Part 4: Solve for a in terms of m, g, 0, and μk. YOU WILL REQUIRE THE EQUATION EDITOR FOR THE GREEK SYMBOLS AND SUBSCRIPTS. Factorize as much as possible. a = g(sine-μcose)

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Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
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Part 4: Solve for a in terms of m, g, 0, and μk
YOU WILL REQUIRE THE EQUATION EDITOR FOR THE GREEK SYMBOLS AND SUBSCRIPTS.
Factorize as much as possible.
a = g(sine-μcos) √
Part 5: Does a depend on m?
no
Cross-Check: Do the dimensions of your answer match that for acceleration?
Discussion: Consider this problem with the x-axis parallel to the ground and y-axis perpendicular to
it; the normal force N and force of friction f have both horizontal and vertical components. The same
is true with the acceleration. What happens if the coordinate system is rotated?
Since coordinate axes are arbitrary, choose the one that simplifies the problem the most. For
inclines, this means that the x-axis is parallel to the incline, while the y-axis is perpendicular to it.
Under this rotated coordinate system, which forces act purely in one direction? Which force has two
non-zero components? How can these be found by vector decomposition? Pay particular attention to
the angle of the incline and how that will affect the decomposition.
Transcribed Image Text:Part 4: Solve for a in terms of m, g, 0, and μk YOU WILL REQUIRE THE EQUATION EDITOR FOR THE GREEK SYMBOLS AND SUBSCRIPTS. Factorize as much as possible. a = g(sine-μcos) √ Part 5: Does a depend on m? no Cross-Check: Do the dimensions of your answer match that for acceleration? Discussion: Consider this problem with the x-axis parallel to the ground and y-axis perpendicular to it; the normal force N and force of friction f have both horizontal and vertical components. The same is true with the acceleration. What happens if the coordinate system is rotated? Since coordinate axes are arbitrary, choose the one that simplifies the problem the most. For inclines, this means that the x-axis is parallel to the incline, while the y-axis is perpendicular to it. Under this rotated coordinate system, which forces act purely in one direction? Which force has two non-zero components? How can these be found by vector decomposition? Pay particular attention to the angle of the incline and how that will affect the decomposition.
[Fx
=
N-Wy
Wx-for = ma (1)
1. Drag and drop the heads and tails of the vectors to construct the free-body diagram.
2. Note that angles do not need to be exact and magnitudes are not considered.
=0 (2)
Y
1. An object of mass m is sliding down an incline that makes an angle with the horizontal with an
acceleration a. The coefficient of kinetic friction between the block and the incline is Mk.
Part 1: Set-up Newton's Second Law Equations
Using the diagram in Part 1, set-up Newton's Second Law along the x and y axes in terms of the
components of the weight wx
and Wy'
the normal force N and the friction force f.
What is the acceleration along the x direction? What is the acceleration along the y-direction?
REMEMBER TO USE THE SUBSCRIPTS FOR W.
REMEMBER TO USE THE CORRECT SIGNS ACCORDING TO THE COORDINATE SYSTEM IN PART 1.
X
f; 153.43
wy; 243.43°
Wx; 333 43°
ΣΕ, -
Part 2: In terms or m, g and 0, the magnitude of the x and y components of weight w are given by:
(i) Wx=
Transcribed Image Text:[Fx = N-Wy Wx-for = ma (1) 1. Drag and drop the heads and tails of the vectors to construct the free-body diagram. 2. Note that angles do not need to be exact and magnitudes are not considered. =0 (2) Y 1. An object of mass m is sliding down an incline that makes an angle with the horizontal with an acceleration a. The coefficient of kinetic friction between the block and the incline is Mk. Part 1: Set-up Newton's Second Law Equations Using the diagram in Part 1, set-up Newton's Second Law along the x and y axes in terms of the components of the weight wx and Wy' the normal force N and the friction force f. What is the acceleration along the x direction? What is the acceleration along the y-direction? REMEMBER TO USE THE SUBSCRIPTS FOR W. REMEMBER TO USE THE CORRECT SIGNS ACCORDING TO THE COORDINATE SYSTEM IN PART 1. X f; 153.43 wy; 243.43° Wx; 333 43° ΣΕ, - Part 2: In terms or m, g and 0, the magnitude of the x and y components of weight w are given by: (i) Wx=
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