Scalars, vectors and resultants — questions

1. identify

Supplement. Is each quantity a scalar or a vector?

Write the number of the matching option.

1. scalar: size only
2. vector: size and direction

• speed: ______
• velocity: ______
• time: ______
• weight: ______
• mass: ______
• gravitational field strength: ______
• energy: ______

Nudge (only if you are stuck): For each one, ask: does it make sense to say which way it points?

2. identify / give

Supplement. Which statement gives the difference between a scalar and a vector? Then give one example of each.

Circle one answer.

• A scalar has size only; a vector has size and direction
• A scalar is always positive; a vector can be negative
• A scalar is measured; a vector can only be calculated
• A scalar has a unit; a vector is a number with no unit

One example of a scalar and one of a vector

Nudge (only if you are stuck): Test each statement on two quantities you know: the mass of a bag and the pull of a rope on it. Which statement is true for both?

3. identify / explain

Supplement. Three trains move along straight tracks. Train X moves at 30 m/s towards the north, train Y at 30 m/s towards the south, and train Z at 25 m/s towards the north. Which row of the table compares them correctly? Then explain your choice for X and Z.

Circle one answer.

• A
• B
• C
• D

Explain your choice for X and Z

Nudge (only if you are stuck): Speed tells you how fast. What does velocity tell you as well?

4. calculate

Supplement. On the air table, meter E pulls the puck east with 0.15 N, and meter N pulls it north with 0.10 N, at the same time. Calculate the size of the resultant force on the puck, and its angle north of east.

Size of the resultant force: ______________ unit ________

Angle north of east: ______________ unit ________

Nudge (only if you are stuck): The two pulls are at right angles. Draw them tip to tail: what kind of triangle do they make with the resultant?

5. describe

Supplement. Two tugboats pull a barge: one with 50 kN towards the east, the other with 20 kN towards the north (1 kN = 1000 N). Put the steps of a scale drawing in order, to determine the resultant force on the barge.

Write the number of each step in order.

1. From the tip of that arrow, draw an arrow 2.0 cm long towards the north
2. Measure the resultant’s length and its angle from the east line, and change the length back into kilonewtons with the scale
3. Choose a scale, such as 1 cm = 10 kN
4. Draw the resultant from the start of the first arrow to the tip of the second
5. Draw an arrow 5.0 cm long towards the east

• Step 1: ______
• Step 2: ______
• Step 3: ______
• Step 4: ______
• Step 5: ______

Nudge (only if you are stuck): The two arrows go tip to tail, like two stages of a walk. What must you decide before you draw anything?

6. calculate

Supplement. A kayak points straight across a river. The current carries the water downstream at 0.70 m/s. A GPS watch shows that the kayak’s resultant velocity over the river bed is 1.9 m/s. Calculate the kayak’s speed through the water.

Speed through the water: ______________ unit ________

Nudge (only if you are stuck): The resultant is the longest side of the right-angled triangle. Which side are you looking for?

7. identify / explain

Supplement. Which of these are vectors? Choose all that are vectors. Then explain your choice for the temperature.

Tick every correct statement.

• A distance of 2.0 km
• The momentum of a moving trolley
• An electric field strength
• A temperature of −10 °C
• An acceleration of 2.0 m/s²
• An energy of 500 J
• A force of 5.0 N

Explain your choice for the temperature

Nudge (only if you are stuck): Picture each one on a map: could you draw it as an arrow pointing a certain way?

8. determine / give

Supplement. Two tow lines pull a barge in a wide harbour. One pulls towards the east with 350 N, and the other pulls towards the north with 600 N. Hana finds the resultant force by scale drawing, with a scale of 1 cm = 50 N. (a) Determine the length of the arrow she must draw for the 600 N force. (b) Her resultant arrow is 13.9 cm long, at 60° to her east arrow. Determine the size of the resultant force. Then give its direction.

(a) Length of the arrow for 600 N: ______________ unit ________

(b) Size of the resultant force: ______________ unit ________

The direction of the resultant force

Nudge (only if you are stuck): Write the scale in words: each centimetre of arrow stands for 50 N.

9. calculate

Supplement. A light aircraft heads north through the air at 60 m/s. A wind blows the air east at 15 m/s. Calculate (a) the size of the aircraft’s resultant velocity over the ground, to 2 significant figures, and (b) its angle east of north, to the nearest degree.

(a) Size of the resultant velocity: ______________ unit ________

(b) Angle east of north: ______________ unit ________

Nudge (only if you are stuck): Draw the two velocities tip to tail. For (b), which velocity is the side opposite the angle at north?

10. calculate / explain

Supplement. A hot-air balloon rises at a steady 2.0 m/s through the air. A wind carries the air east at 5.0 m/s. (a) Calculate the size of the balloon’s resultant velocity, and its angle from the vertical. (b) Calculate how long the balloon takes to rise 300 m. (c) Calculate how far east it drifts in that time. (d) On another day the wind blows at 8.0 m/s, and the balloon again rises at 2.0 m/s through the air. Explain whether it takes more time, less time or the same time to rise 300 m. (e) Leo says the balloon’s resultant velocity in (a) is 2.0 m/s + 5.0 m/s = 7.0 m/s. Explain why he is wrong, using the words scalar and vector.

(a) Resultant velocity

(b) Time to rise 300 m

(c) Distance east

(d) A stronger wind

(e) Leo’s claim

Nudge (only if you are stuck): Draw the two velocities tip to tail. For (b) and (d), which part of the velocity carries the balloon upwards?