Required_Basic_Math_Worksheet_for_VectorNotation_DAY8
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FND71095 Foundation Module (Electronic Systems Engineering) Name: ID Show all your steps for calculations and indicate by boxing your final answer. Vector Notations: Components of vectors: Q1 Determine the x- and y-component of each of the force vectors shown in Figure below: Where ⃗F
⃗
1
is 40 N, ⃗F
⃗
2
is 50 N, and ⃗F
⃗
3
is 30 N (Note: the drawing is not to the scale) Fig D8-1 Component of vectors in x-y plane Part 1: Determine the x- and y- components of each vector: i.e)
F1x = |F1|cos53
=(40N)cos53
=24.07
F1y = |F1|sin53 =(40)sin53 =31.9
F2x= |F2|cos45 = (50)cos45 = -35.36 F2y = |F2|sin45 = 34.09
F3x= |F3|cos30 = (30)cos30 = -25.98 F3y= |F3|sin30 = -15
Date: page /8
FND71095 Foundation Module (Electronic Systems Engineering) Name: ID Part 2: Determine the sum of the three forces shown in Figure D8-1. You can use the results of the component calculation in Part1: Rx = F1x + F2x + F3x = 24.07 + (-35.36) + (-25.98) = -37.27
Ry = F1y +F2y +F3y = 31.9 + 34.10 + (-15) = 51
Part 3: Express the resultant Force in unit vector notation R = (F1x+F2x+F3x)i + (F1y+F2y+F3y)j
= -37.27i + 51j
Part 4: Find the magnitude of the resultant Force. R= Part 5: Which quadrant is the resultant vector in? (circle the correct quadrant) I II III IV Part 6: Determine the angle relative to the x-axis. (provide the resultant vector.) Date: page /8
FND71095 Foundation Module (Electronic Systems Engineering) Name: ID Part 7: breakout room: come up with a potential real-life scenario
that would require this type of mathematical problem solving: Hint: Adam Betty, and Carl are stranded on a clam water. They only have one tube to hang on to. Each of them pulls to the direction indicated by the force. Which direction eventually will they drifted towards at what force? Island is located on the 4
th
quadrant; will they be able to reach the land eventually? Group 1 Group 2 Group 3 Adam, Betty and Carl are competing in a 3 – way tug of war contest and each contestant is pulling towards themselves. Each of them are pulling towards the direction indicated by their force. Which direction will the others be pulled towards? Who will win the game?
Group 4 Date: page /8
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FND71095 Foundation Module (Electronic Systems Engineering) Name: ID Q2: Interactions of charged objects: Two equal-mass small aluminium foil balls A and B have electric charge +q (on A) and +3q (on B)
Part1:
Compare the magnitude of the electric force that the foil ball with the smaller charge exerts on the ball with the larger charge (F
A_on_B
) to the force that the larger charged ball exerts on the smaller charged ball (F
B_on_A
). Justify your answer. Part2:
If the balls are suspended by equal-length strings from the same point, will one string hang at a greater angle from the vertical than the other? Justify your answer. STEP1: Sketch and Translate
(the word into mathematically solvable problem: a ladled sketch of the situation below) STEP2: Simplify and diagram (FBD: Free Body Diagram – model the balls as point-like objects) STEP3: Present mathematically: 𝐹
𝐴_𝑜𝑛_𝐵 = 𝑘
𝐶
𝑟𝑞
𝐴𝐵2𝐴
𝑞
𝐵 = 𝑘
𝐶
𝑟𝑞
𝐴𝐵2𝐵
𝑞
𝐴 = 𝐹
𝐵_𝑜𝑛_𝐴
Date: page /8
FND71095 Foundation Module (Electronic Systems Engineering) Name: ID (this answers Part1 based on Coulomb’s Law and Newton’s 3
rd
Law) Q3 (Complete the following Exercise and submit to the drop box) Here are three vectors in meters: ⃗
⃗
𝑑⃗
1
= −3.0 𝑖̂ + 3.0 𝑗̂ + 2.0 𝑘̂
⃗
⃗
𝑑⃗
2
= −2.0 𝑖̂ − 4.0 𝑗̂ + 2.0 𝑘̂
⃗
⃗
𝑑⃗
3
= 2.0 𝑖̂ + 3.0 𝑗̂ + 1.0 𝑘̂
What results from (a)
) (b)
× ⃗𝑑⃗
3
) (c)
⃗
⃗
𝑑⃗
1
× (⃗𝑑⃗
2
+ ⃗𝑑⃗
3
) Date: page /8
FND71095 Foundation Module (Electronic Systems Engineering) Name: ID Q4 More challenging Question on the unit vector: The
three vectors given are 𝑎 = 5.0 𝑖̂ + 4.0 𝑗̂ + 6.0 𝑘̂
𝑏⃗ = −2.0 𝑖̂ + 2.0 𝑗̂ + 3.0 𝑘̂
𝑐 = 4.0 𝑖̂ + 3.0 𝑗̂ + 2.0 𝑘̂
The vector equation 𝑟 = 𝑎 + 𝑏⃗ + 𝑐 Part1: What is 𝑟 in the unit vector notation. 𝑟 =
Part2:
Calculate the angle between the resultant vector 𝑟 and the positive z-axis Part3: What is the component of 𝑎 along the direction of 𝑏⃗ Date: page /8
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FND71095 Foundation Module (Electronic Systems Engineering) Name: ID Q5: Vector 𝑎 lies in the xy plane, has a magnitude of 18 units, and points in a direction 250°
from the positive direction of the x axis. Also, vector 𝑏⃗ has a magnitude of 12 units and
points along the positive direction of the z axis. What is the vector product 𝑐 = 𝑎 × 𝑏⃗ ? note: Angle: SUMMARY: Date: page /8 Vector product’s Magnitude:
FND71095 Foundation Module (Electronic Systems Engineering) Name: ID Q6: Copy the summary on page 5 below Q5 on this page and write it down with your own handwriting. Creative your own sample question to use the given equations with. It will be selected as exercise question for your classmate. Date: page /8