Grade 11, U1C-L1, Vector Comp
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The document discusses breaking vectors into perpendicular components. It provides an example of resolving a displacement vector of Janice walking 10 km northeast, then 4 km west, and 1.9 km north into its east and north components. The total displacement is calculated to be 3.1 km east and 9 km north, for a total displacement of 9.5 km in a northeast direction. Practice problems are provided to reinforce working with vector components.
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![ Like forces, all vectors can be broken into twoLike forces, all vectors can be broken into two ⊥⊥
components.components.
Example:Example: Janice walks 10.0 km [NE], then 4.0 km [W], andJanice walks 10.0 km [NE], then 4.0 km [W], and
finally walks 1.9 km [N]. Determine Janice’s totalfinally walks 1.9 km [N]. Determine Janice’s total
displacement.displacement.
Solution:Solution: Below, the 10.0 km displacement vector is brokenBelow, the 10.0 km displacement vector is broken
(or “(or “resolvedresolved”) into two”) into two ⊥⊥ components which are then addedcomponents which are then added
to the other vectors.to the other vectors.
ΔΔdd TotalTotal = 7.1 km [E] + 4.0 km [W] + 7.1 km [N] + 1.9 km [N]= 7.1 km [E] + 4.0 km [W] + 7.1 km [N] + 1.9 km [N]
= 7.1 km [E] - 4.0 km [E] + 7.1 km [N] + 1.9 km [N]= 7.1 km [E] - 4.0 km [E] + 7.1 km [N] + 1.9 km [N]
= 3.1 km [E] + 9.0 km [N]= 3.1 km [E] + 9.0 km [N]
1 0 . 0 k m
1 0 . 0 ( c o s 4 5 ) k m =
7 . 1 k m
10.0(sin45)km=
7.1km N
W E](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
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This document discusses solving vector problems in two dimensions. It explains that most problems will involve adding two non-collinear vectors to form a right triangle, which can then be solved using trigonometry. Several example problems are provided to demonstrate breaking vectors into components, adding vectors head-to-tail, and using trigonometry to solve for lengths and angles. The key steps are to carefully draw vector diagrams, break vectors into x and y components if needed, then use trigonometric functions like SOH CAH TOA to solve for unknown values.
Motion in one direction
This document introduces key concepts of 1-D kinematics including:
1) Distance refers to the total path traveled while displacement refers to the change in position from initial to final point.
2) Kinematics describes motion without considering causes, and 1-D kinematics refers to motion in a straight line.
3) Graphs can distinguish between distance and displacement, with displacement being the straight line segment between initial and final points.
4) Key concepts such as average speed, average velocity, acceleration, and free fall are introduced along with relevant equations and demonstrations.
Motion in one direction
This document provides an introduction to 1-dimensional kinematics, including distance, displacement, average speed, average velocity, acceleration, and position-time and velocity-time graphs. It defines key terms like distance, displacement, speed, velocity, acceleration, and discusses the relationships between these quantities. Examples and practice problems are provided to illustrate concepts like the difference between distance and displacement, calculating average speed and velocity, determining acceleration from graphs, and using kinematic equations.
Hugh_D_Young_&_Roger_A_Freedman_Física_Universitaria_12ed_Manual.pdf
1. The document provides examples of converting between different units of measurement, such as miles to kilometers, gallons to liters, seconds to years, etc. Conversions involve setting up proportional relationships between units and calculating using conversion factors.
2. Examples show calculating uncertainties in measurements based on the precision of the measuring instrument. Uncertainty is estimated as a percentage error relative to the measured quantity.
3. To determine average values and uncertainties, the document uses the maximum and minimum possible values based on the precision of the original measurements. The uncertainty is taken as half the range between the maximum and minimum average values.
Fisica_Universitaria_Sears_Zemansky_12va_Edicion_Solucionario.pdf
1. The document provides examples of converting between different units of measurement, such as miles to kilometers, gallons to liters, seconds to years, etc. Conversions involve setting up proportional relationships between units and calculating using conversion factors.
2. Examples show calculating uncertainties in measurements based on the precision of the measuring instrument. Uncertainty is estimated as a percentage error relative to the measured quantity.
3. To determine average values and uncertainties, the document uses the maximum and minimum possible values based on the precision of the original measurements. The uncertainty is taken as half the range between the maximum and minimum average values.
Dynamics Kinematics Curvilinear Motion
This document provides information about a dynamics course taught by Professor Nikolai V. Priezjev. The course will cover kinematics and dynamics using the textbook "Vector Mechanics for Engineers: Dynamics" by Beer, Johnston, Mazurek and Cornwell. Kinematics deals with the geometric aspects of motion without forces or moments. The course objectives are to derive relations between position, velocity and acceleration for various motion types using concepts like the s-t graph and rectangular components.
Vectors phy2 chp7
This chapter discusses vectors and their application to motion and forces. It covers adding and subtracting vectors, resolving vectors into components, projectile motion, and forces in two dimensions. The key topics are using vectors to describe changes in position, calculating vector components, determining the range of a projectile given an initial velocity vector, and using force vectors to solve two-dimensional equilibrium problems. Example problems demonstrate calculating vector magnitudes and components, adding velocity vectors, and analyzing vertical and horizontal motion of projectiles.
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Horizontal projectile motion involves motion in two dimensions: up-down and horizontal. This document focuses on horizontal projectile motion, where the initial velocity only has a horizontal component. It examines how the horizontal velocity does not affect the rate of falling, but must be considered along with vertical motion to determine the total velocity and range of the projectile. The range of a projectile is calculated using the formula R = (2h/g)1/2v1, where h is the initial height, g is the acceleration due to gravity, and v1 is the initial horizontal velocity.
Grade9, L11-U3Habitat loss and fragmentation
Farmland, settlements and highways have replaced much of Ontario's deciduous forest. Habitat loss and fragmentation are threats, with loss most extreme in conversion to farmland and urban development. This divides ecosystems and exposes more habitat to pollution. To protect sustainability, conservation aims to maintain large, connected areas with low external influences. Threats also impact aquatic ecosystems through activities like shoreline development, dredging, sedimentation and wetland drainage.
Grade 9, U3-L10 pesticides and biomagnification
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Grade 9-U3-L9-Invasive species
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The document discusses factors that affect population size and growth rates, including births and deaths, as well as immigration and emigration. It notes that population change equals births minus deaths plus immigration minus emigration. Density-dependent factors like competition for resources and disease can control populations. Density-independent factors like environmental conditions also impact populations. An example calculates the population change for a town based on births, deaths, immigration, and emigration to show that the population increased.
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Ecological succession describes how communities of plants and animals change over time following a disturbance of an area. It can be primary succession, which occurs in areas without previous life like after a volcanic eruption, or secondary succession, which follows a disruption but not destruction of a community like after a forest fire. Succession proceeds as hardier species first colonize an area, gradually changing the environment to allow less hardy species to establish themselves until a stable community forms, though it may take a hundred years to fully recover from severe disturbances. Aquatic and coastal ecosystems like bogs and sand dunes also undergo successional changes as vegetation grows and transforms the landscape over long periods.
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All organisms require energy, which primarily comes from sunlight through photosynthesis. During photosynthesis, producers like plants use sunlight to convert carbon dioxide and water into oxygen and energy-rich sugars. Producers and consumers then undergo cellular respiration, using the sugars and oxygen to produce energy, carbon dioxide, and water. This cycle of photosynthesis and cellular respiration allows energy from the sun to flow through ecosystems and be used by all organisms.
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Grade 11, U1C-L1, Vector Comp
- 1. Vector Components Break, or Resolve, a Vector intoBreak, or Resolve, a Vector into Two Perpendicular ComponentsTwo Perpendicular Components Nelson Reference Pages:Nelson Reference Pages: Pages 66 - 70Pages 66 - 70
- 2. Like forces, all vectors can be broken into twoLike forces, all vectors can be broken into two ⊥⊥ components.components. Example:Example: Janice walks 10.0 km [NE], then 4.0 km [W], andJanice walks 10.0 km [NE], then 4.0 km [W], and finally walks 1.9 km [N]. Determine Janice’s totalfinally walks 1.9 km [N]. Determine Janice’s total displacement.displacement. Solution:Solution: Below, the 10.0 km displacement vector is brokenBelow, the 10.0 km displacement vector is broken (or “(or “resolvedresolved”) into two”) into two ⊥⊥ components which are then addedcomponents which are then added to the other vectors.to the other vectors. ΔΔdd TotalTotal = 7.1 km [E] + 4.0 km [W] + 7.1 km [N] + 1.9 km [N]= 7.1 km [E] + 4.0 km [W] + 7.1 km [N] + 1.9 km [N] = 7.1 km [E] - 4.0 km [E] + 7.1 km [N] + 1.9 km [N]= 7.1 km [E] - 4.0 km [E] + 7.1 km [N] + 1.9 km [N] = 3.1 km [E] + 9.0 km [N]= 3.1 km [E] + 9.0 km [N] 1 0 . 0 k m 1 0 . 0 ( c o s 4 5 ) k m = 7 . 1 k m 10.0(sin45)km= 7.1km N W E
- 3. The two components mustThe two components must be added and this isbe added and this is shown in the diagram.shown in the diagram. The angle is calculated asThe angle is calculated as TanTan-1-1 (9.0/3.1) = 71(9.0/3.1) = 7100 Δd Total = 9.5 km [E 710 N] 3 .1 k m 9.0km N W E dTotal=9.5km
- 4. Practice Questions Nelson TB: Page 75 # 1, 2, 3Page 75 # 1, 2, 3 (for # 2 & 3 use components) Page 75 #7Page 75 #7 (Ensure you are comfortable adding components from 3, 4 or more vectors) Go to lesson 5 (scaled vector diagrams), of Kinematics Unit, and redo the following problem using components. “A boat heads from port…”