11.5. SHM Problem Set http://www.ck12.org
- A pendulum with a string of 0.750 m and a mass of 0.250 kg is given an initial amplitude by pulling it upward
until it is at a height of 0.100 m more than when it hung vertically. This is pointP. When it is allowed to
swing it passes through pointQat a height of.050 m above the equilibrium position, the latter of which is
called pointR.
a. Draw a diagram of this pendulum motion and at pointsP,Q,andRdraw velocity and acceleration vectors.
If they are zero, state that also.
b. At pointPcalculate the potential energy.
c. At pointRcalculate the speed of the mass.
d. At pointQcalculate the speed of the mass.
e. If the string were to break at pointsP,Q,andRdraw the path the mass would take until it hits ground for
each point.
f. Find the tension in the string at pointP.
g. Find the tension in the string at pointR.
h. Find the period of harmonic motion.
Answers to Selected Problems
- a. Buoyant force and gravity b.T=6 s,f= 1 /6 Hz
- a. 9. 8 × 105 N/m b. 0.5 mm c. 22 Hz, no,
- 2 × 103 N/m
- a. 110 N/m d.v(t) = ( 25 )cos(83t)
5..
6.. - a. 0.0038 s b. 0.0038 s
8..
9.. - 4 times
- 0.04 m
- a. 16 Hz b. 16 complete cycles but 32 times up and down, 315 complete cycles but 630 times up and down c.
0 .063 s - a. 24.8 J,165 N,413 m/s^2 b. 11.1m/s, 0 ,0 c. 6.2 J, 18 .6 J, 9 .49 m/s, 82 .5 N,206 m/s^2 d..169 sec, 5 .9 Hz
- b..245 J c. 1.40m/s d. 1.00 m/s f. 2.82 N g. 3.10 N