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Worksheet H: Friction and dynamics of circular motion.
1
. A box of mass
m
= 1.2 kg sits on a plane whose inclination
θ
can be
changed. The
coefficients of friction between the box and the plane are
μ
s
= 0.40 and
μ
k
= 0.20.
a.
Draw the free body diagram of the box.
b.
What is the magnitude of the friction force when the angle is 5º? (The box does not
move at this angle, as you will prove in part c)
Newton’s second law along the incline:
()
2
sin
0
sin
1.2 kg
9.8 m/s
sin5
1.0 N
s
s
mg
f
fm
g
−=
=
=°
=
c.
Find the critical angle
c
for which the box starts to slide.
This happens when static friction achieves its maximum value.
max
max
sin
0
s
ss
mg
f
with f
N
µ
=
Newton’s 2
nd
law in the direction perpendicular to the incline:
cos
0
cos
Nm
g
g
=
Thus,
sin
0
sin
cos
0
tan
s
mg
N
mg
mg
µθ
→
−
=
↓
=
1
tan
s
θµ
−
↓
=
1
tan (0.40)
22
−
=
m
mg
N
f
s
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d.
What is the acceleration of the box at this angle?
Right when the box begins sliding, the friction becomes kinetic. Newtons’ second law
then reads:
()
() ()
22
sin
with
cos
cos
0
cos
sin
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This homework help was uploaded on 03/27/2008 for the course PHYS 221 taught by Professor Herrerasiklody during the Fall '08 term at Iowa State.
 Fall '08
 HerreraSiklody
 Circular Motion, Friction, Mass, Work

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