Mechanics 2: Linear and Rotational Dynamics - 3D Math Primer for Graphics and Game Development - page 641

6. (a) A weight with mass m is hung from a spring with a stiffness of k,
causing the spring to increase in length by a distance x 0 . What is the
formula that relates m, x 0 , and k?
(b) A 5.00 kg object is suspended from a spring, causing the spring to
increase in length by 10.0 cm. What is the spring constant k? (Make
sure to include the proper units.)
(c) A different object is hung from the same spring, this time causing the
spring to lengthen by 17.0 cm. What is the mass of this other object?
(d) Later, in a different environment, a 1.00 kg weight is hung from this
same spring, this time causing an increase in length of 8.0 cm. What
can you say about this environment that is different from the original
environment? What are some possible explanations for these differ-
ences?
7. A horizontal spring with stiffness 1.00 ×10 2 N/m is fixed at one end, and
a 5.00 kg mass is connected on the other end, such that the mass slides
back and forth on a frictionless surface. The spring is extended from its
rest position by a distance of 14.7 cm.
(a) What is the frequency of the oscillation?
(b) What is the amplitude of the oscillation?
(c) What is the speed of the mass as it crosses the rest position?
8. A man weighing 75.0 kg is standing at one end of a train car. The car
weighs 1.00 × 10 3 kg, is 20.0 m long, and is from the future, where they
have invented a special type of wheel that rolls over the tracks with zero
friction. Use a coordinate space where the forward direction is +x. The
man walks from the back end of the car to the front end at a rate of
1.25 m/s.
(a) What are velocities of the man and the car, relative to Earth, during
the man's walk?
(b) When the man reaches the end of the car, how far have the man and
the car moved, in world coordinates?
(c) What if, rather than walking at a constant velocity, the man builds
up as much speed as he can and then comes to an abrupt stop at
the end of the car. What would change about the motion of the car?
What about the final positions?
The experiment is repeated (the man walks with a constant velocity), only
this time the car and man have an initial velocity of +5.00 m/s.
(d) What are velocities of the man and the car, relative to Earth, during
the man's walk?
(e) At the moment the man reaches the end of the car, how far have the
man and the car been displaced relative to Earth?