Download Physics 6B Practice midterm 1

Physics 6B Practice midterm
1.
A mass on a spring oscillates with a period T. If both the mass and the force
constant of the spring are doubled, what will the new period be?
2.
The motion of a piston in an automobile engine is approximately simple
harmonic. If the stroke (twice the amplitude) of an engine is 0.100 meters and
the engine runs at 3500 rpm, A) compute the acceleration at the endpoint of its
stroke. B) If the piston has mass 0.450 kg, what net force must be exerted on
it at this point? C) What are the speed and kinetic energy of the piston at the
midpoint of its stroke?
3.
A certain simple pendulum has a period on Earth of 1.60 seconds. What is its
period on the surface of Mars, where the acceleration due to gravity is 3.71
meters per second squared?
4.
The equation describing a transverse wave on a string is:


y( x, t )  (1.50mm) sin (157s 1 )t  (41.9m 1 ) x
a) Find the wavelength, frequency and amplitude of this wave.
b) Find the propagation velocity of the wave.
c) The transverse displacement of a point on the string when t=0.100s and
x=0.360m.
5.
A wind chime consists of an open tube 30cm long. Find the frequency and
wavelength of the fundamental mode, and the first two overtones.
6.
Green light has a wavelength of 500nm. Yellow light has a wavelength of
550nm. How fast would I have to drive toward a traffic light in order to make
a yellow light appear green? (You can use c for the speed of light.)
7.
An ore sample weighs 17.5N in air. When the sample is suspended by a light
cord and totally immersed in water, the tension in the cord is 11.2N. Find the
total volume and density of the sample.
8.
You are designing a hydraulic lift for an automobile garage. It will consist of
two oil filled cylindrical pipes of different diameters. A worker pushes down
on a piston at one end, raising the car on a platform on the other. To handle a
full range of jobs, you must be able to lift cars up to 3000kg, plus the 500kg
platform on which they are parked. To avoid injury to your workers, the
maximum amount of force a worker should need to exert is 100N. The
diameter of the piston the worker pushes down on is 25cm. A) What should
be the diameter of the pipe under the platform? B) If the worker pushes down
with a stroke 50cm long, by how much will he raise the car at the other end?
9.
Air streams horizontally past a small airplane’s wings such that the speed is
70.0 m/s over the top surface and 60.0 m/s over the bottom surface. If the
plane has a mass of 1340 kg and a wing area of 16.2 square meters, what is
the net vertical force (including gravity) on the airplane? The density of air is
1.20 kg/m^2.
10.
Water is flowing in a pipe with varying cross-sectional area, and at all points
the water completely fills the pipe. At point 1, the cross-sectional area of the
pipe is 0.070 square meters and the magnitude of the fluid velocity is 3.50m/s.
What is the fluid speed at points in the pipe where the cross-sectional area is
A) 0.105 m^2, B)0.047 m^2?
11.
Two positively charged
masses hang from the ceiling
as in the figure. The masses
have equal charge and mass.
Each mass is 100g, the
length of each string is
40cm, and the masses are in
equilibrium when they hang
at a 30 degree angle from the
vertical.
a) Find the charge on each mass
b) Find the tension in each string
12.
Consider
the
following
arrangem
ent of
charges.
A +2
microcoul
omb
charge
lies at the
origin of the x-y plane. A -3 microcoulomb charge lies at the coordinates
(3,4).
a) What is the magnitude and direction of the force exerted on the positive
charge by the negative charge?
b) What is the magnitude and direction of the electric field at point P0,
located at (3,0)?
c) What is the electric potential at point P0, assuming the electric potential
very far away is zero?
d) How much work would it take to move a charge of +1 microcoulomb from
very far away to point P0?
13.
An electron
passes
through a
region with a
downward
oriented
electric field
with an
initial
velocity of v0
to the right.
If the
magnitude of
the electric
field is E, and the length of the region with the electric field is l, find:
a) The direction the electron is deflected.
b) The distance the electron is deflected.
c) The energy the electron gains while passing through the electric field.
d) The magnitude and direction of the electron’s final velocity.
Note: use m for the mass of the electron, q for the charge
on the electron, E for the strength of the electric field, l for
the length of the region, and v0 for the electron’s initial
velocity.