Transcript PHY126-08:MidTerm1 - Stony Brook University

PHY 126 Final Exam A
Problem 1 (30 points)
converging
lens
plane
mirror
x cm
85.0 cm
As shown in Fig., an arrow is placed at a position, x cm from a plane mirror,
and 85.0 cm from a converging lens of focal length 32.0 cm. The arrow is seen
through the lens from the right-hand side of the lens. In this problem we are
concerned with the final image of the arrow reflected on the mirror and then focused
through the converging lens. First assume that x = 20.0 cm unless otherwise stated.
(a) Draw a principal-ray diagram that locates the final image (5 points).
(b) Calculate the location of the final image (5 points).
(c) Is the final image real or virtual and is it erect (upright) or inverted
with respect to the original object (1+1 points)?
(d) If x is changed to 22.0 cm, where is the location of the final image (3 points)?
(e) If the mirror is moving from x=20.0 cm to x=22.0 cm at a speed of 1.00 cm/s,
what is the corresponding speed of its final image viewed through the lens
(5 points)?
Problem 2 (30 points)
In this problem use the table of densities below if needed.
(a) A rod is attached to a pivot on the wall
wire
at one end and suspended at the other
end by a wire horizontally (See Fig.). The
30  rod
rod has mass M=1.0 kg and length L=2.0 m.
At the end suspended, an object made of
L
concrete (mass mc, volume V=1.0x10-3 m3) is
pivot
hung by a wire and the hanging wire is long
enough so that the object can be inside the
water
water below. Find the tension T on the wire
concrete
that suspends the rod and the object. The
wire makes 30o with respect to the rod.
densities:
3
3
(b) Instead of a concrete if the object is made


1
.
0

10
kg
/
m
water
of ice (the same volume), what is the tension T
3
3
on the wire that suspends the rod and the ice? concrete  2.0 10 kg / m
ice  0.92 103 kg / m3
Problem 3 (3+3+3+3+4+4+10 points)
c
In the figure on the right pV diagram for a Sterling engine
p
is shown. Processes from a to b, and c to d are isothermal c
at temperature TC and TH, respectively. Processes from
b to c and d to a are isochoric at volume Vb=Va/r and Va,
respectively. In the following use r and Va instead of Vb,
pd
heat capacities CV and Cp, the number of moles n, and
pb
b
the gas constant R if needed.
pa
(a) Calculate Q, W and DU in terms of variables given in
the figure for process a to b. (1 point each)
Vb=Va/r
(b) Do the same for process b to c. (1 point each)
(c) Do the same for process c to d. (1 point each)
(d) Do the same for process d to a. (1 point each)
(e) What is the net work done for one cycle?
(f) What is the heat added for one cycle? Ignore the heat exchanged
during the isochoric processes.
(e) Calculate the efficiency of the engine and compare it with that of
a Carnot cycle engine.
d
a
Va