1. Two objects with masses, m1 and m2, have the same kinetic energy and are
both moving to the right. The same constant force 𝐹
is applied to the left to
both masses. If m1 = 4m2, what is the ratio of the stopping distance of m1 to
that of m2? Derive your solution.
2. A man pushes an 80-N crate a distance of 5.0 m upward along a frictionless
slope that makes an angle of 30 with the horizontal. His force is parallel to
the slope. If the speed of the crate decreases at a rate of 1.5 m/s2, then what is
the work done by the man? Derive your solution
3. A man pushes an 80-N crate a distance of 5.0 m upward along a frictionless
slope that makes an angle of 30 with the horizontal. The force he exerts is
parallel to the slope. If the speed of the crate is constant, then what is the work
done by the man? Derive your solution
4. A particle starts from rest at time t = 0 and moves along the x axis. If the net
force on it is proportional to t, its kinetic energy is proportional to:
A) t
B) t2
C) t4
D) 1/t2
E) none of the above
Derive your solution.
5. When a certain rubber band is stretched a distance x, it exerts a restoring force
of magnitude F = Ax, where A is a constant. What is the work done by a
person in stretching this rubber band from x = 0 to x = L? Derive your
solution.
6. A 50-N force is the only force on a 2-kg crate that starts from rest. At the
instant the crate has gone 2 m what is the rate at which the force is doing
work? Derive your solution
7. A 0.20-kg particle moves along the x axis under the influence of a
conservative force. The potential energy is given by
U(x) = (8.0 J/m2)x2 + (2.0 J/m4)x4,
where x is in coordinate of the particle. If the particle has a speed of 5.0 m/s when it is
at x = 1.0 m, what is the speed when it is at the origin? Derive your solution.
