8 . B —Work is force times parallel displacement. The force acting here is the force of friction, and the
displacement is 2.0 m parallel to the force of friction. The friction force is equal to the coefficient of
friction (0.10) times the normal force. The normal force in this case is equal to the block’s weight of 5
N (because no other vertical forces act). Combining all these equations, the work done is (2.0 m) (0.1)
(5 N) = 1.0 J.9 . D —Look at the total energy of the block, which is equal to the potential energy plus the kinetic
energy. Initially, the total energy was 2200 J. At the end, the total energy was 1000 J. What happened
to the extra 1200 J? Because friction was the only external force acting, friction must have done 1200 J
of work.10 . B —Impulse is equal to the change in an object’s momentum. Ball 1 changes its momentum from
something to zero. But ball 2 changes its momentum from something to zero, and then to something in
the other direction. That’s a bigger momentum change than if the ball had just stopped. (If we had been
asked to find the force on the ball, then we’d need the time of collision, but the impulse can be found
without reference to force or time.)
11 . B —Momentum is a vector , meaning direction is important. Call the rightward direction positive.
Ball A has +5 kg·m/s of momentum; ball B has −2 kg·m/s of momentum. Adding these together, we get
a total of +3 kg·m/s. This answer is equivalent to 3 N·s to the right. (The units kg·m/s and N·s are
identical.)
12 . D —The law of conservation of momentum requires that all objects involved in a collision be taken
into account. An object can lose momentum, as long as that momentum is picked up by some other
object.
13 . C —“Uniform” circular motion means that an object’s speed must be constant. But velocity includes
direction, and the direction of travel changes continually. The velocity of the object is always along
the circle, but the acceleration is centripetal; i.e., center-seeking. The direction toward the center of
the circle is perpendicular to the path of the object everywhere.
14 . A —Period is equal to 1/frequency, regardless of the amplitude of harmonic motion.
15 . E —The maximum displacement is the amplitude. Energy of a spring is ½kx 2 . So, at x = A , the
energy is ½kA 2 .
16 . E —An object’s rotational inertia can be thought of as a rotational equivalent of mass; rotational
inertia, like mass, is a property of an object and the axis about which it rotates. Rotational inertia does
not depend on the speed of rotation. Angular momentum, equal to rotational inertia times angular
velocity, does depend on the speed of rotation. Because the rotation rate doubled, so did angular
momentum.
17 . C —In an orbit, gravity provides a centripetal force. So, GmM/r 2 = mv 2 /r . Solving for v ,where M is the mass of the moon. If the speed gets bigger, then the radius of orbit (in the denominator)
must get smaller to compensate.