IPSG PPT ChQns

L I M S I E W E N G & L E N A L U IR A F F L E S I N S T I T U T I O N

8th Physics IPSG Sharing 2016

CHALLENGING PHYSICS QUESTIONS

CHALLENGING PHYSICS QUESTIONS

Rationale • To provide an enrichment activity for students who wish to

learn slightly beyond the A-Level syllabus.

Types of challenging questions • do not require additional knowledge outside of H2 A-Level

syllabus• Require beyond H2 knowledge

Where to find them?• Books• Online• Past Olympiad question papers• Create your own

Challenging Physics Questions

OUTLINE OF EXAMPLES

1. Relative velocity (Kinematics) refer to Q1

2. Extension of Projectile Motion (Kinematics) – the safety parabola and finding maximum range for a projectile launched from a cliff edge.

refer to Q2, Q 3.

3. Differential equations in Physics – can be applied in Kinematics, Dynamics, Oscillations, Radioactivity etc.


OUTLINE OF EXAMPLES

4. Extension of a topic – e.g:5. (i) Gravitational field (H2 requires knowledge of

Newton’s Law of Gravitation but not Kepler’s Laws of planetary motion) refer to Q5;

6. (ii) Electromagnetism (crossed E and B fields, but velocity vector is parallel to the E field instead of being perpendicular to it refer to Q6.


+V

E B

aC

x

Crossed-field Photomultiplier

OUTLINE OF EXAMPLES

5. Real world context 6. E.g. what is the shape of a hanging chain?

7. Resembles a parabola, but is a catenary.


Q1 : RELATIVE VELOCITY

• A car of width b is moving with constant velocity V close to the edge of a straight road. If a cat steps on to the road at a point distance d in front of the car, what is the least uniform velocity at which it must be able to walk in order to cross the road in safety?

Example Questions

?b

Q2 : SAFETY PARABOLA

• If a projectile is fired from a point O with an initial velocity u but at an arbitrary direction, determine the safe area in which one cannot be hit by the projectile regardless of the angle that the initial velocity makes with the horizontal plane.

Example Questions

Q3 (MAX RANGE FOR “OFF THE CLIFF” THROWS)

• A ship battled against its enemy stationed at a fort which was at a height above the guns on the ship. If the guns in both the ship and the fort had the same muzzle velocity of , where is a constant; and if and were the greatest (horizontal) ranges at which the fort and ship respectively can engage, prove that .

Q4 DIFFERENTIAL EQUATIONS IN PHYSICS

• A particle of mass m is released from rest at a point, height h above horizontal ground. The particle moves in a medium which exerts a resistance of magnitude , where v is the speed of the particle and k is a positive constant. The coefficient of restitution between the particle and the ground is . Show that, after one bounce on the ground the particle reaches a maximum height H, where H is given by .

Q5 EXTENSION OF A TOPIC (GRAVITATION)

• Kepler’s First Law states that all planets move in elliptical orbits with the Sun at one focus. • Show that the path of a planet moving around the

Sun is an ellipse.

Q6 EXTENSION OF TOPIC (E, B FIELDS) – SPHO 2009

• The figure below shows the principle of operation of a crossed-field photomultiplier. A sealed and evacuated enclosure contains two parallel plates called dynodes. These plates provide the electric field. An external permanent magnet superimposes a magnetic field . A photon ejects a low energy photoelectron.

+V

E B

aC

x


• The electron accelerates upwards under the electric field but it is deflected to the negative dynode by the magnetic field. On impact with the dynode it ejects a few secondary electrons and the process repeats itself until eventually the electrons impinge on a collector C.


+V

E B

aC

x



(i) write down differential equations to describe the horizontal and vertical velocity of the electrons as a function of x and y, (ii) solve the differential equations for and (this trajectory is a cycloid).(iii) find the maximum value of y, and(iv) determine the value of . +V

E B

aC

x


Q7 REAL WORLD CONTEXTDerive the equation of the Catenary.

http://www.carondelet.pvt.k12.ca.us/Family/Math/03210/page5.htm

Q7 SOLUTION

• To derive the equation of a catenary:

T0C

T

P

A B

x

0

THANK YOU!

• Questions?

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