AP Physics First Semester Exam Review
1. A 0.50 kg cart moves on a straight horizontal track. The graph of velocity vx versus time t for
the cart is given below.
(a) Indicate every time t for which the cart is at rest.
(b) Indicate every time interval for which the speed (magnitude of velocity) of the cart is
increasing.
(c) Determine the horizontal position x of the cart at t = 9.0 s if the cart is located at x = 2.0 m at
t =0.
(d) On the axes below, sketch the acceleration a versus time t graph for the motion of the cart
from t = 0 to t = 25 s
(e) From t = 25 s until the cart reaches the end of the track, the cart continues with constant
horizontal velocity. The cart leaves the end of the track and hits the floor, which is 0.40 m below
the track. Neglecting air resistance, determine each of the following.
i. The time from when the cart leaves the track until it first hits the floor
ii. The horizontal distance from the end of the track to the point at which the cart first hits
the floor.
iii. The kinetic energy of the cart immediately before it hits the floor.
2.
Blocks 1 and 2 of masses m1 and m2 respectively, are connected by a light string, as shown
above. These blocks are further connected to a block of mass M by another light string that
passes over a pulley of negligible mass and friction. Blocks 1 and 2 move with a constant
velocity v down the inclined plane, which makes an angle ϴ with the horizontal. The kinetic
frictional force on block 1 is f and that on block 2 is 2f.
(a) On the figure below, draw and label all the forces on block m1.
Express your answers to each of the following in terms of m1, m2, g, ϴ, and f
(b) Determine the coefficient of kinetic friction between the inclined plane and block 1.
(c) Determine the value of the suspended mass M that allows blocks 1 and 2 to move with
constant velocity down the plane.
(d) The string between blocks 1 and 2 is now cut. Determine the acceleration of block 1 while it
is on the inclined plane.
3.
Block A of mass 2.0 kg and Block B of mass 8.0 kg are connected as shown above by a spring of
spring constant 80 N/m and negligible mass. The system is being pulled to the right across a
horizontal frictionless surface by a horizontal force of 4.0 N, as shown, with both blocks
experiencing equal constant acceleration.
(a) Calculate the force that the spring exerts on the 2.0 kg block.
(b) Calculate the extension of the spring
The system is now pulled to the left, as shown below, with both blocks again experiencing equal
constant acceleration.
(c) Is the magnitude of the acceleration greater than, less than, or the same as before?
_______ Greater
_______Less
______The same
Justify your answer
(d) Is the amount the spring has stretched greater than, less than, or the same as before?
________Greater
Justify your answer
_______Less
_______The same
4.
The concave mirror shown above has a focal length of 20 cm. An object 3 cm high is placed 15
cm in front of the mirror.
(a) Using at least two principal rays, locate the image on the diagram above.
(b) Is the image real or virtual? Justify your answer.
(c) Calculate the distance of the image from the mirror
(d) Calculate the height of the image
5. A thin converging lens of focal length 10 cm is used as a simple magnifier to examine an
object A that is held 6 cm from the lens.
(a) On the figure below, draw a ray diagram showing the position and size of the image formed.
(b) State whether the image is real or virtual. Explain your reasoning.
(c) Calculate the distance of the image from the center of the lens
(d) Calculate the ratio of the image size to the object size.
(e) The object A is now moved to the right from x = 6 cm to a position of x = 20 cm, as shown
above. Locate the image using at least two principle rays. Describe the image size and
orientation when the object is at x = 20 cm
6.
The triangular prism shown in Figure I above has index of refraction 1.5 and angles of 37o, 53o,
and 90o. The shortest side of the prism is set on a horizontal table. A beam of light, initially
horizontal, is incident on the prism from the left.
(a) On Figure I above, sketch the path of the beam as it passes through and emerges from the
prism.
(b) Determine the angle with respect to the horizontal (angle of deviation) of the beam as it
emerges from the prism.
(c) The prism is replaced by a new prism, which is set in the same position. The beam
experiences total internal reflection at the right surface of this prism. What is the minimum
possible index of refraction of this prism?
The new prism having the index of refraction found in part (c) is then completely submerged in
water (index of refraction = 1.33) as shown in Figure II below. A horizontal beam of light is
again incident from the left.
(d) On Figure II, sketch the path of the beam as it passes through and emerges from the prism.
(e) Determine the angle with respect to the horizontal (angle of deviation) of the beam as it
emerges from the prism.
7.
A microwave source is placed behind two identical slits, as represented in the diagram above.
The slit centers are separted by a distance of 0.20 m, and the slit widths are small compared to
the slit separation but not negligible. The microwave wavelength is 2.4 X 10-2 m. The resulting
interference pattern is centerd on a screen 0.60 m wide, located 2.5 m from the slits.
(a) Calculate the frequency of the microwave radiation.
(b) On the graph below, where the x-axis represents the distance along the screen and x = 0
represents the center of the pattern, sketch the intensity of the interference pattern expected for
that arrangement.
(c) Consider points on the screen located at x = 0.00m, x = 0.15, and x = 0.30 m. Rank the
intensity at those points from the highest to lowest, with number 1 corresponding to the highest
intensity. If two points have equal intensity, give thme the same ranking.
_______ x = 0.00 m
Justify your ranking
_______ x = 0.15 m
________ x = 0.30 m
(d) Suppose the microwave wavelength is decreased by a factor of three, to 0.80 X 10-2 m.
Sketch the resulting interference pattern below.
(e) Suppose the material separating the two slits is removed so that there is now one slit
approximately 0.20 m in width. The wavelength is held at 0.80 X 10-2 m. Sketch the resulting
diffraction pattern below.
8.
Two small speakers S are positioned a distance of 0.75 m from each other, as shown in the
diagram above. The two speakers are each emitting a constant 2500 Hz tone, and the sound
waves from the speakers are in phase with each other. A student with is standing at point P,
which is a distance of 5.0 m from the midpoint between the speakers, and hears a maximum as
expected. Assume that reflections from nearby objects are negligible. Use 343 m/s for the speed
of sound.
(a) Calculate the wavelength of these sound waves
(b) The student moves a distance Y to point Q and notices that the sound intensity has decreased
to a minimum. Calculate the shortest distance the student could have moved to hear this
minimum.
(c) Identify another location on the line that passes through P and Q where the student could
stand in order to observe a minimum. Justify your answer.
(d)
i. How would your answer to (b) change if the two speakers were moved closer together? Justify
your answer
ii. How would your answer to (b) change if the frequency emitted by the two speakers was
increased? Justify your answer.
9. To demonstrate standing waves, one end of a string is attached to a tuning fork with frequency
120 Hz. The other end of the string passes over a pulley and is connected to a suspended mass M
as shown in the figure above. The value of M is such that the standing wave pattern has four
“loops”. The length of the string from the tuning fork to the point where the string touches the
top of the pulley is 1.20 m.
(a) Determine the wavelength of the standing wave.
(b) Determine the speed of the transverse waves along the string.
(c) The speed of waves along the string increases with increasing tension in the string. Indicate
whether the value of M should be increased or decreased in order to double the number of loops
in the standing wave pattern. Justify your answer.
(d) If a point on the string at an antinode moves a total vertical distance of 4 cm during one
complete cycle, what is the amplitude of the standing wave?
10. A hollow tube of length l, open at both ends as shown right, is held in midair. A
tuning fork with a frequency fo vibrates at one end of the tube and causes the air in the
tube to vibrate at its fundamental frequency. Express your answer in terms of l and fo.
(a) Determine the wavelength of the sound.
(b) Determine the speed of sound in the air inside the tube.
(c) Determine the next higher frequency at which this air column would resonate.
The tube is submerged in a large, graduated cylinder filled with water. The tube
is slowly raised out of the water and the same tuning fork, vibrating with
frequency fo, is held a fixed distance from the top of the tube.
(d) Determine the height h of the tube above the water when the air column
resonates for the first time. Express your answer in terms of l.