Mass and Weight Worked ExamplesIGCSE Physics 0625

(a) Rearrange $g = \dfrac{W}{m}$ to give $W = mg$.

(b) Convert the prefix first: $1.47\text{ kN} = 1470\text{ N}$.

Rearrange for mass.

(a) Mass is a measure of the quantity of matter in an object (at rest relative to the observer) (1).

(b) Weight is the gravitational force on an object that has mass — the effect of a gravitational field on a mass (1).

(c) Gravitational field strength is the force per unit mass (1).

(d) It is equivalent to the acceleration of free fall (1) — so $9.8\text{ N/kg}$ and $9.8\text{ m/s}^2$ are the same quantity.

Statement 1 is the definition of mass, not weight — incorrect.

Statement 2 is correct: weight is the gravitational force on an object that has mass — the effect of a gravitational field on that mass.

Statement 3 is incorrect: weight is a force, measured in newtons. Kilograms are the unit of mass.

Statement 4 is correct: weight is a vector, acting towards the centre of the Earth (or planet).

So the answer is B. Options C and D each add one of the two tempting errors to the correct pair.

(a) At the surface $g = 9.8\text{ N/kg}$.

(b) Read up from $12.8$ on the distance axis to the curve, then across: each small square on the $g$ axis is $0.2\text{ N/kg}$, and the reading is about $2.45\text{ N/kg}$ (1).

Multiply by the mass (1).

(c) $1200\text{ kg}$ (1). Mass is the quantity of matter in the satellite, which does not depend on where it is; only the gravitational field strength, and so the weight, has changed (1).

(a) Use $W = mg$.

(b) Find the field strength from $g = \dfrac{W}{m}$ (1), then match it to the table (1).

(c) The mass is still $180\text{ kg}$ everywhere, so the weight depends only on $g$. The largest $g$ is on Jupiter (1).

On Earth the weight is only $1764\text{ N}$ and on Mars $666\text{ N}$, both below $2000\text{ N}$. So Jupiter is the only body where the legs could not support the rover (1).

(a) Subtract the mass of the empty beaker from the total (1 for working shown).

(b) Convert grams to kilograms before using $W = mg$: $125.3\text{ g} = 0.1253\text{ kg}$.

(c) Any one: check that the balance reads zero with nothing on it (zero or tare the balance); make sure the balance is on a level surface; place the beaker in the centre of the pan.

(a) Draw a horizontal line from $9.1\text{ cm}$ on the length axis to the best-fit line, then a vertical line down to the mass axis (1 for construction lines). Each small square on the length axis is $0.2\text{ cm}$, so $9.1$ is half a square above $9.0$.

The vertical line meets the mass axis at $170\text{ g}$ (1). Check with the line's equation: length $= 4.0 + 0.030 \times$ mass.

(b) Convert to kilograms, then use $W = mg$.

(c) No (1). A spring stretches because of the weight hanging on it, not the mass. On the Moon the stone's weight is smaller, so the spring stretches less and the graph (made on Earth) gives a mass that is too small — about $28\text{ g}$ (1).

(a) Each small division is $0.2\text{ N}$. X: three divisions above $2\text{ N}$, so $2.6\text{ N}$. Y: four divisions above $7\text{ N}$, so $7.8\text{ N}$.

(b) Use $m = \dfrac{W}{g}$ for each block.

(c) Both blocks are in the same gravitational field, so the one with the larger weight has the larger mass: Y has three times the weight, so three times the mass (1). Mass is the quantity of matter, so Y contains more matter in the same volume — the blocks are made of different materials (1).

(a) At a steady speed the resultant force is zero, so the upward force equals the weight of the box.

(b) Work done = force × distance moved in the direction of the force (1). Use the force in newtons, not the mass.

Evaluate, with the unit (1).

(a) The pallet moves at constant velocity, so the resultant force on it is zero (1). The upward force therefore balances the weight: $W = 7.35\text{ kN}$ (1).

(b) Convert to newtons, then use $m = \dfrac{W}{g}$.

(a) Use $W = mg$.

(b) The two forces act in opposite directions along the same line, so subtract (1).

(c) Use $F = ma$ with the resultant force.

A balance does not detect mass directly: it measures the downward force on its pan and divides by $g$ to show grams. So the reading of $65.0\text{ g}$ means the downward force on the pan is

The block's weight has not changed (its mass is still $180\text{ g}$).

The block is at rest, so the upward forces (magnet + pan) balance its weight. The magnet supplies the rest.

So the answer is B. A is the force on the pan; C is the weight of the block; D adds the two readings instead of subtracting.