- This paper consists of two sections; A and B
- Answer all the questions in section A and B in the spaces provided
- All working must be clearly shown.
- Mathematical tables and electronic calculators may be used
- Candidates should answer the questions in English.
- Take g=10N/kg
SECTION A: 25mks (Answer all the questions)
- State one assumption made when determining the size of a molecule in an oil drop experiment (1 Mark)
- Air is blown into the horizontal tube as shown below.
- Indicate the levels of water in tubes A and B when air passes through the horizontal tube at a high velocity. (1 Mark)
- Explain your observation in (a) above (1 Mark)
- Sketch a velocity – time graph of a body moving with uniform velocity. (1 Mark)
- The figure below shows an empty wine glass.
- How is its stability affected when filled with wine? (1 Mark)
- Explain the observation in (a) above (1 Mark)
- State one factor that affects heat transfer in solids. (1 Mark)
- The figure below shows a uniform bar of length 1 metre. Calculate the weight of the bar. (3 Marks)
- The figure below shows a u-tube containing the liquids X and Y. Given that the density of liquid X is 1.8g/cm3, calculate the density of liquid Y in g/cm3. (3 Marks)
- Name one factor that affects surface tension. (1 Mark)
- When a liquid is heated in a glass flask, its level first falls and then starts rising. Explain this observation. (2 Marks)
- The figure below shows two identical springs with negligible weight. The extension produced on the system is 10cm.
Determine the spring constant of each spring. (3 Marks) - A body A of mass 2kg moving with a velocity of 5m/s collides with a body B of mass 30kg travelling at 2m/s in the opposite direction. If the collision is perfectly inelastic, find their common velocity after collision. (3 Marks)
- The figure below shows a velocity time graph for a trolley
From the graph, calculate the distance covered by the trolley in the first 10 seconds (2 Marks) - State the reason why gases are easier to compress than solids. (1 Mark)
SECTION B: 55mks
-
- State the Hooke’s law (1 Mark)
- The table below shows the extension produced in a spring by various forces.
Extension (cm) 0 0.3 0.7 1.10 1.5 1.9 Force (N) 0 1.0 1.9 3.0 4.1 5.0 - Plot a graph of force against extension. (5 Marks)
- From the graph, determine the spring constant. (3 Marks)
- What force would cause an extension of 1.2cm on the spring? (2 Marks)
- The figure below shows a block and tackle system
- State the velocity ratio of the system (1 Mark)
- Mark the direction of tension in the strings (1 Mark)
- If an effort of 2N is applied, calculate the mechanical advantage of the system. (3 Marks)
- Calculate the efficiency of the system. (3 Marks)
- State why the efficiency of the system is less than 100%. (1 Mark)
- A body of mass 2kg is thrown vertically upwards with a velocity of 14m/s. Determine;
- The maximum height reached by the body (3 Marks)
- Its velocity after 0.5 seconds. (3 Marks)
- The time taken to reach maximum height. (3 Marks)
- Calculate the net force acting on the ball as it moves upwards if it experiences an air resistance of 8N. (2 Marks)
-
- State the Newton’s 2nd law of motion (1 Mark)
- A lady of mass 90kg is standing on the floor of a lift. Determine the reading on the weighing machine when
- Lift is at rest (2 Marks)
- Lift is moving upwards with an acceleration of 3m/s2 (2 Marks)
- Two masses of 4kg and 2kg are connected by a light string passing over a frictionless pulley as shown below.
Calculate the acceleration of the masses when left to move freely. (3 Marks) - A block of mass 35kg is pushed along a horizontal surface whose frictional force is 20N. If the force moving the block is 100N, calculate the co-efficient of friction between the block and the surface. (3 Marks)
- The figure below shows a hydraulic brake system.
A force of 20 N is applied on the foot pedal connected to a piston of area 0.05m2. This causes a stopping force of 5000N on one wheel. Calculate.- Pressure in the master cylinder (3 Marks)
- Area of the slave piston. (3 Marks)
- Velocity ratio of the system. (3 Marks)
- Give two reasons why oil is used in the hydraulic brake system. (2 Marks)
- State two factors affecting pressure in liquids. (2 Marks)
MARKING SCHEME
- State one assumption made when determining the size of a molecule in an oil drop experiment (1 Mark)
- The drop is perfectly spherical
- The layers/ patch is one molecule thick.
any one = ✔1 Mark
- Air is blown into the horizontal tube as shown below.
- Indicate the levels of water in tubes A and B when air passes through the horizontal tube at a high velocity . (1 Mark)
- Explain your observation in (a) above (1 Mark)
- In tube A, velocity of air above it is higher ✔than velocity of air above tube B
- Therefore in table A, pressure is lower than tube B
- Indicate the levels of water in tubes A and B when air passes through the horizontal tube at a high velocity . (1 Mark)
- Sketch a velocity – time graph of a body moving with uniform velocity. (1 Mark)
- The figure below shows an empty wire glass.
- How is its stability affected when filled with wine? (1 Mark)
- Stability is reduced ✔
- Explain the observation in (a) above (1 Mark)
- The position of the centre of gravity is raised ✔1 when more weight is added on the upper side, reducing stability
- How is its stability affected when filled with wine? (1 Mark)
- State one factor that affects heat transfer in solids. (1 Mark)
- Length of the conductor
- Cross sectional area
- Temperature difference of the source
- Nature of the material making the conductor.
any one=✔1
- The figure below shows a uniform bar of length 1 metre. Calculate the weight of the beam. (3 Marks)
Clockwise moments = Anti clockwise moments
0.1×W = 0.4m×20N ✔ W = 0.4×20✔
0.1
W=80N ✔ - The figure below shows a u-tube containing the liquids X and Y. Given that the density of liquid X is 1.8g/cm3, calculate the density of liquid Y in g/cm3. (3 Marks)
pxhxg = pxhxg ✔
pxhx = pxhx
1.8g/cm3 × 18cm= py × 8cm ✔
py = 1.8×18
8
py = 4.05g/cm3 ✔ - Name one factor that affects surface tension. (1 Mark)
- Temperature
- Impurities
Any= ✔1
- When a liquid is heated in a glass flask, its level first falls and then starts rising. Explain this observation. (2 Marks)
- The level first dropped due to expansion of glass ✔1
- The level then started rising when the heat reaches the water. ✔1
- The figure below shows two identical springs with negligible weight. The extension produced on the system is 10cm. Determine the spring constant of each spring. (3 Marks)
combined spring constant = k1 + k2
for identical spring, ke = 2k
f = 2ke✔
30N = 2k × 0.1m✔
2k = 30N
0.1m
2k = 300N/m
k = 150N/m ✔ - A body A of mass 2kg moving with a velocity of 5m/s collides with a body B of mass 30kg travelling at 2m/s in the opposite direction. If the collision is perfectly inelastic, find their common velocity after collision. (3 Marks)
m1u1 + m2u2 = (m1+m2)V✔
(2kg × 5m/s ) + (30kg× − 2m/s ) = (30kg + 2kg)V ✔
10kgm/s − 60kgm/s = 32kgV
V = −1.56m/s
moves in the direction of 30kg body - The figure below shows a velocity time graph for a trolley
From the graph, calculate the distance covered by the trolley in the first 10 seconds (2 Marks)
Distance = Area under the graph from 0-10seconds
Area = (6 + 10) × 25✔
2
8 × 25 = 200m
Distance = 200m ✔ - State the reason why gases are easier to compress than solids. (1 Mark)
- Gas particles have larger intermolecular distances than solids ✔
SECTION B: 55mks
-
- State Hook’s law (1 Mark)
- For a helical spring or any other elastic material, the extension is directly proportional to the stretching force, provided that elastic limit is not exceeded. ✔
- The table below shows the extension produced in a spring by various forces.
- Plot a graph of force against extension. (5 Marks)
- From the graph, determine the spring constant. (3 Marks)
Gradient = Spring constant
K = 5 − 2 ✔
1.85-0.75
K = 3 ✔
1.1
K = 2.73 N/cm ✔ - What force would cause an extension of 1.2cm on the spring? (2 Marks)
Force = Ke
F = 2.73N/cm X 1.2cm✔
F = 3.276 N✔
- Plot a graph of force against extension. (5 Marks)
- State Hook’s law (1 Mark)
- The figure below shows a block tackle system
- State the velocity ratio of the system (1 Mark)
- 3 ✔
- Mark the direction of tension in the springs (1 Mark)
- All vertical tensions✔1
- If an effort of 2N is applied, calculate the mechanical advantage of the system. (3 Marks)
MA = Load ✔
Effort
MA = 4.5N ✔
2N
MA=2.25 ✔ - Calculate the efficiency of the system. (3 Marks)
Efficiency = MA × 100% ✔
VR
2.25 × 100% ✔
3
Eff=75% ✔ - Explain why the efficiency of the system is less than 100%. (1 Mark)
- Weight of the pulley blocks/ dead weight ✔1
- Friction
- State the velocity ratio of the system (1 Mark)
- A body of mass 2kg is thrown vertically upwards with a velocity of 14m/s. Determine;
- The maximum height reached by the body (3 Marks)
V2 = U2 − 2gh✔
V = 0
U2 2gh
142 = 2 × 10 × h✔
h = 196
20
h = 9.8m ✔ - Its velocity after 0.5 seconds. (3 Marks)
V = u − gt✔
V = 14m/s − (10 × 0.55)✔
V = 14 − 5
V = 9m/s ✔ - The time taken to reach maximum height. (3 Marks)
V = u − gt✔
O = 14m/s − 10t
10t = 14✔
T = 14/10 = 1.4 seconds✔ - Calculate the net force acting on the ball as it moves upwards if it experiences an air resistance of 8N. (2 Marks)
Net force = mg − Air resistance
= (2kg×10N/kg) − 8 N✔
=20N − 8N
=12N✔
- The maximum height reached by the body (3 Marks)
-
- State the Newton’s 2nd law of motion (1 Mark)
- The rate of change of momentum of a body is directly proportional to the force applied and take place in the direction of the force ✔
- A lady of mass 90kg is standing on the floor of a lift. Determine the reading on the weighing machine when
- Lift is at rest (2 Marks)
At rest Reaction = mg
= 90Kg ×10N ✔
kg
= 900N✔ - Lift is moving upwards with an acceleration of 3m/s2 (2 Marks)
R = mg + ma
=90×10 + (90×3)✔
= 900N + 270N
=1170N✔
- Lift is at rest (2 Marks)
- Two masses of 4kg and 2kg are connected by a light string passing over a frictionless pulley as shown below.
Calculate the acceleration of the masses when left to move freely. (3 Marks)
Net force = 40N − 20N = 20N ✔
Force= Mass × acceleration
20N = 6kg × a ✔
a = 20N = 3.33m/s2 ✔
6kg - A block of mass 35kg is pushed along a horizontal surface whose frictional force is 20N. If the force moving the block is 100N, calculate the co-efficient of friction between the block and the surface. (3 Marks)
μ = FR ✔
μ = 20N ✔
350N
μ = 0.06 ✔
- State the Newton’s 2nd law of motion (1 Mark)
- The figure below shows a hydraulic brake system.
A force of 20 N is applied on the foot pedal connected to a master piston of area 0.05m2. This causes a stopping force of 500N on one wheel. Calculate.- Pressure in the master cylinder (3 Marks)
Pressure = force ✔
area
= 20N ✔
0.05m2
Pressure = 400N/m2 ✔ - Area of the slave piston. (3 Marks)
Pressure is transmitted equally
400N = 5000N ✔
m2 Area
Area = 5000 ✔
400
Area = 12.5m2✔ - Velocity ratio of the system. (3 Marks)
V.R = Area of the load piston ✔
Area of effort piston
V = R = 12.5 ✔
0.05
=250 ✔ - Give two reasons why oil is used in the hydraulic brake system. (2 Marks)
- Incompressible ✔1
- Does not corrode the system ✔1
- State two factors affecting pressure in liquids. (2 Marks)
- Density
- Depth of the liquid Each = ✔1
- Pressure in the master cylinder (3 Marks)
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