Assignment 4
Reading
: Dynamics 2
Key concepts
: Radial forces, effective gravity.
1.
A block of mass
m
slides at constant speed down an incline of angle
θ
.
a.
What is the coefficient of kinetic friction
μ
k
?
Ans
:
μ
k
=
tan
θ
.
b.
The same block is sent up the incline, starting with speed
v
0
. How far up
the incline will it slide before coming momentarily to rest?
Ans
:
v
0
2
2
g
1
sin
θ
+
μ
k
cos
θ
.
c.
Will it slide back down by itself? Justify your answer.
2.
Questions about a car rounding a curve of radius 216 m. Use
g
=
10 m/s
2
and
ignore air effects.
a.
Suppose the curve is on level ground. How fast can a car go around it if
μ
s
between tires and road is 0.6?
Ans
:
36 m/s
.
b.
Suppose the curve is banked so a car at this speed does not need friction to
round the curve. What is the banking angle
θ
?
Ans
:
tan
θ
=
0.6
.
c.
Now suppose there is rain on the banked curve, which reduces
μ
s
to 0.3.
What is the minimum speed a car must maintain on the curve to avoid
sliding down the bank?
Ans
:
23.4 m/s
.
3.
A bucket is sliding to the right across a floor, and the
level of the water in the bucket makes the angle
shown with the horizontal.
a.
Is the bucket speeding up or slowing down?
b.
What is the magnitude of its acceleration, in
terms of
g
and
θ
? [What angle does the water surface make with
g
eff
?]
Ans
:
a
=
g
tan
θ
.

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