Question 1
1
A student investigates the relationship between the pressure in a ball and the maximum force that the ball produces when it rebounds. A pressure gauge measures a difference \(\Delta p\) between the atmospheric pressure and the pressure in the ball. A force sensor measures the maximum force \(F_{\text {max }}\) exerted on it by the ball during the rebound.
structured0 marks
Question 1(a)
1(a)
State one variable that needs to be controlled during the investigation. The student collects the following data. The student initially hypothesizes that \(F_{\text {max }}\) is proportional to \(\Delta p\).
Easystructured1 marks
Answer
height «of drop» OR velocity «of ball» OR kinetic energy «of ball» OR temperature/mass/radius/surface area/volume of ball Allow reference to controlling spin on the ball Do not accept bald temperature, mass, surface area or volume. 1
Question 1
1
The density of a metal sphere is determined using a digital caliper and a mass balance. The digital caliper is used to measure the diameter D of the sphere by placing the sphere in the jaws of the digital caliper. This reading is shown. The sphere is then removed and another reading is taken immediately afterwards with the jaws closed.
structured0 marks
Question 1(b)
1(b)
State one way in which the procedure for the measurement of D can be improved using the same digital caliper.
Mediumstructured1 marks
Answer
Make multiple measurements AND average OR Make multiple measurements across different diameters OR Zero the caliper Do not allow use of multiple metal spheres [1]
Question 1
1
A group of students uses pressurized air to move a piston that forces a nail into a block of wood. A gauge is used to measure the pressure P of compressed air above atmospheric pressure. The nail enters the wood perpendicular to its surface. The students use a ruler to measure the length of the nail which remains above the surface of the wood as shown. The depth of the nail inside the wood is d. All necessary length measurements are recorded using a ruler with uncertainty \(\pm 1 \mathrm{~mm}\).
structured0 marks
Question 1(b)
1(b)
The students systematically increase the pressure and calculate d.
structured0 marks
Question 1(b)(i)
1(b)(i)
State one variable that needs to be controlled when collecting the data.
Easystructured1 marks
Answer
Diameter/mass/length/type/sharpness/surface of nail OR Type/material/density/stability/surface of wood OR Rate/time which pressure is applied Do not award MP for references to temperature, atmospheric pressure or changes to piston
Question 1
1
The density of a metal sphere is determined using a digital caliper and a mass balance. The digital caliper is used to measure the diameter D of the sphere by placing the sphere in the jaws of the digital caliper. This reading is shown. The sphere is then removed and another reading is taken immediately afterwards with the jaws closed.
structured0 marks
Question 1(b)
1(b)
State one way in which the procedure for the measurement of D can be improved using the same digital caliper.
Mediumstructured1 marks
Answer
Make multiple measurements AND average OR Make multiple measurements across different diameters OR Zero the caliper Do not allow use of multiple metal spheres [1]
Question 1
1
A student performs an experiment with a rod that is free to oscillate in a horizontal plane. Two identical small spheres, each of mass m, are placed at equal distances from the centre of the rod. The student records values of the period of oscillation of the rod T in seconds for different values of the distance of separation of the spheres d, in metres. The student plots the variation with d of T, keeping m constant.
structured0 marks
Question 1(a)
1(a)
0 marks
Question 1(a)(i)
1(a)(i)
Explain why m was kept constant.
Easystructured1 marks
Answer
identifies m as a controlled variable OR recognizes that «the variation of» m affects T OR identifies d as the independent variable O R relationship between d and T could not be found if m changes OR acknowledges that only one variable is to be changed at a time OR highlights the need of the same conditions throughout the experiment OWTTE.
Question 1(a)(iii)
1(a)(iii)
State one other feature of the experiment that the student should keep constant.
Easystructured1 marks
Answer
amplitude/angle of release / use of small angle OR number of oscillations OR any measurable feature of the cable, e.g. length or diameter OR any measurable feature of the rod OR cable holding the rod at its mid-point OR shape of masses Do not accept same cable/rod/ spheres without any other reference. Do not accept any environmental reference as e.g. temperature.
Question 1
1
A student performs an experiment with a rod that is free to oscillate in a horizontal plane. Two identical small spheres, each of mass m, are placed at equal distances from the centre of the rod. The student records values of the period of oscillation of the rod T in seconds for different values of the distance of separation of the spheres d, in metres. The student plots the variation with d of T, keeping m constant.
structured0 marks
Question 1(a)
1(a)
0 marks
Question 1(a)(i)
1(a)(i)
Explain why m was kept constant.
Mediumstructured1 marks
Answer
identifies m as a controlled variable OR recognizes that «the variation of» m affects T OR identifies d as the independent variable OR relationship between d and T could not be found if m changes OR acknowledges that only one variable is to be changed at a time OR highlights the need of the same conditions throughout the experiment OWTTE.
Question 1(a)(iii)
1(a)(iii)
State one other feature of the experiment that the student should keep constant.
Easystructured1 marks
Answer
amplitude/angle of release / use of small angle OR number of oscillations OR any measurable feature of the cable, e.g. length or diameter OR any measurable feature of the rod OR cable holding the rod at its mid-point OR shape of masses Do not accept same cable/rod/ spheres without any other reference. Do not accept any environmental reference as e.g. temperature.
Question 1
1
In an investigation to measure the acceleration of free fall a rod is suspended horizontally by two vertical strings of equal length. The strings are a distance d apart. When the rod is displaced by a small angle and then released, simple harmonic oscillations take place in a horizontal plane. The theoretical prediction for the period of oscillation T is given by the following equation where c is a known numerical constant.
structured0 marks
Question 1(b)
1(b)
A student records the time for 20 oscillations of the rod. Explain how this procedure leads to a more accurate measurement of the time for one oscillation T.
Mediumstructured2 marks
Answer
measured uncertainties «for one oscillation and for 20 oscillations» are the same/similar/OWTTE OR \% uncertainty is less for 20 oscillations than for one dividing «by 20» / finding mean reduces the random error
Question 1
1
In an investigation to measure the acceleration of free fall a rod is suspended horizontally by two vertical strings of equal length. The strings are a distance d apart. When the rod is displaced by a small angle and then released, simple harmonic oscillations take place in a horizontal plane. The theoretical prediction for the period of oscillation T is given by the following equation where c is a known numerical constant.
structured0 marks
Question 1(b)
1(b)
A student records the time for 20 oscillations of the rod. Explain how this procedure leads to a more precise measurement of the time for one oscillation T.
Mediumstructured2 marks
Answer
measured uncertainties «for one oscillation and for 20 oscillations» are the same/similar/OWTTE OR \% uncertainty is less for 20 oscillations than for one dividing «by 20» / finding mean reduces the random error
Question 1
1
Ion-thrust engines can power spacecraft. In this type of engine, ions are created in a chamber and expelled from the spacecraft. The spacecraft is in outer space when the propulsion system is turned on. The spacecraft starts from rest. The mass of ions ejected each second is \(6.6 \times 10^{-6} \mathrm{~kg}\) and the speed of each ion is \(5.2 \times 10^{4} \mathrm{~m} \mathrm{~s}^{-1}\). The initial total mass of the spacecraft and its fuel is 740 kg . Assume that the ions travel away from the spacecraft parallel to its direction of motion.
structured0 marks
Question 1(b)
1(b)
An initial mass of 60 kg of fuel is in the spacecraft for a journey to a planet. Half of the fuel will be required to slow down the spacecraft before arrival at the destination planet.
structured0 marks
Question 1(b)(ii)
1(b)(ii)
Outline why scientists sometimes use estimates in making calculations.
Easystructured1 marks
Answer
problem may be too complicated for exact treatment to make equations/calculations simpler when precision of the calculations is not important some quantities in the problem may not be known exactly 1 max
Question 2
2
An experiment is conducted to determine how the fundamental frequency f of a vibrating wire varies with the tension T in the wire. The data are shown in the graph, the uncertainty in the tension is not shown.
structured0 marks
Question 2(b)
2(b)
It is proposed that the frequency of oscillation is given by \(f^{2}=k T\) where k is a constant.
structured0 marks
Question 2(b)(ii)
2(b)(ii)
Write down a pair of quantities that, when plotted, enable the relationship \(f^{2}=k T\) to be verified.
Mediumstructured1 marks
Answer
\(f^{2}\) AND T OR f AND \(\sqrt{T}\) OR \(\log f\) AND \(\log T\) OR \(\ln f\) AND \(\ln T \vee\)