4C.3.3 Toppling and sliding of rigid bodies Quiz: Pearson Edexcel Further Maths, Unit 32

The 20 questions

1. Where does the vertical line through the centre of mass pass when a rigid box topples?

   • Inside base
   • Beyond base edge
   • Through the centre
   • Above top edge

2. What condition on the inclination angle theta causes a body on a rough plane to slide?

   • cos theta > mu
   • tan theta > mu
   • theta > 45 degrees
   • sin theta > mu

3. A uniform block has base half-width b and centre of mass at height h above the base, on a slope of angle theta. Which condition gives toppling?

   • tan theta > h/b
   • tan theta < b/h
   • tan theta > 2b/h
   • tan theta > b/h

4. What does the friction force equal when a body is on the point of sliding?

   • mu R
   • R / mu
   • mu / R
   • zero

5. Where does the normal reaction act when a block is on the verge of toppling?

   • Distributed evenly
   • At the pivot edge
   • Outside the base
   • At the centre

6. What condition ensures a pushed block on a horizontal plane does not topple?

   • Normal force zero
   • Height exceeds width
   • Friction exceeds force
   • Weight line in base

7. In which direction does friction act when a block is about to slide up a rough incline?

   • down the slope
   • up the slope
   • vertically upwards
   • horizontally

8. What physical parameter represents the maximum angle of a rough incline before sliding occurs?

   • Angle of friction
   • Limiting angle
   • Critical angle
   • Toppling angle

9. A uniform box with a square base of width 0.6 m has its centre of mass 0.8 m above the base. What is the critical value of tan theta for toppling on a slope?

   • 1.33
   • 0.3
   • 0.375
   • 0.75

10. What is the state of a block if tipping moments about its lower edge exactly balance?

    • accelerating
    • stable equilibrium
    • sliding
    • verge of toppling

11. A 5 kg block rests in equilibrium on a rough slope at 20 degrees without sliding (g = 10 m/s^2). What is the friction force?

    • 17.1 N
    • 18.2 N
    • 47.0 N
    • 1.7 N

12. A block is on the point of sliding on a rough plane with coefficient of friction 0.75. What is the angle of the plane?

    • 36.9 degrees
    • 48.8 degrees
    • 41.4 degrees
    • 53.1 degrees

13. For a uniform block on a rough slope, what condition ensures it topples before sliding?

    • b/h = mu
    • b/h > mu
    • b/h < mu
    • h/b < mu

14. A 4 kg block rests on a rough horizontal floor with coefficient 0.3 (g = 10 m/s^2). It is pushed horizontally with 10 N and stays at rest. What is the friction force?

    • 12 N
    • 40 N
    • 0 N
    • 10 N

15. A 2 kg block is on a rough slope where tan theta = 0.5 and friction is limiting (g = 10 m/s^2). What is the normal reaction?

    • 8 sqrt(5) N, about 17.9 N
    • 4 sqrt(5) N, about 8.9 N
    • 20 N
    • 10 N

16. A block has base half-width 0.4 m and centre of mass height 1.2 m, and rests on a rough slope with coefficient 0.6. As the slope angle increases, what happens first?

    • Sliding, at tan theta = 0.6
    • Toppling, at tan theta = 0.6
    • Toppling, at tan theta = 1/3
    • Sliding, at tan theta = 1/3

17. A uniform cube of side a rests on a rough slope with coefficient of friction greater than 1. At what slope angle does it topple?

    • arctan(2), about 63.4 degrees
    • 30 degrees
    • 45 degrees
    • 60 degrees

18. A uniform block of weight 50 N has base half-width 0.2 m and centre of mass height 0.5 m. It is pushed horizontally at the height of its centre of mass on a rough floor. What push first causes toppling?

    • 50 N
    • 20 N
    • 5 N
    • 10 N

19. What geometric property of a rigid body makes toppling occur before sliding on an incline?

    • Narrow base
    • Smooth surface
    • Heavy mass
    • Wide base

20. A block has b/h = 0.5 and coefficient of friction 0.8 on a rough slope. At what angle does it first move, and how?

    • 14.0 degrees, by toppling
    • 26.6 degrees, by toppling
    • 45 degrees, by sliding
    • 38.7 degrees, by sliding

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