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.
183 exam-style questions on CIE IGCSE Physics 1.5.1a Forces, resultant force and motion. Each one has a worked solution and a mark scheme showing where the marks go.