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Midterm, November 13th 2009 --- 1206EL MULTIPLE CHOICE PART
Dr. Christine Kraus
(1 Point each)
Please mark your answer clearly in the exam booklet, giving the number and then a), b),
c) or d). In every case choose the best answer - just one.
1.) Which of the following quantities is not a scalar?
a) Energy
b) Work
c) Force
d) Power
2.) One movable pulley does
a) change direction only
b) distribute the forces equally to each rope
c) nothing
d) leave only one third of the force on the rope you are pulling on
3.) Archimedesʼ principle describes the relation between
a) Pressure and area
b) Energy components for fluids
c) the magnitude of the buoyant force and the weight of the displaced fluid
d) the displaced fluid and the probability for an object to swim
4.) What is the unit for density?
a) kg/m3
b) m3 per kg
c) Density unit
d) Nm/s
5.) When an acceleration is present, it needs to be caused by
a) a counter acceleration
b) the work done
c) a force
d) friction
6.) Gravitational potential energy depends on
a) mass and height
b) mass and acceleration due to gravity
c) acceleration due to gravity, mass and height
d) none of the mentioned parameters
7.) For a stone thrown horizontally from a building with height h, the horizontal
component can be treated
a) the same as the horizontal
b) as accelerated motion, but the horizontal part has to be accounted for
c) independently from the horizontal and has no acceleration
d) independently from the horizontal and has acceleration
Midterm, November 13th 2009 --- 1206EL Dr. Christine Kraus
8.) An empty and full cylinder made from the same material are rolling down an incline.
The solid cylinder is
a) slower
b) same speed
c) faster
d) twice as fast
9.) Angular momentum depends on angular velocity
a) quadratic
b) linear
c) not at all
d) linear but like 1/x
10.) A feather and a stone released from the top of a building will hit the ground
a) at the same time
b) the stone will be earlier
c) the feather will be earlier
d) it can be either way
SHORT QUESTIONS (1 POINT each, unless otherwise noted)
Answer the following questions shortly, but with sufficient information. None of these
should take you longer than one minute (or two). Make sure, you note the number with
your answer.
11.) Formulate Newtonʼs second law in your own words!
12.) Draw a free body diagram of a floating raft.
13.) Describe kinetic energy in your own words (include formula).
14.) Explain why (and how) angular momentum is conserved for a spinning skater with
arms out compared to arm pulled close the the body. (2 points)
15.) In linear motion with constant acceleration the following equation is true:
vf2 = vi2 + 2ad with vi initial velocity, vf final velocity, a acceleration and d
displacement. How does this expression change for rotational motion - write down
the formula and name the parts as done above.
16.) How would you determine the density of an irregularly shaped rock? (2 points)
17.) What do we mean, when we talk about the center of gravity - describe in your own
words.
18.) Describe what we mean, when we are talking about an inelastic collision?
Midterm, November 13th 2009 --- 1206EL Dr. Christine Kraus
19.) A bomb, initially at rest, explodes into several pieces. Is linear momentum of the
system conserved? Is kinetic energy of the system conserved? (2 points)
20.) Two thin-walled drinking glasses having equal base areas but different crosssectional areas above the base, are filled to the same level with water. According to
the expression P = P0 + ρgh, the pressure is the same at the bottom of both
glasses. Why does one glass weigh more than the other? (2 points)
SHORT QUESTIONS (3 points each, unless otherwise noted)
21.) A 2.0 kg block of slippery cheese that slides along a frictionless track from point a to
point b. The cheese travels through a total distance of 2.0 m along the track, and a net
vertical distance of 0.80 m. How much work is done on the cheese by the gravitational
force?
a
b
22.) (4 points) Calculate the force exerted on your eardrum due to the water when you
are swimming at the bottom of a pool that is 5.0 m deep. Assume that the pressure
of the air inside you ear is 1.0 x 105 Pa and the surface area of the eardrum is
1 x 10-4 m2
23.) A cylinder is standing on one of itʼs sides, it has a radius of 5 cm. How much
pressure does the ground underneath experience?
24.) How is elastic potential energy defined? Describe the relations.
25.) To write down a formula for Happiness H, we know about the following relations:
o H is increasing linear when more laughter L is in your life
o H is inverse proportional to tragedies T
o H is proportional to “falling in love” square, where falling is love is symbolized by F
What does this formula for Happiness look like, assuming the stated are all the
important values?
Midterm, November 13th 2009 --- 1206EL Dr. Christine Kraus
PROBLEMS
Remember to always start with a drawing, including all relevant parameters. Donʼt forget
to reason and write down what you are doing. Note, if you think your result is wrong and
why.
A.) The end of a ski jump (15 points)
A ski jumper leaves the ski track moving in the horizontal direction with a speed of
25.0 m/s. The landing incline below him falls off with a slope of 35.0°.
(a) Where does she land on the incline? (10 points)
(b) Suppose everything in this example is the same except the ski jump is curved so
that the jumper is projected upward at an angle from the end of the track. Is this
design better in terms of maximizing the length of the jump? Explain your answer.
(5 points)
B.) Letʼs go the Loop-the-Loop! (15 points)
A pilot of mass m in a jet aircraft executes a loop-the-loop. In this maneuver, the aircraft
moves in a vertical circle of radius 2.70 km at a constant speed of 225 m/s.
a) Make a drawing of the situation and indicate the velocity vector at the top and the
bottom of the circle
(1 point)
b) Draw two free body diagrams for the pilot - one on the top of the circle and one on
the bottom
(4 points)
c) Determine the area of the circle and its circumference (2 points)
d) Determine the force exerted by the seat on the pilot at the bottom of the loop.
Express your answer in terms of the weight of the pilot. (5 points)
e) Determine the force exerted by the seat on the pilot at the top of the loop.
(3 points)
C.) The Spring-Loaded Popgun (15 points)
The launching mechanism of a popgun consists of a spring of unknown spring constant.
The spring is compressed by 0.120 m, when the gun is fired vertically (up), it is able to
launch a 35.0 g projectile to a maximum height of 20.0 m above the position of the
projectile as it leaves the spring.
a) Neglecting all resistive forces, determine the spring constant (8 points)
b) Find the speed of the projectile as it moves through the equilibrium position of the
spring, just before it leaves the spring. (7 points)
D.) Proton-Proton Collision
(15 points)
A proton collides elastically with another proton that is initially at rest. The incoming
proton has an initial speed of 3.50 x 105 m/s and makes a glancing collision with the
second proton. After the collision, one proton moves off at an angle of 37° to the original
direction of motion and the second deflects at an angle of Φ to the same axis.
a) Make a drawing of the collision (before, during, after) and include all important
parameters (4 points)
b) Find the final speed of the two protons (after the collision) (8 points)
c) Determine the angle Φ (3 points)