15.1 Fundamental and derived SI quantities and units — Practise

Work through these on your own. Before you write a number, decide which quantity it measures and which unit belongs with it. Check the direction of every conversion.

Both the questions and the answers below come from a set that is checked by computer every time the book is built.

Convert $2.5$ km to metres.
Convert $340$ cm to metres.
Convert $90$ km/h to m/s.
Convert $15$ m/s to km/h.
Find the weight of a mass of $7.5$ kg. Take $g = 9.8$ m/s $^2$ .
Find the moment of a force of $36$ N acting at a perpendicular distance of $0.25$ m from a pivot.
A mass of $8$ kg accelerates at $2.5$ m/s $^2$ . Find the force that acts on it.
A force of $45$ N acts on a mass of $9$ kg. Find the acceleration.
Convert $250$ ms to seconds.
A bag has a mass of $2$ kg $400$ g. Write the mass in kilograms, and find its weight. Take $g = 9.8$ m/s $^2$ .
A cyclist travels $3.6$ km in $5$ minutes. Find the average speed in m/s.
A force produces a moment of $18$ N m at a perpendicular distance of $0.6$ m from the pivot. Find the force.

Answers and concise solutions

1. The length in metres

Answer: Kilo means $1000$ , so multiply by $1000$ : $2.5 \text{ km} = 2500$ m.

2. The length in metres

Answer: Centi means $0.01$ , so divide by $100$ : $340 \text{ cm} = \dfrac{340}{100} = 3.4$ m.

3. The speed in m/s

Answer: Multiply by $\dfrac{5}{18}$ : $90 \times \dfrac{5}{18} = 25$ m/s. The number in m/s is smaller than in km/h, as expected.

4. The speed in km/h

Answer: Multiply by $\dfrac{18}{5}$ , which is $3.6$ : $15 \times 3.6 = 54$ km/h. The number in km/h is larger than in m/s, as expected.

5. The weight

Answer: Weight is a force, so use $W = mg$ : $W = 7.5 \times 9.8 = 73.5$ N.

6. The moment

Answer: Multiply the force by the perpendicular distance: $36 \times 0.25 = 9$ N m.

7. The force

Answer: Use $F = ma$ : $F = 8 \times 2.5 = 20$ N.

8. The acceleration

Answer: Rearrange $F = ma$ to $a = \dfrac{F}{m}$ : $a = \dfrac{45}{9} = 5$ m/s $^2$ .

9. The time in seconds

Answer: Milli means $0.001$ , so divide by $1000$ : $250 \text{ ms} = \dfrac{250}{1000} = 0.25$ s.

10. The mass in kg and the weight

Answer: Convert the grams first: $400 \text{ g} = 0.4$ kg, so the mass is $2.4$ kg. Then $W = mg = 2.4 \times 9.8 = 23.52$ N.

11. The average speed

Answer: Change the units first: $3.6 \text{ km} = 3600$ m and $5$ minutes $= 300$ s. Then divide: $\dfrac{3600}{300} = 12$ m/s.

12. The force

Answer: Rearrange the moment formula, $\text{moment} = Fd$ : $F = \dfrac{18}{0.6} = 30$ N.