CM HW10: Potential Energy and Conservative Forces
PE HW1. A particle is constrained to move in one dimension along the x axis and is acted
upon by a force given by F(x) = −k/x3 i where k is a constant with units appropriate to
the SI system. Find the potential energy function U(x), if U is arbitrarily defined to be
zero at x = 2.0 m so that U(2.0 m) = 0.
Ans. U(x) = −k/2x2 + k/8
PE HW 2. If U = 3x2 + 2xy + 4y2z, what is the force F?
PE HW 3. A 75-gram Frisbee is thrown from a point 1.1-meter above the ground with a
speed of 12 m/s. When it has reached a height of 2.1 m its speed is 10.5 m/s. What was
the reduction in Emechanical of the Frisbee−Earth system because of air drag?
0.535 J
PE HW 4. A 3.5 kg block is accelerated from rest by a compressed spring of spring
constant 640 N/m over a frictionless surface. The block leaves the spring at the spring’s
relaxed length and then travels over a wooden horizontal floor with a coefficient of
kinetic friction µk, = 0.25. The frictional force stops the block in distance d = 7.8 meters.
a. What is the increase in the thermal energy of the block−floor system?
67 J
b. The maximum kinetic energy of the block?
c. The original compression distance of the spring?
46 cm
Potential Energy
PE HW 5. The potential energy of the two atoms in a diatomic (two-atom) molecule can
be written
a
b
U ( r )   6  12 , where r is the distance between the two atoms and a and b are
r
r
positive constants.
a. At what values of r is U(r) a minimum? A maximum?
r = (2b/a)1/6 (min), r = 0 (max)
b. At what values of r is U(r) = 0?
c. Sketch U(r) as a function of r from r = 0 to r at a value large enough for all the features
in (a) and (b) to show.
d. Let F be the force one atom exerts on the other. Determine F as a function of r.
e. For what value of r is F = 0 (the equilibrium position)?
f. The binding energy of a two-particle system is defined as the energy required to
separate the two particles from their state of lowest energy to r =  . Determine the
binding energy for this diatomic molecule.
a2/4b