Mechanics: Quantities and units in mechanicsEdexcel A-Level Maths: Topic test

1. 1
   A parcel of mass $2500$ g is placed on the floor of a lift. Take $g=9.8$ m s$^{-2}$.

   (a)

   What is the mass of the parcel in kilograms?

   [1 mark]

   • A$2.5$ kg
   • B$25$ kg
   • C$0.25$ kg
   • D$2500$ kg

   (b)

   What is the weight of the parcel?

   [1 mark]

   • A$2.5$ N
   • B$245$ N
   • C$24.5$ N
   • D$0.26$ N

   (c)

   Express the weight of the parcel in terms of the S.I. base units kilogram, metre and second.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A train travels at a constant speed of $108$ km h$^{-1}$ past a station platform.

   (a)

   What is the speed of the train in m s$^{-1}$?

   [1 mark]

   • A$388.8$
   • B$30$
   • C$1.8$
   • D$108\,000$

   (b)

   How far does the train travel in $40$ seconds?

   [1 mark]

   • A$4320$ m
   • B$120$ m
   • C$12\,000$ m
   • D$1200$ m

   (c)

   Later the train slows to $15$ m s$^{-1}$. Express this speed in km h$^{-1}$.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A ball is thrown from a window and is modelled as a particle moving freely under gravity, with $g=9.8$ m s$^{-2}$.

   (a)

   State three modelling assumptions that are made in this model.

   [3 marks]

   (b)

   Explain how two of these assumptions may be unrealistic and say how each would affect the real motion of the ball.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A uniform beam $AB$ has mass $20$ kg and length $4.0$ m. It is horizontal and hinged at $A$. A load exerts a downward force of $50$ N at a point on the beam $150$ cm from $A$. The weight of the beam and the force from the load both tend to turn the beam in the same direction about $A$. Take $g=9.8$ m s$^{-2}$.

   (a)

   Find the total moment about $A$ of the weight of the beam and the force from the load, giving the unit of your answer in S.I. base units.

   [6 marks]

   (b)

   State the modelling assumptions about the beam that are implied by the words 'uniform' and 'rigid'. In fact the centre of mass of the beam is $2.4$ m from $A$. Find the total moment about $A$ for this beam and comment on the effect of the uniform assumption.

   [6 marks]

   Total for question 4: 12 marks

5. 5
   A motorcyclist's speed increases uniformly from rest to $28$ m s$^{-1}$ in $7$ s.

   (a)

   What is the acceleration of the motorcycle?

   [1 mark]

   • A$4$ m s$^{-1}$
   • B$196$ m s$^{-2}$
   • C$0.25$ m s$^{-2}$
   • D$4$ m s$^{-2}$

   (b)

   What is the final speed in km h$^{-1}$?

   [1 mark]

   • A$7.78$
   • B$100.8$
   • C$1.68$
   • D$28\,000$

   (c)

   Express the acceleration of the motorcycle in km h$^{-2}$.

   [2 marks]

   Total for question 5: 4 marks

6. 6
   A box is pulled along a horizontal floor by a light, inextensible rope.

   (a)

   What does it mean to model the rope as light?

   [1 mark]

   • AThe rope cannot stretch.
   • BThe rope has no thickness but has a large mass.
   • CThe mass of the rope is negligible.
   • DThe tension is zero.

   (b)

   What does it mean to model the rope as inextensible?

   [1 mark]

   • AThe length of the rope does not change when it is pulled.
   • BThe rope has negligible mass.
   • CThe rope exerts no force on the box.
   • DThe rope is rough.

   (c)

   The box is also modelled as a particle. State what this assumption means and give one situation in which it would not be appropriate.

   [2 marks]

   Total for question 6: 4 marks

7. 7
   A hiker walks at a constant speed of $4.5$ km h$^{-1}$ for $2$ hours and $20$ minutes.

   (a)

   Find the distance walked, in metres.

   [3 marks]

   (b)

   A student writes 'distance $=4.5\times140=630$ km'. Explain the error and find the correct distance in kilometres.

   [4 marks]

   Total for question 7: 7 marks

8. 8
   A trolley of mass $12.0$ kg carries 30 identical books, each of mass $850$ g. It is pushed $36$ m along a corridor in $40$ s at a constant speed. Take $g=9.8$ m s$^{-2}$.

   (a)

   Find the total weight of the trolley and books in newtons, and the speed of the trolley in km h$^{-1}$.

   [6 marks]

   (b)

   The trolley is modelled as a particle moving at a constant speed along a smooth horizontal floor. Identify three modelling assumptions and, for each, give one way in which the real motion could differ.

   [6 marks]

   Total for question 8: 12 marks

End of questions