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PC1201 Fundamentals of Physics

Semester-1, AY2022/2023

Test-1 (Bonus Question)
(100% individual and compulsory)
r>Total Score: Up to 30 marks will be added to Test-1 (Actual Test)

Your upload of solution file will due on 7 October 2022, Friday 10am at
“Repository for Test-1 (Bonus)” at Canvas’s Assignment

This bonus question is 100% individual. You are reminded of the NUS Code of Student Conduct
at all times.

The values given in all questions are infinitely accurate. E.g., 21.24 is regarded as 21.240000….
The final answer needs to have only 2 decimal places if necessary.

We do not answer any individual emails and any individual consultations about this

If you are using a tablet, you can use a digital pen to write on the soft copy and save the contents
as a pdf file.


If desired, you can solve the questions on papers, and take photo for each solution. If you
do it this way, you will have to cut and paste the images of the solutions into a docx (or
pdf) file, and upload only one docx (or pdf) file.

The filename of your submission should have the assigned serial number, followed by your
name. Please refer to the last 6 pages for your serial number.
E.g., 204-Tay-Seng-Chuan.docx

You cannot insert the links of the objects to the document as the images must be pasted to
the self-contained document.

The details in your calculations must be clearly written. You do not have to copy the
questions to the submission file.

We do not accept any zip file (containing many files). You can only upload one docx file
or one pdf file.

The first 3 lines of your first page must be as follows:

Serial Number (refer to the last 2 pages):
NUS Student Number:


The following drawing shows two frictionless inclines that begin at ground level
(h = 0 m) and slope upward at the same angle θ. One track is longer than the other,
however. Identical blocks are projected up each track with the same initial
speed v0.

On the longer track the block slides upward until it reaches a maximum height H
above the ground.

On the shorter track the block slides upward, flies off the end of the track at a
height H1 above the ground, and then follows the parabolic trajectory of projectile
motion. At the highest point of this trajectory, the block is a height H2 above the
end of the track. The initial total mechanical energy of each block is the same and
is all kinetic energy.

Assume that the air resistance is negligible, and model each block as a point mass.

(i) When the block on the longer track reaches its maximum height, is its final
total mechanical energy all kinetic energy, all potential energy, or some of
each? Justify your answer. (5 marks)

(ii) When the block on the shorter track reaches the top of its trajectory after
leaving the track, is its final total mechanical energy all kinetic energy, all
potential energy or some of each? Justify your answer. (5 marks)

(iii) Which is the greater height above the ground: H or H1 + H2? Why? (You have
to provide the qualitative explanation.) (6 marks)

(iv) If the initial speed of each block is v0 = 7.00 m/s, and each incline slopes
upward at an angle of θ = 50.0°, and the block on the shorter track leaves
the track at a height of H1 = 1.25 m above the ground, find

(a) the height H for the block on the longer track (2 decimal places needed)
(6 marks)

(b) the total height H1 + H2 for the block on the shorter track (2 decimal
places needed) (8 marks)

Examples of file description (Serial Number-Name.docx, or Serial Number-Name.pdf) to be
uploaded to Canvas Assignment, “Repository for Test-1 (Bonus)”:

1- Adam-Ho-Keng-Yuen.docx
7- Ang-Shi-Ya.pdf

The submission folder will be closed at 10am, 7 October 2022, Friday. Only the last copy will
be marked. The solution will be discussed at 5pm by Zoom session.

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