raises the maximum rate, provided substrate remains in excess. This comparison assume

After one half-life, about half the original nuclei remain undecayed. After two, about a quarter remain. Each half-life halves what is left, not the starting number. These fractions describe a large sample, not when an individual nucleus will decay. After three half-lives, what percenta

Halfway between two equal positive charges, the electric fields cancel. Their potentials add. With zero potential defined at infinity, the midpoint has zero field but positive potential. What changes if both charges are negative?

Make the slit narrower and the central bright band spreads out. Keep the wavelength and screen distance unchanged. At small angles, halving the slit width nearly doubles the central band’s width. The graphs compare width, not brightness: their peaks are scaled equally. With the same sli

At the turning point, an oscillator stops for an instant before moving back towards the centre. Its velocity is zero, but its acceleration is not. In ideal simple harmonic motion, acceleration points towards equilibrium and grows in magnitude with displacement. At equilibrium, the reverse

The wave rises twice as far from equilibrium. Its intensity becomes four times as large, not twice. For the same wave type, frequency and medium, intensity is proportional to amplitude squared: I ∝ A². Halve the amplitude and the intensity falls to one quarter. If the intensity becomes

When two carts collide and stick, total momentum is conserved if external impulse is negligible. The carts then share one final velocity. Kinetic energy is not conserved in the collision; some energy is transferred to other stores, including internal energy. Work through the numbers, then

Zero acceleration does not mean zero speed. As a falling object speeds up, air resistance increases and its downward acceleration decreases. At terminal velocity, air resistance balances weight, so the object keeps falling at constant speed. This model assumes vertical fall from rest in st

Circular Motion. Constant speed. Changing direction. Is acceleration constant?

The light gets brighter, but no electrons leave the metal. Below the threshold frequency, increasing intensity cannot trigger emission in the ordinary single-photon photoelectric effect. At a fixed frequency, greater intensity means more photons arriving per second over the same area, not mor