Section A box Answer all questions in this section. 0 1 A hacksaw blade is a thin flexible strip of metal. Figure 1 shows a blade clamped between two blocks above a horizontal bench. A pen is attached to the free end of the blade. Figure 1 The free end of the blade is displaced and released. The blade oscillates in a horizontal plane as shown in Figure 2. Figure 2 The time for each oscillation is T. 3 *03* Turn over ► IB/M/Jun24/7407/2 Do not write outside the 0 1 box . 1 Table 1 shows repeated measurements of 60T. Table 1 Measurements of 60T / s 25.20 25.05 24.97 25.10 Show that T is about 0.42 s. [1 mark] Question 1 continues on the next page 4 *04* IB/M/Jun24/7407/2 Do not write outside the box Figure 3 shows a trolley placed on a ramp that is inclined at a small angle to the bench. A piece of graph paper is fixed to the upper surface of the trolley. The blade and pen are positioned so that the tip of the pen rests on the graph paper. The dashed line shows the rest position of the pen. Figure 3 5 *05* Turn over ► IB/M/Jun24/7407/2 Do not write outside the The free end of the blade is displaced box as shown in Figure 4a. The blade and the trolley are then both released at the same moment. The blade oscillates horizontally. The pen remains in contact with the graph paper as the trolley moves. Figures 4b and 4c show the trolley as it moves down the ramp with uniform acceleration. Question 1 continues on the next page 6 *06* IB/M/Jun24/7407/2 Do not write outside the box Figure 5 shows the graph paper. Points P and Q mark the start and end of the continuous line drawn by the pen after the trolley is released. Figure 5 7 *07* Turn over ► IB/M/Jun24/7407/2 Do not write outside the box TPQ is the time for the pen to draw the line from P to Q. s is the displacement of the trolley during TPQ. 0 1 . 2 Determine TPQ. Assume that the time for each full oscillation of the blade is 0.42 s. [2 marks] TPQ = s 0 1 . 3 Determine s. The scale of the graph paper is shown on Figure 5. [1 mark] s = m 0 1 . 4 Determine the acceleration a of the trolley. [2 marks] a = m s−2 Question 1 continues on the next page 8 *08* IB/M/Jun24/7407/2 Do not write outside the 0 1 box . 5 A teacher suggests that the absolute uncertainty in s is ±2 mm. Explain why this is a valid suggestion. [2 marks] 0 1 . 6 The percentage uncertainty in TPQ is 0.46%. Determine the percentage uncertainty in your result for a. [2 marks] percentage uncertainty = % 9 *09* Turn over ► IB/M/Jun24/7407/2 Do not write outside the 0 1 box . 7 Figure 6 is a diagram drawn by a student to explain why the trolley accelerates. The diagram is incomplete because the student has ignored the friction forces involved. Figure 6 Using Figure 6 it can be shown that: sin a g = where a is the acceleration of the trolley. The student determines g using this equation. State and explain how the student’s value of g compares with 9.81 m s−2 . [2 marks] Turn over for the next question 12 10 *10* IB/M/Jun24/7407/2 Do not write outside the 0 2 box The Brinell test determines the hardness of the surface of a material. Figure 7 shows a steel sphere on the surface of a material being tested. Figure 7 In the test, a load F is applied to a steel sphere of diameter D and an indentation of depth h is produced in the material. Figure 8 shows one test. Figure 8 The Brinell hardness number B is given by F B gDh = π where F is in N, g is in N kg−1 and D and h are in mm. The unit of B is kg mm−2 . Using the same steel sphere, the value of h was measured for five materials. B was calculated for each material. For each material: • F was the same • D = 10.0 mm. 11 *11* Turn over ► IB/M/Jun24/7407/2 Do not write outside the Figure 9 box is a plot of B against h. Figure 9 Question 2 continues on the next page 12 *12* IB/M/Jun24/7407/2 Do not write outside the 0 2 box . 1 Determine the value of F that was used to produce Figure 9. [1 mark] F = N 0 2 . 2 Brass was not one of the five materials tested. When brass was tested using these values of F and D, the value of h = 1.60 mm. Determine, using Figure 9, B for brass. [2 marks] B for brass = kg mm−2 0 2 . 3 B for lead is about 5 kg mm−2 . Show that this result cannot be obtained with the steel sphere and the value of F used to produce Figure 9. Go on to suggest how the test can be modified to determine B for lead. [2 marks