Suggested Solutions for 2011 J1 H2 Physics Paper Which of the following is a unit of pressure?

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1 Suggested s for 2011 J1 H2 Physics Paper 1 1. Which of the following is a unit of pressure? kg m s -1 kg m -1 s -2 kg m 2 s -2 kg m -2 s -1 [] P = Force/area Units of pressure, P = (kg m s -2 ) / m 2 = kg m -1 s Which of the following is not equal to 6.02 x 10-10? 1 [] 602 p 60.2 n 6.02 x x k 602 p = 602 x = 6.02 x n = 60.2 x 10-9 = 6.02 x 10-8 [Wrong] 6.02 x 10-4 = (6.02 x 10-4 )x10-6 = 6.02 x x k = (6.02 x ) x 10 3 = 6.02 x Four students measured and calculated the elementary charge, e. The table shows the results obtained. Which student obtained a set of results that could be described as accurate and precise? [e = 1.60 x ] Student Electronic charge, e / [] l avg = 1.602, range = = 0.03 l avg = 1.602, range = = 0.07 l avg = 1.582, range = = 0.03 l avg = 1.620, range = = 0.08 Hence, [] is accurate (average close to TRUE value) & precise (small range/scatter) 4. Which pair includes a vector quantity and a scalar quantity? displacement, acceleration

2 2 [] work, potential energy power, time force, kinetic energy oth vector quantities oth scalar quantities oth scalar quantities 5. The diagram below shows a vector of magnitude F and two of its components of magnitudes F 1 and F 2. These components are at right angles to each other. Which of the following statements is true? F 1 F F 2 F F F [] 1 2 F = F 2 sin F F F F 2 = F cos Use of vector addition 6. motorist travelling at 15 m s -1 approaches traffic lights which turn red when he is 12 m away from the stop line. His reaction time is 0.10 s and the car can be brought to rest with a uniform deceleration in 1.2 s when the brakes are applied. If he brakes fully, how far from the stop line will he stop? [] 1.5 m 2.3 m 3.0 m 4.5 m Using v = u + at 0 = 15 + a(1.2) a = m s -2 istance traveled during reaction time = 15 x 0.1 = 1.5 m Using v 2 = u 2 + 2as 0 = (15) 2 + 2(-12.5)(s) s = 9.0 m Total distance traveled =

3 = 10.5 m istance from stop line = = 1.5 m 3 7. t a height of 120 m from the ground, a loose bolt detaches from the rocket when it is travelling vertically upwards at 10.0 m s -1. alculate the time taken for the bolt to strike the ground. [] 4.0 s 4.9 s 6.1 s 12 s Using s = ut + ½ at = 10.0 (t) + ½ (-9.81)(t) 2 t = 6.1 s 8. stone is thrown vertically upwards. student plots the variation with time of its velocity. What is the vertical displacement of the stone from its starting point after 5 seconds? [] 15 m 20 m 25 m 65 m rea under v-t graph = displacement isplacement of stone = ½ x 30 x 3 + ½ ( 20) (5 3) = 25 m 9. toy rocket is launched vertically from Earth with a constant acceleration. fter some time, the fuel is used up and the toy rocket falls freely back to Earth. Which of the following velocity-time graphs best represents the journey?

4 4 Neglect air resistance. [] Initially the toy rocket accelerates uniformly. Hence the velocity of the rocket should increase (hence and are wrong). When the fuel is used up, the rock still move upwards due to its inertia. However it is moving upwards with decreasing velocity until it reaches the maximum height (velocity = 0 m s -1 ). fter which it will move downwards and fall back to Earth. Hence there should be both positive and negative velocity shown in the v-t graph. 10. tennis ball is released from rest at the top of a tall building. ssuming air resistance is significant, which graph best represents the variation with time t of the acceleration a of the ball as it falls?

5 5 [] When the ball is released (at t = 0), the ball's acceleration is g. So answer and is eliminated. s air resistance is not negligible, the acceleration of the ball will not be constant (cannot be answer ). Instead, the acceleration of the ball will decrease to zero after some time ( the point where terminal velocity has been attained ) 11. The force-extension graph of a spring is shown in the figure below. The work done in extending the spring from x 1 to x 2 is given by ½(F 1 + F 2 ) (x 2 x 1 ) ½(F 2 + F 1 ) (x 2 + x 1 ) ½(F 2 - F 1 ) (x 2 - x 1 ) F 2 x 2 - F 1 x 1 Work done = area under the graph = trapezium area for the straight line 12. Two springs P and Q both obey Hooke s Law. They have spring constants 2k and k respectively. The springs are stretched separately by the same force. The elastic potential energies stored in springs P and Q are W P and W Q respectively. How is W P related to W Q?

6 6 W P = ¼ W Q W P = ½ W Q W P = 2 W Q W P = 4 W Q y Hooke s Law, F = k x For spring P, F = (2k) x P x P = F 2k For spring Q, F = (k) x Q X Q = F k Work done on spring: W = ½ F x Since F is constant, W x W W W W P Q P Q x x P Q F 2k 1 F 2 k W P = ½ W Q 13. The given diagram shows a column of dry air trapped by mercury in a narrow test tube. Which graph best shows how the length l of the air column varies with the angle of the tube to the vertical?

7 7 When = 0, the force on the trapped air is maximum, hence the trapped air is most compressed, hence l is minimum. 14. student makes some observations of a ball falling through identical beakers of fluids with different viscosity after it is released in each of them. Which of the following observations could be used to identify the most viscous fluid? The ball initially moves with the largest acceleration. The ball takes the longest time to reach constant speed. The maximum displacement of the ball is the same. The ball moves at the smallest constant speed. is wrong. - This depends on upthrust which depends on density, not viscosity. is wrong. - In the more viscous fluid, the ball experiences higher drag force. Thus it will reach the equilibrium state earlier. is wrong. - The maximum displacement is constrained by the beaker depth instead of depending on the fluid viscosity. is correct. - t terminal velocity, the weight of the ball is balanced by the drag force. The more viscous fluid has a higher drag force at the same velocity. Thus to balance the same weight, the ball moving through a more viscous fluid would have a smaller terminal velocity.

8 8 15. In 2001, the leaning tower of Pisa was stabilized by a bundle of steel cable anchored to the ground as shown by the simplified sketch below. Tower Steel able Ground The weight of the tower is W, the tension in the cable is T and the reaction from the ground is R. Which vector triangle best represents the forces acting on the tower? T T W W R R T T W R W R R must be normal to the base, wrong Horizontal component of T must be leftward & wrong 16. Two blocks, X and Y of masses m and 2m respectively, are accelerated along a smooth horizontal surface by a force F applied to block X as shown in the diagram below.

9 9 F X Y What is the magnitude of the force exerted by block Y on block X during this acceleration? 0 F 3 2F 3 F F of X & Y F F (3 m) a a 3m F of X OR F of Y FXonY 2ma F FYonX ma F 2F F 2F FXonY 2m FYonX F m 3 m 3 3 m 3 2F y N3L, FYonX space-research rocket stands vertically on its launching pad. Prior to ignition, the mass of the rocket and its fuel is 1.7 x 10 3 kg. On ignition, gas is ejected from the rocket at a speed of 2.5 x 10 3 m s -1 relative to the rocket, and the fuel is consumed at a constant rate of 7.4 kg s -1. alculate the resultant force acting on the rocket on ignition x 10 3 N 1.67 x 10 4 N 1.85 x 10 4 N 3.52 x 10 4 N F on gas by rocket y N3L, F 3 m( v u) 7.4( ) N t N on rocket by gas Re sult F ( )(9.81) N 18. ball falls vertically and bounces on the ground. The following statements are about the forces acting while the ball is in contact with the ground. Which statement is correct? The force that the ball exerts on the ground is always equal to the weight of the ball.

10 10 The force that the ball exerts on the ground is always equal in magnitude and opposite in direction to the force the ground exerts on the ball. The force that the ball exerts on the ground is always greater than the weight of the ball. The weight of the ball is always equal and opposite to the force that the ground exerts on the ball. y N3L, the force by the ball on the ground is always equal in magnitude but opposite in direction to the force by the ground on the ball 19. The diagram shows two trolleys, X and Y, about to collide and gives the momentum of each trolley before the collision. 20 N s 12 N s X Y fter the collision, the directions of motion of both trolleys are reversed and the magnitude of the momentum of X is then 2 N s. What is the magnitude of the corresponding momentum of Y? 6 N s 8 N s 10 N s 30 N s y conservation of linear momentum, 20 + (-12) = p Y + (- 2) p Y = 10 N s 20. Three identical stationary discs, P, Q and R are placed in a line on a horizontal, flat and frictionless surface. isc P is projected straight towards disc Q. P Q R If all consequent collisions are perfectly elastic, what will be the final motion of the three discs? P Q R moving left moving left moving left stationary stationary moving left stationary stationary moving right moving right moving right moving left

11 11 Since all collisions are perfectly elastic, there is a complete transfer of KE from disc P to Q and Q to R. Only disc R will be moving towards the right after the collision while disc P and Q will remain stationary. 21. all X slides down a frictionless slope while all Y falls freely from the same height. oth balls are initially at rest and the gradient of the slope is vertical at the starting position of X as shown below. X Y H Which ball has a higher speed after moving through the same height H? X Y X and Y will have the same speed X or Y, depending on which is heavier Using conservation of energy, For all X, PE Top + KE Top = PE bottom + KE bottom m X gh + 0 = 0 + 1/2m X v X 2 v X 2 = 2gH For all Y, PE Top + KE Top = PE bottom + KE bottom m y gh + 0 = 0 + 1/2m y v y 2 v y 2 = 2gH Hence, both balls will have the same speed after falling through the same height H. 22. body is projected at an angle above the horizontal with a given speed. ir resistance may be taken as negligible. Which one of the following statements is correct? The kinetic energy of the body is a maximum at the maximum height attained. The potential energy of the body increases uniformly with time during ascent. The total energy of the body is constant throughout the motion. The momentum of the body is constant throughout the motion.

12 12 The total energy of the body is constant throughout the motion. With negligible air resistance, the total energy of the body is constant kg mass, with an initial kinetic energy of 20 J, moves up a smooth slope as shown below. 2.0 m 30 What is the speed of the mass after it has moved a distance of 2.0 m? 0 m s -1 5 m s m s m s -1 PE Top + KE Top = PE bottom + KE bottom (1.0)(9.81)2sin30 o + KE Top = KE Top = 10.2 J 1/2mv 2 = KE Top = 10.2 J v 2 = 20.4 v = 4.51 m s -1

13 mass hanging on a spring oscillates vertically between X and Z. Its equilibrium position is at Y. The spring has negligible mass. X Y Z Which of the following gives the correct description of energy and force? Elastic potential energy of spring is minimum when mass is at Largest net upward force acts on mass when it is at Z Y X Z X Y Z Z Elastic potential energy When the mass it at X, the spring should have the least extension. Hence, the EPE would be the minimum at X. Net upward force Throughout the oscillation, the tension in the spring would be the highest when the mass is at Z while the weight of the mass remains constant. The net upward force would be the highest based on these 2 forces acting on the mass.

14 toy car of mass 2.0 kg is travelling at constant speed for 5.0 s. The car engine is providing 160 W of useful power and driving force on the car is 80 N. t what speed does it travel? 0.5 m s m s m s m s -1 Using Power = Force x onstant Velocity Velocity = Power / Force = 160 / 80 = 2.0 m s The temperatures of two beakers of water of different amounts are measured using the same thermometer. The temperatures registered are both 32 and are steady. eaker eaker The water in one beaker is then poured into the other beaker. ssume no heat loss during pouring, which one of the following statements is correct? The final temperature of the water will be less than 32 since beaker has less energy. The final temperature of the water will be more than K since beaker has more energy. Since the mass and the specific heat capacity of water are unknown, the temperature of the water cannot be determined. The water from beaker will be at thermal equilibrium with the water from beaker. : Thermal equilibrium 27. small quantity of water of mass m at a temperature (in o ) is poured on to ice of mass M which is at its melting point (M >> m).

15 15 If c is the specific heat capacity of water and L the specific latent heat of fusion of ice, then the mass of ice melted is given by ML mc Mc L mc ML mc L : mc ( 0) = m ice L m ice = mc L 28. The graph shows the variation of temperature T against time t of a certain substance which was originally a liquid at t = 0 s. Heat was removed from it at a constant rate until it became a solid. T / K t / s Which one of the following could be correct? Specific heat capacity of solid Specific heat capacity of liquid / J kg 1 K 1 / J kg 1 K : Pt = mc For liquid: P (100 ) = mc liq ( ) (1)

16 16 For solid: P ( 50 ) = mc sol ( ) (2) (1) (2) : = c liq = 2 c liq = 2c sol c sol 29. The expansion of a mass m of an ideal gas at a constant pressure P is shown by line in the volume-temperature graph below. Which line shows the expansion of a mass 2 m of the same gas, at a pressure of 4 P? Volume Temperature : For the new situation: pv = nrt V T = nr p V T = n 2 p 4 2 gradient = 4 T R gradient = 8 T (line ) (line ) 30. When the pressure of a fixed mass of ideal gas is doubled by heating at constant volume, the number of molecules per unit volume doubles. the mean square speed of the molecules doubles. the density of the gas doubles. the temperature of the gas remains constant. : pv = nrt (1) 2pV = nrt (2) (2) (1) : 2 = T 2 T T 2 = 2T Since 1 2 m<c2 > T When T is doubled, <c 2 > is also doubled.