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Destrio
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1. A block slides along a track with elevated ends. The flat part has length L = 0.2m, and the object is released from a height of 0.1m. The curved portion of the track is frictionless, but the flat part has uk = 0.15 . where does the object finally come to rest?
Etotal = Ui + Ki = Uf + Kf + work done by friction
mgy + 0 = mgy' + 0 + ukFn
mg(.1) = mgy' + (.15)mg
.1 = y' + .15
y' = -.05
this doesn't seem right, will I have to do multiple calculations of conservation of energy, since there is a section with friction and a section without. Do I have to consider angular momentum since its sliding down a slope at first?
2. Several planets possesses nearly circular surrounding rings, perhaps composed of material that failed to form a satellite. In addition, many galaxies contain ring-like structures. Consider a homogeneous ring of mass M and radius R.
a) Find an expression for the gravitational force exerted by the ring on a particle of mass m located a distance x from the center of the ring along its axis.
b) Suppose that the particle falls from rest as a result of the attraction of the ring of matter. Find an expression for the speed with which is passes through the center of the ring.
since we are dealing with a ring, should I use inertia of the ring instead of mass?
F = -GMm/r^2
I of ring = mr^2
F = -G(MR^2)m/x^2
W = Fd = -G(MR^2)m/x
Etotal = U - K
-G(MR^2)m/x = (1/2)mv^2
v = -sqrt(2G(MR^2)/x)
thanks
Etotal = Ui + Ki = Uf + Kf + work done by friction
mgy + 0 = mgy' + 0 + ukFn
mg(.1) = mgy' + (.15)mg
.1 = y' + .15
y' = -.05
this doesn't seem right, will I have to do multiple calculations of conservation of energy, since there is a section with friction and a section without. Do I have to consider angular momentum since its sliding down a slope at first?
2. Several planets possesses nearly circular surrounding rings, perhaps composed of material that failed to form a satellite. In addition, many galaxies contain ring-like structures. Consider a homogeneous ring of mass M and radius R.
a) Find an expression for the gravitational force exerted by the ring on a particle of mass m located a distance x from the center of the ring along its axis.
b) Suppose that the particle falls from rest as a result of the attraction of the ring of matter. Find an expression for the speed with which is passes through the center of the ring.
since we are dealing with a ring, should I use inertia of the ring instead of mass?
F = -GMm/r^2
I of ring = mr^2
F = -G(MR^2)m/x^2
W = Fd = -G(MR^2)m/x
Etotal = U - K
-G(MR^2)m/x = (1/2)mv^2
v = -sqrt(2G(MR^2)/x)
thanks