Tutorial Question 1
Are you confused about SI and non-SI, derived and base unit? This may help you.
Main learning point
i. have to memorise the 7 base units
Are you confused about SI and non-SI, derived and base unit? This may help you.
Main learning point
i. have to memorise the 7 base units
Tutorial Question 2
Main learning points
a. the standard steps in getting the SI base unit
i. think of the equations which relates to the quantity and simplify equation until the base units of the quantities in the equation are known
ii. do not equate quantities with units, i.e. W = kg m s^-2 x m is wrong. Make use of square brackets if you want.
iii. check that your answer consists of only base units.
b. base units of any forms of energy are the same, be it GPE, KE, thermal energy or work.
c. *hint* - potential difference is essentially work done per unit charge i.e. V = W/Q
answer should be kg m^2 A^-1 s^-3. Given up? - solution to 2c
i. the usual sequence of the units should be units with positive power (in increasing order) followed by units with negative power (in decreasing order)
Alternative solution - there are many other approaches depending on the equations used and they should point towards the same answer.
Main learning points
a. the standard steps in getting the SI base unit
i. think of the equations which relates to the quantity and simplify equation until the base units of the quantities in the equation are known
ii. do not equate quantities with units, i.e. W = kg m s^-2 x m is wrong. Make use of square brackets if you want.
iii. check that your answer consists of only base units.
b. base units of any forms of energy are the same, be it GPE, KE, thermal energy or work.
c. *hint* - potential difference is essentially work done per unit charge i.e. V = W/Q
answer should be kg m^2 A^-1 s^-3. Given up? - solution to 2c
i. the usual sequence of the units should be units with positive power (in increasing order) followed by units with negative power (in decreasing order)
Alternative solution - there are many other approaches depending on the equations used and they should point towards the same answer.
Tutorial Question 3
*Hint* - look at the main learning points below to see if you are able to figure out the solution
answer should be kg m^2 A^-1 s^-2. Given up? - solution to 3
Main learning points
i. unit of e.m.f is volts. Hence the base unit of e.m.f is the same as the base unit of potential difference.
ii. derivative of a quantity e.g. dY/dX means how will Y change when X is changed by an infinitesimal (or infinitely small) amount
mathematically it could be written as (Y2 - Y1) / (X2 - X1) just that (X2 - X1) is very small (or infinitely small)
*Hint* - look at the main learning points below to see if you are able to figure out the solution
answer should be kg m^2 A^-1 s^-2. Given up? - solution to 3
Main learning points
i. unit of e.m.f is volts. Hence the base unit of e.m.f is the same as the base unit of potential difference.
ii. derivative of a quantity e.g. dY/dX means how will Y change when X is changed by an infinitesimal (or infinitely small) amount
mathematically it could be written as (Y2 - Y1) / (X2 - X1) just that (X2 - X1) is very small (or infinitely small)
Tutorial Question 4
*Hint* - 6 apples = 4 apples + 2 apples (there is no way that you can add 4 kg to 2 cm) - Think about it
Given up? - solution to 4
Main learning points
i. equation is said to be homogeneous when the unit of each term in the equation agree with one another.
however, this does not mean that the equation is correct. For example, KE = mv^2 would be homogeneous but it is incorrect as it is missing the coefficient 1/2.
a correct equation however is definitely homogeneous.
*Hint* - 6 apples = 4 apples + 2 apples (there is no way that you can add 4 kg to 2 cm) - Think about it
Given up? - solution to 4
Main learning points
i. equation is said to be homogeneous when the unit of each term in the equation agree with one another.
however, this does not mean that the equation is correct. For example, KE = mv^2 would be homogeneous but it is incorrect as it is missing the coefficient 1/2.
a correct equation however is definitely homogeneous.
Tutorial Question 5
There is no video link for this question. Basically, for estimation questions, you will usually need to provide an estimate of the order of magnitude and not the exact value.
For volume of wooden metre rule, we know that the length is 1 m. For the width, you should look at your plastic rule and make an approximation, probably around 3 cm. The thickness, it should be around 0.5. Then you do the calculation.
Volume = 100 cm x 3 cm x 0.5 = 150 cm^3 (even if you were to use 5 cm as the width and 1 cm as the thickness, the value would be 250 cm^3)
Answer: C
There is no video link for this question. Basically, for estimation questions, you will usually need to provide an estimate of the order of magnitude and not the exact value.
For volume of wooden metre rule, we know that the length is 1 m. For the width, you should look at your plastic rule and make an approximation, probably around 3 cm. The thickness, it should be around 0.5. Then you do the calculation.
Volume = 100 cm x 3 cm x 0.5 = 150 cm^3 (even if you were to use 5 cm as the width and 1 cm as the thickness, the value would be 250 cm^3)
Answer: C
Tutorial Question 6
Again there is no video link for this question. However, you should have the following considerations when determining whether a particular estimate is realistic. In examinations, you may be asked to provide explanations for your approximations, therefore, please learn how to present your explanations clearly.
Please have these workings written in your tutorial.
A. The working principle of a hair dryer is usually have the air passing through a heating element. In order for the heating element to be hot enough, a high current must be passing through it. For normal appliances like lamp or electrical fan, the power is usually 30 W to 100 W, thus the current (power/voltage of 240V) is usually less than 1A. The current we see in the labs is usually in milliamperes. For heating element in the hair dryer, it should take around 5 A to 10 A, this means power of the hair dryer should be 1200 W to 2400 W. (150 W is unrealistic)
B. The mass of a man is around 70 kg. For the speed of the man, you should know that it takes around 12 s to sprint 100 m. Therefore the speed of a running man is around 10 m/s. Using equation of KE, the kinetic energy of the man should be approximately 2400 J. (Realistic)
C. The volume of a canned drink is around 330 ml = 330 cm^3. Knowing that density of water is 1 g/cm^3, the mass of the canned drink (inclusive of the mass of the can and additives other than water) is approximately 400 g. The weight should be around 4 N. (Realistic)
D. Density of water is 1000 kg m^-3. Ice is a little less dense than water. Hence density of ice is possibly 900 kg m^-3. (Realistic)
A link with the approximate power consumption of the home appliances - check out the power consumption of refrigerators, iron, microwave, air conditioner (1000 W to 1500 W)
Again there is no video link for this question. However, you should have the following considerations when determining whether a particular estimate is realistic. In examinations, you may be asked to provide explanations for your approximations, therefore, please learn how to present your explanations clearly.
Please have these workings written in your tutorial.
A. The working principle of a hair dryer is usually have the air passing through a heating element. In order for the heating element to be hot enough, a high current must be passing through it. For normal appliances like lamp or electrical fan, the power is usually 30 W to 100 W, thus the current (power/voltage of 240V) is usually less than 1A. The current we see in the labs is usually in milliamperes. For heating element in the hair dryer, it should take around 5 A to 10 A, this means power of the hair dryer should be 1200 W to 2400 W. (150 W is unrealistic)
B. The mass of a man is around 70 kg. For the speed of the man, you should know that it takes around 12 s to sprint 100 m. Therefore the speed of a running man is around 10 m/s. Using equation of KE, the kinetic energy of the man should be approximately 2400 J. (Realistic)
C. The volume of a canned drink is around 330 ml = 330 cm^3. Knowing that density of water is 1 g/cm^3, the mass of the canned drink (inclusive of the mass of the can and additives other than water) is approximately 400 g. The weight should be around 4 N. (Realistic)
D. Density of water is 1000 kg m^-3. Ice is a little less dense than water. Hence density of ice is possibly 900 kg m^-3. (Realistic)
A link with the approximate power consumption of the home appliances - check out the power consumption of refrigerators, iron, microwave, air conditioner (1000 W to 1500 W)
Tutorial Question 7
This question is quite straight forward. You will need to be able to estimate the diameter of a ping pong ball which is around 4 cm, hence radius is 2 cm.
Using the volume of the classroom, you should be able to determine the number of ping pong ball to be 2 x 10^7. [Show proper workings in your tutorial]
Answer : C
This question is quite straight forward. You will need to be able to estimate the diameter of a ping pong ball which is around 4 cm, hence radius is 2 cm.
Using the volume of the classroom, you should be able to determine the number of ping pong ball to be 2 x 10^7. [Show proper workings in your tutorial]
Answer : C
Tutorial Question 8
*Hint* Read your lecture notes, you should be able to find a similar example.
Main learning points
i. accuracy is a measure of how close the measured value is to the true value. A highly accurate set of measurements has small systematic errors (e.g. zero error)
ii. precision is a measure of how close each measurement agrees with each other (the spread). A highly precise set of measurements contains small random errors (e.g. fluctuation in surrounding temperature)
*Hint* Read your lecture notes, you should be able to find a similar example.
Main learning points
i. accuracy is a measure of how close the measured value is to the true value. A highly accurate set of measurements has small systematic errors (e.g. zero error)
ii. precision is a measure of how close each measurement agrees with each other (the spread). A highly precise set of measurements contains small random errors (e.g. fluctuation in surrounding temperature)
Basics of dealing with uncertainties
Watch this video -> basics of dealing with uncertainties
Main learning points
i. make the quantity, of which the uncertainty is to be determined, the subject of the equation before determining the uncertainty
ii. uncertainties will always add up
iii. when the equation involves purely addition and subtraction, you will use addition of absolute uncertainty
- coefficient is important
iv. when the equation involves purely multiplication and division, you will use addition of fractional uncertainty
- power is important
v. when displaying value with its absolute uncertainty, please make sure
- absolute uncertainty is rounded UP to 1 significant figure
- average value is rounded off to the same decimal place (or 10th/100th/1000th position) as the absolute uncertainty
Watch this video -> basics of dealing with uncertainties
Main learning points
i. make the quantity, of which the uncertainty is to be determined, the subject of the equation before determining the uncertainty
ii. uncertainties will always add up
iii. when the equation involves purely addition and subtraction, you will use addition of absolute uncertainty
- coefficient is important
iv. when the equation involves purely multiplication and division, you will use addition of fractional uncertainty
- power is important
v. when displaying value with its absolute uncertainty, please make sure
- absolute uncertainty is rounded UP to 1 significant figure
- average value is rounded off to the same decimal place (or 10th/100th/1000th position) as the absolute uncertainty
Tutorial Question 9
Make sure you have considered the above 5 points when you solve parts a and b.
Additional learning points
a. average value is left with 4-5 sf during the calculation stage before rounded off during the final answer
b. you do not need to convert to SI units when dealing with fractional uncertainty (e.g. cm to m) as they will cancel each other out
** Questions related with calculation of uncertainty may be tedious, hence, you will need to be very careful in your calculations.
Make sure you have considered the above 5 points when you solve parts a and b.
Additional learning points
a. average value is left with 4-5 sf during the calculation stage before rounded off during the final answer
b. you do not need to convert to SI units when dealing with fractional uncertainty (e.g. cm to m) as they will cancel each other out
** Questions related with calculation of uncertainty may be tedious, hence, you will need to be very careful in your calculations.
Tutorial Question 10
This question is relatively simple.
Main learning point
i. you need to make g the subject first, else you will be getting y - 2x as your answer
This question is relatively simple.
Main learning point
i. you need to make g the subject first, else you will be getting y - 2x as your answer
Tutorial Question 11
*Hint* - the equation is a combination of addition/subtraction together with multiplication/division. Let x be m1 - m2.
Main learning point
i. when you have a combination of addition/subtraction together with multiplication/division, make use of another variable so that the equation becomes purely category I or II.
*Hint* - the equation is a combination of addition/subtraction together with multiplication/division. Let x be m1 - m2.
Main learning point
i. when you have a combination of addition/subtraction together with multiplication/division, make use of another variable so that the equation becomes purely category I or II.
Basics of vector resolution
Watch this video -> basics of vector resolution
Main learning points
i. vector can be resolved into 2 perpendicular components
ii. the component which makes the angle with the vector will be cosine while the other will be sine
iii. the idea of vector resolution applied to force and velocity
Watch this video -> basics of vector resolution
Main learning points
i. vector can be resolved into 2 perpendicular components
ii. the component which makes the angle with the vector will be cosine while the other will be sine
iii. the idea of vector resolution applied to force and velocity
Tutorial Question 12
Main learning points on vector addition
i. need to know the assumed directions of North, East, South and West
ii. resolve vectors so that they are parallel to each other to allow simple addition of vectors to take place
iii. make use of pythagoras theorem to determine the resultant magnitude
iv. make use of vector diagram with labelled angle to determine the direction
v. the answer would be the same if you were to draw scaled diagram
Main learning points on vector addition
i. need to know the assumed directions of North, East, South and West
ii. resolve vectors so that they are parallel to each other to allow simple addition of vectors to take place
iii. make use of pythagoras theorem to determine the resultant magnitude
iv. make use of vector diagram with labelled angle to determine the direction
v. the answer would be the same if you were to draw scaled diagram
Tutorial Question 13
Watch this video if you are stuck -> dealing with vector subtraction
Main learning points on vector subtraction
i. need to flip the initial velocity so that the equation could be written as change in velocity = final velocity + (negative initial velocity)
Solution to Question 13
Main learning points
i. resolve vectors so that they are parallel to each other follow to allow simple addition of vectors to take place
ii. make use of pythagoras theorem to determine the resultant magnitude
iii. make use of vector diagram with labelled angle to determine the direction
Watch this video if you are stuck -> dealing with vector subtraction
Main learning points on vector subtraction
i. need to flip the initial velocity so that the equation could be written as change in velocity = final velocity + (negative initial velocity)
Solution to Question 13
Main learning points
i. resolve vectors so that they are parallel to each other follow to allow simple addition of vectors to take place
ii. make use of pythagoras theorem to determine the resultant magnitude
iii. make use of vector diagram with labelled angle to determine the direction
Tutorial Question 14
Watch this video if you are stuck -> hint
Solution to Question 14a & 14b
Main learning points
i. force is a vector, hence the resultant of two or more forces could be determined by using the vector resolution technique
ii. in order for the boat to move straight, the resultant force must be vertically upwards, this means that the horizontal component of the resultant force must be zero
Watch this video if you are stuck -> hint
Solution to Question 14a & 14b
Main learning points
i. force is a vector, hence the resultant of two or more forces could be determined by using the vector resolution technique
ii. in order for the boat to move straight, the resultant force must be vertically upwards, this means that the horizontal component of the resultant force must be zero
Tutorial Question 15
This question requires you to make use of cosine rule rather than vector resolution. Sketch the two vector diagrams (parallelograms) and think of how to formulate the two equations using cosine rule.
Watch this video if you are stuck -> hint
Solution to Question 15
(Do not be too worried if you find this question extremely hard)
This question requires you to make use of cosine rule rather than vector resolution. Sketch the two vector diagrams (parallelograms) and think of how to formulate the two equations using cosine rule.
Watch this video if you are stuck -> hint
Solution to Question 15
(Do not be too worried if you find this question extremely hard)