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PHYS 116
Name___________________________________
Practice Exam 1 Problem 1
Spring 2009
Show all work to get full credit. Points per problem given in [ ].
Consider an object of mass m hanging on a vertical spring of force constant k = 1800
N/m. At time t = 0, the object is at rest and has been pulled down a maximum
displacement of –2.50 cm from its equilibrium position. Once released from rest, it
oscillates with a frequency of 5.50 Hz.
[1] (a) Find m.
[2] (b) Find the amount the spring is stretched from its relaxed length when the object is
in equilibrium.
[3] (c) Sketch graphs of position x, velocity v, and acceleration a as a function of time t
over one full period of oscillation using the axes given below. Note that I should
be able to extract quantitative as well as qualitative information from your sketch
in order for you to receive full credit. Show any calculations that you made to
help you decide how to draw your graphs on the back of this page.
a (cm/s2)
v (cm/s)
x (cm)
t (s)
t (s)
[4] (d) Describe the object’s velocity when its position corresponds to a maximum
displacement from equilibrium. Do the same for its acceleration.
t (s)
PHYS 116
Name_____________________________________
Practice Exam 1 Problem 2
Spring 2009
Show all work to get full credit. Points per problem given in [ ].
Useful information:
g = 9.8 m/s 2
A 12-kg object hangs in equilibrium from a string
of total length L = 5.0 m and linear mass density
μ = 0.0010 kg/m. The string is wrapped around
two light, frictionless pulleys that are separated by a
a distance d = 2.0 m (see left half of figure).
[3] (a) Determine the tension in the string.
[3] (b) At what frequency must the string between the pulleys vibrate in order to form the
standing-wave pattern shown in the right half of the figure?
[2] (c) At what frequency must the string between the pulleys vibrate in order to form a
standing-wave pattern with a single antinode?
[2] (d) In mechanics (studied in PHYS 115), massless strings are often assumed. Why is
this not a good assumption when discussing waves on strings?
PHYS 116
Name_____________________________________
Practice Exam 1 Problem 3
Spring 2009
Show all work to get full credit. Points per problem given in [ ].
Useful information: vsound = 340 m/s
A car is approaching a reflecting wall. A stationary observer behind the car hears a
sound of frequency 745 Hz directly from the car horn and a sound of frequency 863 Hz
reflecting from the wall.
[4] (a) How fast is the car traveling?
[2] (b) What is the frequency of the car horn?
[2] (c) What frequency does the car driver hear reflected from the wall?
[2] (d) A blowing whistle is attached to the roof of a car that moves around a circular
race track. Assuming you’re standing near the outside of the track, explain the
nature of the sound (frequency and intensity) you hear as the whistle comes by
each time.
PHYS 116
Name_____________________________________
Practice Exam 1 Problem 4
Spring 2009
Show all work to get full credit. Points per problem given in [ ].
Two identical point charges +q are located on the y–axis at y = +a and y = –a.
[3] (a) What is the electric field along the x–axis at x = b?
[2] (b) Sketch representative electric field lines in the vicinity of the two charges using
y
the diagram below.
q
a
x
a
q
A circular ring of charge of radius a has a total positive charge Q distributed uniformly
around it. The ring is in the x = 0 plane with its center at the origin.
[3] (c) What is the electric field along the x–axis at x = b due to the ring of charge?
(Hint: Consider the charge Q to consist of many pairs of identical point charges
positioned at the ends of diameters of the ring, and consider again your answer to
part (a) above.)
[2] (d) Sketch representative electric field lines in the y–z plane near the ring using the
diagram below.
y
z
x