Question

You are investigating two mysterious objects with mass M = 0.7 kg and diameter R = 0.2 m, which are rolling down a slope without slipping. The slope makes an angle θ = 30 ° with the horizontal. The acceleration of gravity for an object in free fall is 9.8 m/s².

(a) Draw a force diagram, showing all the forces on the object.

[2 marks]

(b) You are measuring the time it takes the objects, from rest and without slipping, to roll down the L = 1.00 m long slope, as measured along the slope. Show that the arrival time at the 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 of repeat measurements. In the following, make sure you quote all answers to an appropriate precision. Your measurements are captured in 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) Find the 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) What is your best guess of the geometry of your objects? Provide reasoning for your guess.

[2 marks]

Answer 1

I have solved your problem which is shown below:

Part c (i)

here I have calculate the value of average time for both objects = 0.792 and 0.904 respectively.

To find standard error =

Similarly using

Using this time I have solved the rest parts which is shown above and below:

(iii) Why two objects have different accelerations?

Answer: For objects value of acceleration depends on the value of t if both objects have different value of c it means both are having a different objects . for example value of c for disc is And value of I for ring is so bodies having different value of t correspond to differnt value of acceleration but as we can see that value of t depends on value of c so as c varies so as t and with respect to t acceleration varies .

The value of c is shown in part 4 which is shown below:

(iv) For disc c= 0.5

For ring c = 1.

In case you have any query please write in a comment. I hope you like it. Thank you