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Summer 2008 – third midterm
 two pages/sides
Attempt in any order
ALWAYS GIVE YOUR REASONING
(1)
(a)
what is the momentary velocity (speed and direction) of the piece of
rubber on the very front
of a bicycle wheel when the bicycle is travelling at
10m/s?
the bottom of the wheel is momentarily stationary, and the wheel rotates about it.
the distance from the bottom of the wheel to the front is
times the distance to
the hub, which is travelling at 10. so the answer is
10
the same answer can be obtained by adding the linear motion forward to the
rotation around the axle hub.
(b)
a solid iron sphere of mass 1kg rolls down a 30 degree slope, for a
distance of 2 meters.
find its speed as it reaches the bottom.
The moment of
inertia of a sphere is
I
=
2
5
MR
2
height lost = 1 meter, so p.e. lost = 1(1g) =10 approx.
this appears as linear +
rotational kinetic energy. with M the total mass,
mgh
≈
10
=
1
2
mv
2
+
1
2
I
ω
2
=
1
2
mv
2
+
1
2
2
5
mR
2
⎛
⎝
⎜
⎞
⎠
⎟
2
=
7
10
mv
2
as v
=
mR
with m
=
1,
v
=
10
7
by coincidence (g~9.8) this is also nearly
14
(2)
(a)
can a ladder lean against a wall if there is a high coefficient of friction
at the wall, but the floor itself is perfectly smooth? say why or why not.
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This note was uploaded on 10/17/2011 for the course PHYSICS 7A taught by Professor Lanzara during the Spring '08 term at University of California, Berkeley.
 Spring '08
 Lanzara
 Physics

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