INSTRUCTIONS TO CANDIDATES
 Attempt ALL questions in sections A and B.
 All your answers must be written in the spaces provided in this question paper.
 All working must be clearly shown.
 Non programmable silent electronic calculators and KNEC mathematics table may be used except where stated otherwise.
SECTION A (25 MARKS)
 The figure below shows a section of a micrometer screw guage with a thimble scale of 50 divisions. When the spindle is in contact with the anvil, the device reads 0.25mm. If the screw guage is used to measure the diameter of a spherical ball, state the actual diameter of the ball. (2mrks)
 When washing clothes, it is easier to remove the dirt using soap in warm water than cold water. Explain (2mrks)
 The figure below shows two identical cylindrical containers of radius 10.5cm with holes drilled at the bottom of each and filled with water to the same height of 42.1cm. The holes are initially closed. Container A has a 24g mass of ice that virtually covers the whole area above it whereas container A is open (density of water = 1000kgm^{−1} )
 State and explain the observation that would be made at the holes when opened (2mrks)
 Determine the pressure exerted at the hole of container A. (3mrks)
 When a litre of milk is poured in 20litres of water, the colour changes to white. Explain (1mrk)
 Give a reason why alcohol in glass thermometer cannot be used when boiling water is to be used in an experiment. (1mrk)
 Otieno prefers going to the beach in the afternoon hoping to get a relief from the scotch of the day while in Mombasa. Explain how the breeze he likes reaches him. (2mrks)
 Kariuki identifies an abandoned circular water well of diameter 2.1m as a breeding zone for mosquitoes. He intends to use engine oil to control the breeding by pouring it on the surface of the water. Given that the thickness of a molecule in the oil is 1.635 x 10^{9}, determine the minimum volume of oil he requires. (3mrks)
 The figure below represents the arm of a lift pump with a force F being applied by the person drawing water. Determine the value of F that just pushes the arm downwards. 3mks
Weight of parts
= 600N  Water flows along a horizontal pipe of cross sectional area 48cm which has a constriction of cross sectional area 12cm^{2} at one place. If the speed of water at the constriction is 4ms^{−1}, calculate the speed in the wider section. (2mrks)
 Determine the extension produced by a pair of parallel identical springs each of constant 1000Nm^{−1} when a mass of 0.2kg is hung below them. (2mrks)
 The figure below shows a conical flask with some water to the level indicated.
 State the change in the stability of the flask when more water is added to it. (1mrk)
 Give a reason for your answer in a) above. (1mrk)
SECTION B (55MARKS)

 A car initially moving with a velocity of 10ms^{−1} accelerates uniformly at 1ms^{−2} until it reaches a velocity of 15ms^{−1}. Calculate,
 The time taken (2mrks)
 The distance travelled during the acceleration. (2mrks)
 The velocity reached 100m from the place where the acceleration began.(3mrks)
 A suspected gang vehicle escapes with a punctured fuel tank after being shot by a chase police unit along the highway. Drops of petrol from the tank fall on the road after every 5 seconds. The distance from the first drop to the second is 5m. 20 more drops fall as the vehicle accelerates before the tank empties. The two last drops fall 50m apart. Determine the,
 Initial velocity of the car (2mrks)
 Final velocity of the vehicle just before it ran out of fuel (1mrk)
 The acceleration of the car. (2mrks)
 A car initially moving with a velocity of 10ms^{−1} accelerates uniformly at 1ms^{−2} until it reaches a velocity of 15ms^{−1}. Calculate,

 state the law of conservation of energy (1mrk)
 Simon slides a refrigerator of mass 71kg along a wooden bar inclined at an angle of 30° with the ground onto a truck for transportation. Given that the distance from the ground to the floor of the truck is 80cm, as shown in the figure below, determine,
 The length of the wooden bar (2mrks)
 Useful work done on the refrigerator (3mrks)
 Work done by Simon in moving the refrigerator along the wooden bar when he applies a force of 4000N (3mrks)
 Efficiency of the inclined plane (2mrks)
 Account for the value of efficiency obtained in iv) above. (1mrk)

 state Newton's second law of motion (1mrk)
 A bullet of mass 40g is fired from a gun of mass 30kg and exits the muzzle at 300ms^{−1}. The bullet travels horizontally to hit a stationary wooden block 30m away after 0.5 seconds. Determine,
 the recoil velocity of the gun (3mrks)
 the force with which the bullet hits the wooden block (3mrks)
 the velocity of the bullet just before hitting the block (3mrks)
 The figure below shows a graph of weights of persons entering a lift against the extension of four spring supporting the lift. From the graph determine,
 The spring constant of the springs (3mrks)
 The spring constant of a single spring (1mrk)
 The mass of passengers that would cause an extension of 0.6m on a single spring.(3mrks)

 define moment of a force (1mrk)
 A sign board made from a uniform metal sheet is supported by a single post as shown in the figure below. It is to be supported by two bolts.
Given that the weight of the board is 20N, determine the force that the lower bolt applies on the plate to maintain it at horizontal (3mrks)
 State one way of reducing the force in i) above. (1mrk)
 Explain how the stands of students' lockers that are slightly inclined outwards improve their stability (2mrks)

 A tennis ball is struck such that it backspins at it crosses the net before landing in the court area of opponent player.
 Explain the trajectory of the ball as it rises above the net. (2mrks)
 Give a possible reason that caused the ball to drop in the opponents court instead of rising continuously (1mrk)
 Explain the following:
 Mountain climbers are highly likely to nose bleed when they reach the mountain top (2mrks)
 A bulldozer easily moves on earth roads while a saloon car cannot. (2mrks)
 A tennis ball is struck such that it backspins at it crosses the net before landing in the court area of opponent player.
MARKING SCHEME
 sleeve scale reading = 2.5mm
thimble scale reading = 0.46mm
screw guage reading
= 2.96mm actual diameter
= 2.96 − 0.25 = 2.71mm  Warm water lowers the surface tension of water making the molecules loose for the soap to act on the dirt molecules

 Hole on A throws water farther than the hole on B
 P_{A} = hρg + pressure due to the mass of ice
= 0.421 × 1000 + 0.24
^{22}/_{7} × 0.105 × 0.105
= 421 + 6.926
= 421.6926Nm^{−2}
 The molecules of milk diffuse in the water until it is homogeneously distributed
 The alcohol in the thermometer vaporizes long before the water boils. (it has a lower boiling point)
 During the day the land gets heated faster than water body, air above the land becomes less dense and rises. Cold air from the sea flows to the land to occupy the space left which contributes to the breeze.
 V = πr^{2}t
=^{22}/_{7} × 1.05 × 1.05 × 1.635 × 10^{−9}
= 5.665 × 10^{−9}m^{3}  sum of clockwise moments = sum of anticlockwise moments
F × 1.25 = 0.14 × 600
F = 0.14 × 600 = 67.2N
1.25  A_{1}v_{1} = A_{2}v_{2}
v_{1} = 12 × 4
48
= 1ms^{−1}  F = ke,
e = ^{F}/_{K} = ^{2}/_{1000}
= 0.002m 
 It becomes less stable
 The position of centre of gravity is raised


 v = u + at
15 = 10 + t
t = 5s  s = ut + ½at^{2} = 10 × 5 + ½ × 125
= 50 + 12.5
= 62.5m or
v^{2} = U^{2} + 2as
15^{2} = 10^{2} + 2 × 1 × S
225 − 100 = 2s
s = 62.5m  v^{2} = u^{2} + 2as
= 100 + 2 × 1 × 100
= 300
v = √300
= 17.32ms^{−1}
 v = u + at

 u = ^{s}/_{t}
=^{5}/_{5}= 1ms^{1}  v =^{50}/_{5}= 10ms^{1}
 a = v − u
t
= 10 − 1
20
= 0.45ms^{−2}
 u = ^{s}/_{t}


 The sum of kinetic energy and potential energy of a system is constant

 L = 80 = 160cm
sin 30°  W = P. E
= mgh
= 71 × 10 × 0.8 = 5680J  W = F × d = 4000 × 1.6
= 6400J  efficiency = work output × 100
work input
= 5680 × 100 = 88.75%
6400  It is not 100% since some energy is lost when overcoming friction
 L = 80 = 160cm

 The rate of change of momentum is directly proportional to the resultant external force producing the change and takes place in the direction of the force.

 momentum before firing = momentum after firing
m_{1}u_{1} + m_{2}u2 = m_{1}v_{1} + m_{2}v_{2}
0 = 0.04 × 300 + 30 × v_{2}
−12 = 30v_{2}v_{2} = −0.4ms^{−1}  s = ut + ½at^{2}30 = 300 × 0.5 + ½ × a × 25
30 = 15 + 12.5a
15 = 12.5a
a = 1.2ms^{−2}
F = ma
= 0.04 × 1.2 = 0.048N  v = u + at
= 300 + 1.2 × 0.5
= 300 + 0.6 = 300.6ms^{−1}
 momentum before firing = momentum after firing

 k = slope = 4000 − 1000
0.2 − 0.05
= 3000 = 20000Nm^{−1}
0.15  k = 20000
4
= 5000Nm^{−1}  four springs,e = 0.6
4
F = 3000N, mass = 30kg
 k = slope = 4000 − 1000

 The product of force and the perpendicular distance between the line of action and the point of support

 sum of clockwise moments = sum of anticlockwise moments
F × 0.35 = 20 × 0.3
F = 20 × 0.3 = 17.143N
0.35 
 Use a lighter board
 Make the board narrower
 Make the board shorter
 sum of clockwise moments = sum of anticlockwise moments
 Widening at the base increases the base area thus increasing the angle of tilt hence more stable


 The air currents above the ball increases while those below the ball decrease causing a corresponding decrease in pressure at the top and increase in pressure at the bottom. The pressure difference gives the ball a lift force.
 The force of gravity acts on the ball thus pushing it down

 Atmospheric pressure decreases at the top thus greater blood pressure under the nose causes the blood capillaries to rapture
 Bulldozer has wider wheels thus they exert a lower pressure on the road than a saloon car that has narrow wheels.

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