​(a) The diagram in the figure below represents a wheel and axle used as a machine, whose efficiency is 80% to raise 400N of building materials. The wheel and axles have diameters of 75cm and 15cm respectively.

The diagram in the figure below represents a wheel and axle used as a machine, whose efficiency is 80% to raise 400N of building materials. The wheel and axles have diameters of 75cm and 15cm respectively.

​(i) Mark on the diagram the correct position and direction of the load to be lifted (1mk)

​(ii) Name the principle on which this machine works (1mk)

​(iii) Calculate the effort needed to raise the load (3mks)

​(iv) The machine is operated manually and raises the load to a height of 5m in 20 seconds. Calculate the power developed by the operator (2mks)

(b)
​(i) State two factors that determines the efficiency of an inclined plane as a machine (2mks)

​(ii) Explain how these factors affect efficiency (2mks)

​Explain what you understand by each of the following terms: 

(​i) Angular velocity (1mk)

​(ii) Centripetal force (1mk)

​b) A bicycle wheel with radius 28cm moves with a linear velocity of 8m/s, determine 

​(i) the angular velocity of the wheel (2mks)

​(ii) the centripetal acceleration of a point on the rim of the wheel (2mks)

​(c) To determine the relationship between angular velocity w and tension T, a student used a smooth disc with a hole at the centre,  a string and cylindrical object of mass m, as shown below

To determine the relationship between angular velocity w and tension T, a student used a smooth disc with a hole at the centre, a string and cylindrical object of mass m, as shown above

​Describe how the student went about determining the relationship, specifying any other necessary material or instrument not shown in the diagram (3mks)

A student set-up the apparatus as shown above to determine the power of an electric heater

(a)
​(i) Other than time, state the measurements that would be used to determine the quantity of heat P absorbed by ice in a unit time (2mks)

​(ii) Complete the circuit to show the connection of the essential circuit components (2mks)

​(iii) Describe how the student would proceed to determine P (3mks)

​(iv) Give a reason why P may not be equal to the value indicated by the manufacturer (1mk)

The readings tabulated below shows how the length of a helical spring varied with the load hanging on it

(a)
​(i) Complete the table to show the values of extension (2mks)

​(ii) Draw a graph of extension (y-axis) against load for the spring (5mks)

​(ii) Determining form the graph the proportionality constant of the spring (2mks)

​(b) Two springs Q and R have proportionality constants 20N/M and 25N/M respectively. Q weighs 0.2 N while the weight of R is negligible. The two springs are arranged to support a load of 3.0N as shown in the diagram below

Determine the extension in 
(i)  Q……………………………………………..(1mk)

ii)  R ……………………………………………(1mk)

​(c) State two factors that determine the proportionality constant of a helical spring (2mks)

The diagram below shows two trolleys, A and B connected to each other by an elastic strip of negligible mass. The trolleys are pulled apart on a smooth plane till tension in the elastic strip is 4.0N and are then released suddenly

​(a) State with reason the total momentum of the trolleys when they are just released (2mks)

​(b) Calculate the initial acceleration of trolley A when released (3mks)

​(d) Which trolley covers a longer distance before collision? Explain (2mks)

​(e) Explain why the elastic strip may not stretch to the same original length after impact (2mks)

A student holds a sheet of paper at an end so that it hangs in the position A as shown above

​Explain why the paper rises to the position B when the student blows  air in the direction shown by the arrow (2mks)