You are investigating two mysterious objects with massM = 0.7 kg and diameter R = 0.2 m, which arerolling down a slope without slipping. The slope makes an angle θ =30 ° with the horizontal. The acceleration of gravity for an objectin free fall is 9.8 m/s2.
(a) Draw a force diagram, showing all the forces on theobject.
[2 marks]
(b) You are measuring the time it takes the objects, from restand without slipping, to roll down the L = 1.00 m longslope, as measured along the slope. Show that the arrival time atthe bottom for an object with moment of inertia I =cMR2 is
t = 2 ( 1 + c ) L g sin ⡠θ
[3 marks]
(c) Like a good experimentalist, you are taking a number ofrepeat measurements. In the following, make sure you quote allanswers to an appropriate precision. Your measurements are capturedin the following table.
Take | Object 1 (s) | Object 2 (s) |
1 | 0.8 | 0.93 |
2 | 0.74 | 0.93 |
3 | 0.82 | 0.91 |
4 | 0.77 | 0.8 |
5 | 0.83 | 0.95 |
         (i) Findthe average times that the two objects take to roll down the slope.Include the associated uncertainties in your result.
[2 marks]
         (ii)Deduce the accelerations of the two objects, with uncertainties.Show your working.
[2 marks]
         (iii)Explain why the two objects roll with different accelerations.
[2 marks]
         (iv) Whatis your best guess of the geometry of your objects? Providereasoning for your guess.
[2 marks]
