A student is investigating the motion of a wooden block on an inclined plane, as shown in Fig. 1.1. A falling body causes the wooden block to accelerate. string wooden block plane P θ pulley Q -falling body Fig. 1.1 The wooden block is initially at rest at point P and has velocity v at point Q. It is suggested that the relationship between v and the angle of the plane to the horizontal is (B + m)v² / 2s = Bg - mg sin θ where B is the mass of the falling body, m is the mass of the wooden block, s is the distance between P and Q and g is the acceleration of free fall. Design a laboratory experiment to test the relationship between v and θ. Explain how your results could be used to determine a value for g. You should draw a diagram, on page 3, showing the arrangement of your equipment. In your account you should pay particular attention to • the procedure to be followed, • the measurements to be taken, • the control of variables, • the analysis of the data, • any safety precautions to be taken.

Mark scheme

Marking points from the official mark scheme (May/June 2017). The mark or mark type is shown in brackets.

1. [1] (sin) θ is the independent variable and v is the dependent variable or vary (sin) θ and measure v
2. [1] keep s (PQ) constant
3. [1] labelled diagram showing inclined plane with labelled support and P and Q marked
4. [1] method to measure angle e.g. use a protractor to measure θ or use a ruler to measure marked distances from which sin θ or θ may be determined
5. [1] method of timing for an appropriate distance to determine v (at Q) e.g. use a stopwatch/timer or correctly positioned light gate(s) connected to a timer/data-logger or correctly positioned motion sensor connected to data-logger
6. [1] measurement of an appropriate distance to determine v (at Q) e.g. rule to measure an appropriate length or length of a card to interrupt light beam or distance from motion sensor to Q
7. [1] plot a graph of v² against sin θ
8. [1] relationship valid if a straight line produced (not passing through the origin)
9. [1] g = -gradient x (B+m) / 2ms
10. [1] g = y-intercept x (B+m) / 2Bs
11. [D1] use cushion/foam/sandbox for falling body (B)
12. [D2] (sin) θ determined using trigonometry relationship using marked lengths
13. [D3] appropriate equation to determine v (at Q) e.g. v = 2s/t
14. [D4] repeat experiment for each θ and average v or t
15. [D5] use of balance to measure mass of wooden block m and falling body B and rule to measure s
16. [D6] y-intercept = 2Bsg / (B+m)
17. [D7] clean surfaces of blocks/inclined plane/ensure surface of the plane is smooth
18. [D8] keep B and m constant or keep mass of block and mass of falling body constant
19. [D9] method to ensure that wooden block starts at the same position P, e.g. put a mark on the block or align front or back of block
20. [D10] method to prevent plane slipping so that angle being measured remains the same, e.g. a mass as a stop