A student measures the spring constant k k\,k of a spring by two different methods.
The student connects a mass m=400 gm = 400\text{ g}m=400 g to the spring, pulls it down slightly, and releases it so that it oscillates.
The student measures the time t t\,t taken for 25 oscillations. The digital stopwatch displays:
00:15.50 00:15.50 00:15.50Record the time t t\,t in seconds.
Calculate the period T T\,T of the oscillations.
Suggest how the oscillation timing procedure can be improved to increase the accuracy of the result.
Calculate the value of the spring constant k1 k_1\,k1 using the equation:
k1=15.8T2 k_1 = \frac{15.8}{T^2} k1=T215.8The student measures the stretched length of the spring with the 400 g mass attached. On a diagram drawn to a scale of one-third (1:3) of full size, the length L L\,L of the spring is measured as 3.2 cm.
Calculate the actual stretched length l l\,l of the spring.
After repeating the measurement for several other masses, the student plots a graph of stretched length l/cml/\text{cm}l/cm (yyy-axis) against mass m/gm/\text{g}m/g (xxx-axis). The gradient G G\,G of the line of best fit is found to be 0.024 cm/g.
Calculate the spring constant k2 k_2\,k2 using the equation:
k2=1G k_2 = \frac{1}{G} k2=G1Two quantities can be considered equal within the limits of experimental accuracy if their values are within 10% of each other. Compare your values of k1 k_1\,k1 and k2k_2k2. State whether your results indicate that these values can be considered equal. Support your statement with a calculation.
245 exam-style questions on CIE IGCSE Physics 1.5 Forces, covering 1.5.1a Forces, resultant force and motion, 1.5.1b Load–extension graphs and the spring constant, 1.5.1c Friction and drag, 1.5.1d Force, mass and acceleration, 1.5.1e Motion in a circular path, 1.5.2a Moment of a force, 1.5.2b Principle of moments and equilibrium, and 1.5.3 Centre of gravity and stability. Each one has a worked solution and a mark scheme showing where the marks go.