SECTION A (25 MARKS)
Answer ALL the questions in this section in the spaces provided.
 The figure below shows the scale of a measuring instrument when measuring the thickness of an object.
 Name the instrument to which the scale belongs. (1 mark)
 Find the reading of the instrument shown. (2 marks)
 A solid weighs 32.5N on the surface of the moon. The force of gravity on the moon is 1.7Nkg^{1}. Determine the mass of the solid. (3 marks)
 A mercury barometer reads 760mmHg at sealevel and 700mmHg at the top of a mountain. If the density of mercury is 13,600kg/m^{3} and average density of air is 1.30kg/m^{3}, calculate the height of the mountain. (3 marks)
 Briefly explain why rooms are at a lower level and ventilators at a higher level. (2 marks)
 Figure 2 below shows a piece of wood fitted into a copper pipe and a piece of paper wrapped tightly around the junction.
Explain why the side of the paper around wood burns first when flame is applied at the junction. (2 marks)  A student pulls a block of wood along a horizontal surface by applying a constant force. State the reason why the block moves at a constant. (1 mark)
 How much current is taken by a bulb whose rate is 100W and which is designed for mains supply of 240V? (3 marks)
 What is the gravitational potential energy stored in a spring when stretched through 4cm by a force of 2N. (2 marks)
 State two conditions necessary for an object to be in equilibrium. (2 marks)
 The diagram below shows an empty wine glass.
 State the effect on its stability when wine is put into the glass. (1 mark)
 Explain your answer in (a) above. (1 mark)
 A metal bench feels colder than a wooden one when one sits on it on a cold morning even though both are at the same temperature. Explain this observation. (2 mark)
SECTION B (55 MARKS)
Answer ALL the questions in this section in the spaces below.

 Figure 5 below shows a machine being used to raise a load. Use the information given in the figure to answer questions below.
 Determine the velocity ratio of the machine. (1 mark)
 If a load of 800N is raised by applying an effort of 272N, determine the efficiency of the machine (3 marks)
 A crane lifts a load of 2000kg through a vertical distance of 3.0m in six seconds. Determine:
 The work done. (2 marks)
 The power of the crane. (2 marks)
 State two reasons why the efficiency of a machine is not 100%. (2 marks)
 A block of a metal having a mass of 40kg requires a horizontal force of 100N to drag it with uniform velocity along a horizontal surface. Determine its coefficient of friction. (3 marks)
 Figure 5 below shows a machine being used to raise a load. Use the information given in the figure to answer questions below.
 In an experiment to estimate the size of oil molecule an oil drop of diameter 0.05cm spreads over water to form a circular patch whose diameter is 15cm.
 Explain why the oil spreads over water. (1 mark)
 Determine:
 Volume of the drop. (2 marks)
 Area of the patch. (2 marks)
 Size of the oil molecule. (3 marks)
 State two assumptions made in b)(iii) above. (2 marks)

 Distinguish between speed and velocity. (1 mark)
 The figure 6 below shows the motion of a ticker tape through a ticker timer whose frequency is 100Hz.
Determine Velocity at AB and PQ. (4marks)
 Constant acceleration of the tape.(3 marks)
 State Newton’s second law of motion. (1 mark)

 A boy throws a tennis ball vertically upwards from a truck moving at a constant velocity. Give the reason why the ball lands back exactly the same point where it was projected. (1 mark)
 Define impulse in terms of momentum. (1 mark)
 A trailer of mass 30 tonnes travelling at a velocity of 72km/h runs onto a stationary bus of mass 10 tonnes. The impact takes 0.5seconds before the two vehicles move off together at a constant velocity for 15 seconds. Determine,
 The common velocity. (3 marks)
 The distance moved after the impact. (2 marks)
 The impulsive force on the trailer on impact. (3 marks)
 Give a reason why when a passenger jumps from a floating boat, the boat moves backwards. (1 mark)
 Give the reason why a safety seat belt used in a vehicle:
 Should have a wide surface area. (1 mark)
 Should be slightly extensible. (1 mark)

 State Hooke’s law. (1 mk)
 The graph shows how extension e of a helical spring varied with load, hanging on it.
Determine from the graph, the proportionality constant of the spring. (3mks)  State two factors that affect the proportionality constant of a helical spring. (2mks)
 Two springs Q and R have proportionality constants 20Nm^{1} and 25Nm^{1} respectively. Q weighs 0.2 N while the weight of R is negligible. The two springs are arranged to support a load of 3.ON as shown in the diagram below.
Determine the extension in Q (2mks)
 R (2mks)
MARKING SCHEME

 Vernier calliper ✔1
 Main scale 5.00
Vernier scale (2 x 0.01) = 0.02 ✔1
5.00 + 0.02 = 5.02 cm ✔1
 Vernier calliper ✔1
 M = ^{w}/_{g} ✔1
= ^{32.5}/_{1.7} ✔1
= 19.117 kg / 19.12 kg✔1  Difference in pressure 760 – 700 = 60mm✔1
^{60}/_{1000} x 13600 x 10 = h x 1.3 x 10 ✔1
h = ^{8160}/_{1.3 ×10}
h = 627.69 m ✔1  Warm air being lighter raises✔1 and escapes through the ventilators while the colder air gets in through the windows and doors. ✔1
 Wood being a poor conductor of heat✔1 does not allow the excess heat so it gets charred ✔1
 Frictional force is equal to the applied force but in opposite direction
The net applied force is zero
✔1 (Any one)  P = IV / I = ^{P}/_{V} ✔1
= ^{100}/_{240} ✔1
= 0.42 A ✔1  P.E =^{ Fe}/_{2}= ^{2 ×0.04}/_{2} ✔1
= 0.04 Joules ✔1 
 The resultant force acting on the body must be zero. ✓
 The principle of moments must apply. ✓(Clockwise moments = Anticlockwise moment). (2mks)
 The resultant force acting on the body must be zero. ✓
 Stability decreases.¹
 The mass on the upper side of the glass increases raising the position of the c.o.g
 Stability decreases.¹
 Metal is a better conductor of heat than wood hence it will conduct heat away from the body faster than wood.

 V.R = 6
 M.A = ^{800}/_{272} = 2.941
E = ^{MA}/_{VR }x 100
= ^{2.9641}/_{6} x 100 = 49.01% W = F x d
= 200003✔ = 60000 joules ✔  P =^{ w}/_{t} = ^{60000}/_{6} ✔
= 10000W✔1
 W = F x d

 Energy is used to overcome friction✔
 Energy is used to move parts of the machine✔
 u =^{ F}/_{R}R = mg
= 40 x 1 = 400N✔
u =^{ 100}/_{400} ✔ = 0.25✔

 Surface tension of water is stronger than that of oil

 Vol. = ^{4}/_{3}πr^{3}✔
= ^{4}/_{3} x ^{22}/_{7 }x (^{0.05}/_{2})^{3}= 6.5476 x 10^{5} cm^{3}✔  A = πr^{2}= ^{22}/_{7} x (^{15}/_{2})^{2}✔
= 176.786cm^{2}✔  Vol. = πr^{2}✔
h = ^{6.5476 ×105}/_{176.786} ✔
= 3.7037 x 10^{7} cm✔
 Vol. = ^{4}/_{3}πr^{3}✔

 Oil drop is perfectly spherical
 Size of oil molecule is same as thickness of patch.
 Patch is one molecule thick. (Max. 2 marks)

 Speed is scalar quantity while velocity is a vendor quantity
 T= 1 = 1 = 0.01seconds √
F 100 VAB = 12 = 600cm/s or 6m/s √√
2 x 0.01
Vpq= 32 = 1600cm/s or 16m/s √√
2 x 0.01  a = V_{pq}  V_{AB} t
= 16m/s – 6m/s = 10m/s
6x0.01 0.06s
=166.7m/s^{2}
 VAB = 12 = 600cm/s or 6m/s √√

 The ball has the same horizontal velocity as the truck✔1
 Impulse is the change in momentum✔1

 M_{1}V_{1} + M_{2}V_{2} = (M_{1} + M_{2})V
30000 x 20 + 0= (30000 + 1000)V✔1
V = ^{600000}/_{40000} = 15ms^{1}✔1  S = vt✔1
= 1515 = 225m✔1  Ft = m (v  u) ✔1
f = m ^{(vu)}/_{t}= 30000(1520) ✔1
0.5
= 300000N✔1
 M_{1}V_{1} + M_{2}V_{2} = (M_{1} + M_{2})V
 This is due to the passengers reaction force on the boat which acts backwards. ✔1

 To increase area on which force cuts✔1 to reduce pressure due to impulsive force.
 To prolong the period of time the force acts to reduce the impulsive force

 The force applied on an elastic material (Spring) is directly proportional to its extension so long as the elastic limit is not exceeded. 1 mark
 Proportionality constant k = 1/Gradient
Gradient = 18.5 / 4 = (Check student extraction)
K = ¼.625N/cm OR 21.621N/m (1 mark) 
 Mass per unit length (1 mark)
 Material of spring (1 mark)

 Weight supported by Q = 3.0 N (1 mark)
e = 3/20 = 0.15m (1 mark)  Weight supported by R = 3.2 N
e = 3.2 / 25 = 0.129 m (1 mark)
(1 mark) Substitution
(1 mark) Answer
 Weight supported by Q = 3.0 N (1 mark)
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