This preview shows page 1. Sign up to view the full content.
10.76.
Model:
Model the sled as a particle. Because there is no friction, the sum of the kinetic and
gravitational potential energy is conserved during motion.
Visualize:
Place the origin of the coordinate system at the center of the hemisphere. Then
0
yR
=
and, from geometry,
1
y
=
cos .
R
φ
Solve:
The energy conservation equation
11 0 0
K
UKU
+
=+
is
22
2
11
00
1
1
1
cos
2
(1 cos )
2
mv
mgy
mv
mgy
mv
mgR
mgR
v
gR
φφ
+=
+⇒
+
=⇒
=
−
(b)
If the sled is on the hill, it is moving in a circle and the
r
component of
net
F
G
has to point to the center with
magnitude
2
net
/.
Fm
v
R
=
Eventually the speed gets so large that there is not enough force to keep it in a circular
trajectory, and that is the point where it flies off the hill. Consider the sled at angle
.
Establish an
r
axis
pointing toward the center of the circle, as we usually do for circular motion problems. Newton’s second law
This is the end of the preview. Sign up
to
access the rest of the document.
 Fall '09
 geller
 Energy, Friction, Potential Energy

Click to edit the document details