Instructions 1. The test is strictly Physics questions only and it is an OPEN BOOK TEST ( you can use a

textbook or anything that you think can help you answer the questions)

2. You need only answer the FIRST 3 compulsory questions only.

3. Each question contributes 33.33% to towards your final mark of 99.99%.

4. Question 4 is an OPTIONAL BONUS question and only the brave can answer the question.

5. If one chooses to answer the bonus question which counts 50.01% and gets the question

correct, the student will have a final mark of 150%.

6. If one chooses to answer the bonus question and gets it incorrectly 20% will be subtracted

from your test mark!

7. Number your questions according to the numbering system on this test.

8. Show all workings CLEARLY and NEATLY if I don’t see what you wrote you will get a ZERO!!!

Question 1

In the picture above there are Three presidents namely A,B and C bored from talking politics in a

meeting and so they decided to play a game called THE WORLDS STRONGEST PRESIDENT, to see

who is strong than the other. President A (Jacob Ndlovu) pulls a rope at an angle of 600 measured

with respect to the Positive Y-Axis at a force of 50 N. President B (Josh W Bushman) pulls at a force

of 40 N downwards and President C (Boss Mugabe) pulls with a force of 20 N to the Left,

Rules of the game:

If the resultant force lies on the first quadrant then all Presidents have the same strength.

If the resultant force lies on the second quadrant then President Jacob Ndlovu wins.

If the resultant force lies on the third quadrant then President Josh W Bushman wins.

If the resultant force lies on the fourth quadrant then President Boss Mugabe wins.

Hint : use vector methods to first find the resultant force and the direction of the resultant force, then

judge who wins using the direction (angle) found from the x and y component of the net force.

Question 2

1, in the figure above a Physicist decided to play with his children and wanted to find the

acceleration of the system he made in his lab and he used a computer and found it to be

𝑎 = 𝑔 (𝑚3−𝑚1

𝑚1+𝑚2+𝑚3) but then the computer failed to calculate the tensions on the

ropes. He then guessed “out of experience” that the tensions on the left and right side of

the Mass Analyser to be given by,

𝑇1 = 𝑚3𝑔 (2𝑚1+𝑚2

𝑚1+𝑚2+𝑚3) And 𝑇2 = 𝑚1𝑔 (

2𝑚3+𝑚2

𝑚1+𝑚2+𝑚3)

Use Newton’s second law of motion to show that his guess was correct. There is no force of

friction on top of the table and the pulleys.

Hint: choose the direction of the system to accelerate to the right. Draw a free body diagram

or force diagram for each mass then apply newton second law on

𝑀1 𝑎𝑛𝑑 𝑀2 𝑎𝑛𝑑 𝑀3 𝑟𝑒𝑠𝑝𝑒𝑐𝑡𝑖𝑣𝑒𝑙𝑦 and sum up your 3 equations to find the acceleration

then use those equations again to find the tensions.

2, using newton’s laws, explain how a car airbag can save your life. (Write an explanation of

not less than 5 lines)

Question 3

Not drawn to scale, a cross section through the interior of Earth. Rather than being uniform

throughout, Earth is divided into three zones: an outer crest, a mantle, and an inner core.

The dimensions of these zones and the masses contained within them are shown on the

figure. Earth has a total mass of 5.98 × 1024kg and a radius of 6370 km. assume that Earth

is spherical (round).

(a) Calculate the acceleration due to gravity at the surface of the Earth. (Answer 9.83 𝑚 𝑠2⁄ )

(b) Suppose that a bore hole (the Mohole) is driven to the crust-mantle interface at a depth

of 25.0 km; what would be the value of the acceleration due to gravity be at the bottom of

the hole? (Answer 9.84 𝑚 𝑠2⁄ )

Bonus Question Continuing from question 3, suppose that Earth were a uniform sphere (has no layers and

density is the same throughout) with the same total mass and size. What would be the

value of acceleration due to gravity, at a depth of 25.0 km? (Answer 9.79 𝑚 𝑠2⁄ )

Hint: use your knowledge of Newton’s law of universal gravitation and newton’s second law

Useful equations 𝐹 = 𝐺𝑀𝑚

𝑟2 ,𝐹 = 𝑚𝑎 , 𝜌 =𝑀

𝑉= 𝑑𝑒𝑛𝑠𝑖𝑡𝑦 , 𝑉 =

4

3𝜋𝑟3,𝐹 =

4𝜋𝐺𝜌

3𝑟

This test is not bad as you think!!! The bonus question is the easiest question of

them all,it just needs you to think like a Physicist!!