Download Physics PHYS 352 Mechanics II Problem Set #2

Physics PHYS 352
Mechanics II
Problem Set #2
1.
Motion in a Resisting Medium.
A particle moves in a straight line with initial velocity v0 in a medium that
exerts a resisting force proportional to the cube of the velocity. Show that the
time it takes the particle to travel a given distance is a quadratic function of the
distance.
2.
Central Forces.
A particle moves in a straight line under an attractive force which varies
inversely as the 3/2 power of the distance.
a)
b)
c)
Write down the equation of motion.
Obtain the equation connecting the velocity with the displacement if the
particle started with zero velocity from infinity.
Show that the speed acquired falling from infinity to a distance D is the
same as that acquired in falling from rest at D to D/4.
3.
Projectile Motion. (Marion 2-9)
If a projectile moves such that its distance from the point of projection is always
increasing, find the maximum angle above the horizontal with which the
particle could have been projected.
4.
Stable and Unstable Equilibrium (Marion 2-42)
A solid cube of uniform density and side of b is in
equilibrium on top of a cylinder of radius R, as shown
below. The planes of four sides are parallel to the axis
of the cylinder. The contact between the cube and
sphere is perfectly rough. Under what condition is the
equilibrium stable or not stable? (Hint: consider the
potential energy as a function of .)
b
R
5.
Conservation of Energy (Marion 2-25)
A block of mass m slides down a frictionless incline as shown below. The
block is released a height h above the bottom of the loop.
a)
b)
c)
d)
What is the force of the inclined track on the block at the bottom (point
A)?
What is the force of the track on the block at point B?
At what speed does the block leave the track?
How far away from point A does the block land on level ground? Sketch
the potential energy U(x) of the block. Indicate the total energy on the
sketch.
h
R
45
A
2
B
x