1. 1
   A toy designer is developing a wooden rocking horse for young children, which must be able to rock gently back and forth on its curved rockers without tipping over.

   (a)

   A toy designer is developing a wooden rocking horse that must rock gently back and forth without tipping over. Which term describes the single point at which the whole mass of the rocking horse may be thought to be concentrated?

   [1 mark]

   • AThe pivot point
   • BThe centre of mass
   • CThe line of action
   • DThe base of support

   (b)

   The rocking horse is designed with a symmetrical body, so that the left and right sides are mirror images of each other. Along which line would you expect the centre of mass of the horse's body to lie?

   [1 mark]

   • AAlong the axis of symmetry
   • BAlways at the very top of the object
   • CAlways at the very bottom of the object
   • DOutside the object entirely

   (c)

   Explain why placing the rocking horse's centre of mass low down, close to the curved rockers, makes the toy safer and less likely to tip over when a child rocks on it energetically.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A student in a physics practical needs to find the centre of mass of an irregularly shaped thin sheet of cardboard, using a pin, a hole punched near the edge of the shape, and a plumb line (a small weight on a thread).

   (a)

   They hang the cardboard freely from a pin through a hole near its edge, allowing it to swing to rest, then hang a plumb line (a weight on a thread) from the same pin. Why does the student draw a line along the plumb line's thread once the cardboard has settled?

   [1 mark]

   • ABecause the centre of mass must lie somewhere along this vertical line
   • BBecause the plumb line marks the exact edge of the cardboard
   • CBecause the thread shows the direction of air resistance on the cardboard
   • DBecause the line shows where the cardboard is thickest

   (b)

   The student repeats the process, hanging the cardboard from a second, different hole near another part of its edge, and again draws a line along the new plumb line's thread. Why must the student use at least two different suspension points to find the exact location of the centre of mass?

   [1 mark]

   • AThe centre of mass moves each time the cardboard is suspended
   • BThe cardboard becomes heavier after each suspension
   • CA single suspension point only shows a line the centre of mass lies on, not its exact position
   • DTwo points are needed to calculate the cardboard's weight

   (c)

   Explain how the student uses the two lines drawn from the two different suspension points to identify the exact position of the centre of mass of the cardboard shape.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A double-decker bus is loaded with standing passengers distributed across both the lower and upper decks before setting off on a journey along a route with several sharp bends.

   (a)

   A double-decker bus is loaded with standing passengers on both the lower and upper decks before setting off on a journey with several sharp bends. Explain, in terms of the position of the centre of mass, why a bus company might be concerned if too many passengers stand on the upper deck rather than the lower deck.

   [3 marks]

   (b)

   The bus company decides to redesign the vehicle so that heavier components, such as the engine and fuel tank, are positioned as low as possible in the chassis. Explain how this design choice affects the position of the bus's overall centre of mass and its stability, and describe what would happen to the bus if its centre of mass moved so far to one side that the line of action of its weight fell outside its base of support while cornering.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A shipping company is designing a new cargo ship and must decide how to distribute heavy shipping containers on board to keep the ship stable when travelling through rough seas.

   (a)

   Explain, using ideas about centre of mass, line of action of weight, and base of support, how the position of the centre of mass affects the stability of a floating ship, and why loading heavy containers too high on deck could be dangerous.

   [6 marks]

   (b)

   During a storm, the ship rolls to one side and an engineer observes that it always seems to right itself and roll back upright, rather than continuing to tip over. Explain, in terms of centre of mass and the base of support, why a well-designed ship rights itself after rolling in typical conditions, and explain the conditions under which this might fail and the ship could instead capsize.

   [6 marks]

   Total for question 4: 12 marks

End of questions