CHAPTER 4 The Laws of Motion

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Example 2 Sliding Box Problem (Pulled at an
Angle) A dead cat with a mass of 7.5kg is pulled
off the road by a passing motorist. The motorist
pulls the cat by its tail which is at an angle of
37 to the horizontal. A force of 25N is applied.
The force of friction opposing motion is 18N. How
fast does the cat accelerate?
25N
59N
18N
74N
m 7.5kg Fa 25N
Fa,x Fa cos37 20.N Fa,y Fa sin 37 15N
FN Fa,y Fg (up forces equal down forces) Fg
mg 74N FN 74N 15N FN 59N
Ff 18N FNet,x Fa,x Ff ma 20.N 18N
7.5kg a
a .27m/s2
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Forces on an Inclined Plane
Fg is always directed straight down. We then
choose a Frame of Reference where the x-axis is
parallel to the incline and the y-axis
perpendicular to the incline. Fg,x Fg
sin? Fg,y Fg cos? FN Fg,y (in opposite
direction) Fa and Ff will be along our new x-axis
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Example Problem (Inclined Plane) A 25.0kg box is
being pulled up a 30 incline with a force of
245N. The coefficient of kinetic friction between
the box and the surface is .567. Calculate the
acceleration of the box.
Draw a Sketch
Determine the Magnitude of the forces in x and y
directions
25.0 kg
m Fg Fg,x Fg,y
245N (to right along x-axis)
Fa FN Ff
mg 25.0kg 9.80m/s2 245N (down)
Fg cos? 212N (up along y-axis)
Fg sin? 245N sin30 123N (to left along
x-axis)
?kFN .567 212N 120N (to left
along x-axis)
Fg cos? 245N cos30 212N (down along
y-axis)
Label Forces on your sketch Solve the Problem
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Solve the Problem Fa Ff Fg,x
245N 120.N 123N 2N FNet,x max 2N
25.0kg ax
FNet,x
ax .08 m/s2
NOTE The box may be moving up the incline at any
velocity. However, at the specified conditions it
will be accelerating.