Question 1(a) Achieved

Tane has a toy car track: part is a horizontal banked curve of radius 0.750 m, part is a vertical loop of radius 0.250 m. The car has a mass of 0.120 kg. Assume sideways friction on the tyres is negligible.

On a diagram of the car on the banked curve, draw a vector diagram to identify the net force that makes the car go in a horizontal circle. Label the net force.

The 2023 paper, page 2 ↗ Marking schedule, page 1 ↗

Work it out

Try it on paper first. Stuck? Take one hint at a time.

1. 1 With no sideways friction, which two forces act on the car on the banked curve?

   Its weight, mg, straight down, and the track’s reaction force, at right angles to the sloping surface, so tilted in towards the centre of the curve.

2. 2 The car goes round a horizontal circle. Which way must the net force point?

   Horizontally, towards the centre of that circle. The net force is the centripetal force.

3. 3 How do the two forces add up to it on a vector diagram?

   Draw them nose to tail: the weight down, then the reaction force from its tip. The arrow that closes the triangle is horizontal and points to the centre. Label it F_net (or F_c). It is the horizontal part of the reaction force; the vertical part cancels the weight.

What the marker wanted

• Achieved The net force drawn the right way on the diagram (labelled F_c, F_net or the horizontal part of the reaction force), or a vector diagram the right way round.

The schedule’s Merit cell for this part holds a bullet point with nothing after it. Nothing is listed there, so this part is Achieved only.

In our words, from NZQA’s 2023 marking schedule.

Common mistake

How did it go?

Got it moves it further out. Review brings it back tomorrow.