3C.5.1 Oblique impact of spheres Quiz: Pearson Edexcel Further Maths, Unit 29

The 20 questions

1. In an oblique impact of smooth spheres, what is the line of centres?

   • The line joining the centres of the two spheres at the moment of impact
   • The common tangent at the point of contact
   • The direction of the initial velocity of either sphere
   • The horizontal direction, always

2. In an oblique impact of smooth spheres, what happens to the velocity components perpendicular to the line of centres?

   • They reverse direction
   • They are unchanged by the impact
   • They are multiplied by e
   • They become zero

3. To which velocity components does Newton's experimental law apply in an oblique impact?

   • Only the components perpendicular to the line of centres
   • It is not used in oblique impacts
   • The full speeds of the spheres
   • Only the components along the line of centres

4. When a smooth sphere strikes a smooth fixed plane obliquely, what happens to the component parallel to the plane?

   • It is reversed
   • It is unchanged
   • It is reduced by a factor of e
   • It increases

5. When a sphere strikes a smooth fixed plane obliquely, how is the normal component of velocity affected?

   • It is increased by e
   • It is divided by e
   • It is reversed and multiplied by e
   • It is multiplied by (1 - e)

6. In an oblique impact of smooth spheres, which quantities are conserved?

   • Momentum along the line of centres, and the perpendicular velocity components
   • Only kinetic energy is conserved in every case
   • Momentum perpendicular to the line of centres changes
   • The sum of the velocities is zero

7. A sphere with velocity components (parallel component u_t, normal component u_n) strikes a smooth fixed plane. What is its speed after impact?

   • u_t + e u_n
   • sqrt(u_t^2 + u_n^2)
   • sqrt(u_t^2 + e^2 u_n^2)
   • e times the total speed

8. A sphere has velocity (6i + 8j) m/s and hits a fixed smooth vertical wall whose normal is along i, with e = 0.5. What is its velocity after impact?

   • -6i + 4j m/s
   • -3i - 8j m/s
   • 3i + 8j m/s
   • -3i + 8j m/s

9. In the previous setting, what is the speed of the sphere after impact, to 2 decimal places?

   • 10 m/s
   • 8 m/s
   • 8.54 m/s, from sqrt(73)
   • sqrt(41) m/s

10. In the same setting (speed 10 m/s, e = 0.5), how much kinetic energy per unit mass is lost in the impact?

    • 13.5 J/kg
    • 25 J/kg
    • 36.5 J/kg
    • 50 J/kg

11. A sphere of mass 2 kg with velocity (5i + 5j) m/s hits a smooth vertical wall with e = 1. What is the impulse on the sphere?

    • -20i N s
    • -10i N s
    • 20i N s
    • -20j N s

12. A sphere approaches a smooth fixed plane at 30 degrees to the plane with speed 10 m/s, with e = 0.5. What is the component normal to the plane after impact?

    • 2.5 m/s
    • 1.25 m/s
    • 8.66 m/s
    • 5 m/s

13. Two equal smooth spheres of mass m lie with line of centres along x. Sphere 1 has velocity (4i + 2j) and sphere 2 is at rest. With e = 0.5, what is the velocity of sphere 1 after impact?

    • 2i + 2j
    • i + 2j
    • 3i + 2j
    • i

14. A sphere moving at 8 m/s makes an angle of 60 degrees with a smooth fixed plane and strikes it, with e = 0.6. What is its speed after impact, to 2 decimal places?

    • 4.16 m/s
    • 5.77 m/s
    • 4.00 m/s
    • 8.00 m/s

15. A sphere has velocity (3i + 4j) and hits a smooth horizontal plane whose normal is along j, with e = 0.25. What is its velocity after impact?

    • 0.75i - j
    • 3i - 4j
    • 3i - j
    • 3i + 0.25j

16. Two equal smooth spheres of mass m have line of centres along x. Sphere 1 has velocity 6i and sphere 2 is at rest, with e = 0.8. What is the velocity of sphere 2 after impact?

    • 6.0i m/s
    • 3.0i m/s
    • 4.8i m/s
    • 5.4i m/s

17. A smooth sphere approaches a smooth fixed plane at 30 degrees to the plane with speed 10 m/s and e = 0.5. What angle does its velocity make with the plane after impact, to 1 decimal place?

    • 30.0 degrees
    • 60.0 degrees
    • 16.1 degrees
    • 8.1 degrees

18. What is the direction of the impulse from a smooth fixed plane on a sphere striking it obliquely?

    • Parallel to the plane
    • Perpendicular to the plane
    • Zero, since the impact is oblique
    • At 45 degrees to the plane, always

19. Which quantity is unchanged by each impact of a sphere with a smooth fixed plane?

    • The component of velocity parallel to the plane
    • The component of velocity normal to the plane
    • The angle to the plane
    • The total kinetic energy

20. For a perfectly elastic (e = 1) oblique impact with a smooth plane, what is the relation between the angles of approach and rebound?

    • The speed halves and the angle doubles
    • The angle of rebound equals the angle of approach, measured to the plane
    • The angle of rebound is always 90 degrees
    • Only the normal component is preserved

Related quizzes

• Successive oblique impacts Quiz · 3C.5.2 · 20 questions
• Proof by mathematical induction Quiz · 1.1 · 20 questions
• Quadratic equations and complex arithmetic Quiz · 2.1-2.2 · 20 questions
• Matrix arithmetic and inverses Quiz · 3.1-3.2 · 20 questions
• Expectation of discrete random variables Quiz · 3B.1.1 · 20 questions
• The Poisson distribution Quiz · 3B.2.1 · 20 questions
• Geometric and negative binomial models Quiz · 3B.3.1 · 20 questions
• Hypothesis tests for the Poisson distribution Quiz · 3B.4.1 · 20 questions
• Applying the Central Limit Theorem Quiz · 3B.5.1 · 20 questions
• Goodness of fit tests for discrete distributions Quiz · 3B.6.1 · 20 questions