A Projectile is Fired Horizontally From a Launching Device

A projectile is fired horizontally from a launching device, exiting with a speed ux . While the projectile is in the launching device, the impulse imparted to it is J p , and the average force on it is Favg . Assume the force becomes zero just as the projectile reaches the end of the launching device. Express your answers to parts (a) and (b) in terms of ux , J p , Favg , and fundamental constants, as appropriate.

(a) Determine an expression for the time required for the projectile to travel the length of the launching device.(b) Determine an expression for the mass of the projectile. The projectile is fired horizontally into a block of wood that is clamped to a tabletop so that it cannot move. The projectile travels a distance d into the block before it stops. Express all algebraic answers to the following in terms of d and the given quantities previously indicated, as appropriate.

(c) Derive an expression for the work done in stopping the projectile.(d) Derive an expression for the average force Fb exerted on the projectile as it comes to rest in the block.

Now a new projectile and block are used, identical to the first ones, but the block is not clamped to the table. The projectile is again fired into the block of wood and travels a new distance dn into the block while the block slides across the table a short distance D. Assume the following: the projectile enters the block with speed ux , the average force Fb between the projectile and the block has the same value as determined in part (d), the average force of friction between the table and the block is fT , and the collision is instantaneous so the frictional force is negligible during the collision.

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General Certificate of Education (Adv.Level) Examination, 2013

%%%%%%Physics%%%%%%%%%

Grade 12- 1st Term Test 2013

Paper 2 Time 1hours Part B

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(2) Fig (1) shows a properly cut diamond. A diamond sparkles because the intensity of the light coming from is greatly enhanced due to total internal reflection. As shown in the Fig (2) a monochromatic ray of light is incident on to the top surface, AB, of a diamond held in air, with an angle of incidence i. It then refracts with a refracting angle r and strikes the inclined surface, CD, of the diamond. Use the following data for your calculations

sin 5° = 0.0870 sin 24° = 0.4000sin 7.5° = 0.1305 sin 42° = 0.6667sin 10° = 0.1737 sin 80° = 0.9800sin 23° = 0.3920

(a) Determine the critical angle for diamond - air interface. The refractive index of diamond is 2.5.(b) Using the geometrical diagram shown in Fig (2) find out an expression for the angle of incidence, iʹ, of the ray on the inclined surface CD in terms of θ and r. Here θ is the inclination of the surface CD to the horizontal.

(c) (i) For i = 80°, determine r.(ii) Determine the minimum value of θ (θmin) for this ray of light to be just totally internally reflected from the surface CD.

(iii) Hence show that all light rays incident on the surface AB with i values less than or equal to 80° will be totally internally reflected from the surface CD.

(iv) What would happen if θ < θmin?

(d) (i) For a glass structure with the same geometry with θ = θmin as in Fig (2), determine the maximum angle of incidence, i, that a ray must have so that it will be totally internally reflected from the surface CD. (Refractive index of glass = 1.5)


(ii) Hence, giving reasons deduce that the glass structure does not sparkle in the same way as theDiamond

1) Which of the following SI units can be expressed in exactly two base SI units?

A coulomb B tesla C newton D hertz (E) A and C

2) A car is travelling at a velocity of 24 m s -1 due west initially. At a later time, it is seen travelling at a velocity of 10 m s-1 due south. Given that the direction North N, points vertically upwards, which of the following vector R represents the change in velocity of the car?

(E)

N

R

3) A motorist travelling at 10 m s–1 can bring his car to rest in a braking distance of 10 m. In what distance could he bring the car to rest from a speed of 30 m s–1 using the same braking force?

A 17m B 30m C 52m D 90m (E)21m

4) A screw gauge gives the following reading when used to measure the diameter of a wire Main scale reading: 0 mm. Circular scale reading: 52 division Given that 1 mm on main scale corresponds to 100 divisions of the circular scale. The diameter of wire from the above data is


General Certificate of Education (Adv.Level) Examination, 2013

%%%%%%Physics %%%%%%%%%

Grade 12-1St Term Test 2013

Paper 1 Time 1hours Part A

All right reserved All right reserved All right reserved All right reserved All right reserved All right reserved All right reserved All right reserved All right reserved All right reservedAll right reserved All right reserved All right reserved All right reserved All right reserved All right reserved All right reserved All

A0.005 cm B0.52 cm E 0.0125cm C0.052 cm D0.026 cm

5) A bullet fired into a fixed target loses half of its velocity after penetrating 3 cm. How much further it will penetrate before coming to rest assuming that it faces constant resistance to motion?

A 3.0 cm B 2.0 cm E 0 .5cm C 1.5 cm D 1.0 cm6) As shown above, a beam of white light is separated into separate colors when it passes through a glass prism. Red light is refracted through a smaller angle than violet light because red light has a

(A) Slower speed in glass than violet light(B) Faster speed in glass than violet light(C) Slower speed in the incident beam than violet light(D) Faster speed in the incident beam than violet light(E) Greater intensity than violet light

7) The forward thrust provided by the engine of a car moving horizontally with constant velocity of 12 m s -1 on a straight road is 500 N. Which of the following statements is correct?

A The net force on the car is 500 N.B The rate of work done by the engine is 6.0 kW.C The power of the engine is zero as the car is moving at constant velocity.D The power of the engine is 3.0 kW.

8) A tennis ball of mass 100 g is struck by a tennis racket. The velocity of the ball is changed as shown

What is the magnitude of the change in momentum of the ball?

A 1.0 kg m s-1 B 5.0 kg m s-1

C 1000 kg m s-1 D 5000 kg m s-1

E- 5.0 kg m s-1

9) A stationary body explodes into two components of masses m and 2m. The components gain kinetic energy X and Y respectively.

What is the value of the ratio X/Y?

A 0.25 B 0.50C 2.0 D 4.0 E 0


10) Three identical stationary discs P, Q and R are placed in a line on a horizontal, flat, frictionless surface. Disc P is projected straight towards disc Q. If all consequent collisions are perfectly elastic, predict the final motion of the three discs.

P Q RA moving left moving left moving rightB moving left stationary moving rightC stationary stationary moving rightD moving right moving right

moving right E moving left moving left moving left

11) A stone of mass m is projected with velocity v from a point P as shown below. Neglecting the effects of air resistance, the magnitude of the change in momentum between leaving P and arriving at Q isA zero B mv C mv √2 D 2mv E mv/2

12) A uniform rope has a length l and a mass m. It is held stationary with 4/5 of the length of the rope lying on a smooth horizontal table surface and with the remaining 1/5 hanging freely over the edge. The minimum work required to pull the whole rope onto the table surface is

A. 0.01 mgl. B. 0.02 mgl. C. 0.1 mgl. D. 0.2 mgl. E. mgl.

13) Two small spheres A and B of masses 1 kg and 2 kg respectively are released from rest at heights 4h and h above the ground as shown. Which of the following statements is/are correct? (Assume air resistance is negligible)

(1) The acceleration of sphere A doubles that of sphere B.(2) The time taken for sphere A to reach the ground is double that of sphere B.(3) The kinetic energy of sphere A when reaching the ground is double that of sphere B.

A. (1) onlyB. (3) onlyC. (1) and (2) onlyD. (2) and (3) onlyE. (1), (2) and (3)

14) A small object is thrown horizontally towards a vertical wall 1.2 m away. It hits the wall 0.8 m below its initial horizontal level. At what speed does the object hit the wall? (Neglect air resistance.)A. 2 ms-1 B. 3 ms-1

C. 4 ms-1 D. 5 ms-1

E. 7 ms-1


15) Three trolleys of equal mass m are stationary a short distance apart on a frictionless track. The end trolley is given a constant velocity v towards the middle trolley. During the collision between the end trolley and the middle trolley, the two stick together. These two trolleys subsequently collide and stick to the third trolley. What is the total loss of kinetic energy after these two collisions?

E 0

16) An object in equilibrium has three forces, F1 of 30 N, F2 of 50 N, and F3 of 70 N, acting on it. The magnitude of the resultant of F1 and F2 is

A. 10 N B. 20 N C. 40 N D. 70 N E. 80 N

17) A ball of mass 0.5 kg is thrown vertically downwards from the edge of a building of height 65 m. The initial speed of the ball is 20 ms–1. If the ball strikes the ground with a speed of 40 m/s, the energy lost by the ball because of air resistance is (gravitational acceleration, g = 10 ms–2)

(a) 10 J (b) 25 J (c) 30 J (d) 40 J (e) 45 J

18) The above figure shows an open wagon moving with negligible resistance in vertically falling rain. An appreciable amount of rain falls into the wagon and accumulates there. What are the effects of the accumulating rain on the speed, momentum and kinetic energy of the wagon? (Ignore the effects of the raindrops hitting the front of the wagon.)

Speed momentum kinetic energyA. decreased unchanged decreasedB. decreased unchanged unchangedC. decreased decreased decreasedD. unchanged unchanged unchangedE. unchanged increased increased

19) An object slides down an inclined plane passing through points A, B and C. Given that distance AB = 6 m and BC = 10 m, the object takes 2 seconds to move from A to B and also the same time from B to C. The instantaneous velocities of the ball at A, B and C are respectively

A. vA = 2 m s–1, vB = 3 m s–1, vC = 4 m s–1

B. vA = 2 m s–1, vB = 4 m s–1, vC = 6 m s–1

C. vA = 3 m s–1, vB = 4 m s–1, vC = 5 m s–1

D. vA = 3 m s–1, vB = 5 m s–1, vC = 7 m s–1

E. cannot determine because angle is not given


20) In the figure, M and N are two parallel boundaries separating media (I), (II) and (III). A light ray undergoes total internal reflection and then refraction as shown. Arrange the speeds of light in the three media in descending order.

A. (I) > (II) > (III) B. (I) > (III) > (II)C. (II) > (III) > (I) E. noneD. (III) > (I) > (II)

21) A ray incident on a 60° prism of refractive index √2 suffers minimum deviation. The angleof incidence is

1. 0° 2. 45° 3. 60° 4. 75° 5. 400


22) A slab of mass 50 kg is placed on frictionless horizontal floor and a block of mass 10 kg is placed on the slab as shown. The coefficient of static friction and the coefficient of kinetic friction between the slab and the block are respectively 0.4 and 0.2 and the acceleration due to gravity is 10 ms–2. A horizontal force equal to 30 N acts on the block. The acceleration of the slab will be

(a) 0.1 ms–2

(b) 0.2 ms–2 (c) 0.3 ms–2

(d) 0.5 ms–2 (e) 1.2 ms–2

23) The above graph shows the variation of kinetic energy E with the square of velocity v of a moving mass m. What is the momentum of the mass when it is moving at a speed of 2 ms-1?

A. 1 NsB. 2 NsC. 4 NsD. 8 NsE. 16 Ns

24) A glass vessel in the shape of a triangular prism is filled with water, and light is incident normally on the face XY. If the refractive indices for water and glass are 4/3 and 3/2 respectively, total internal reflection will occur at the glass-air surface XZ only for sin θ greater than

1. 1/2.2. 2/3.3. 3/4.4. 8/9.5. 16/27.

25) A mango tree is at the bank of a river and one of the branch of tree extends over the river. A tortoise lives in river. A mango falls just above the tortoise. The acceleration of the mango falling from tree appearing to the tortoise is (Refractive index of water is 4/3 and the tortoise is stationary)


http://1.bp.blogspot.com/_lRKubY9oOyI/TKH-c7naPkI/AAAAAAAABIw/_EBviGro5T0/s1600/Friction1appr28-9-10.jpg

(a) 3g/4 (b) 4g/3 (b) g/4 (d) g (e) 2g/3


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A Projectile is Fired Horizontally From a Launching Device