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Midterm, November 2nd 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.) Centripetal acceleration is caused by the centripetal forceʼs
a) change in magnitude
b) change in direction
c) change of direction and magnitude
d) sometimes magnitude and sometimes direction
2.) One fixed 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.) Total mechanical energy is the sum of
a) kinetic energy and potential energy
b) rotational kinetic energy and linear kinetic energy
c) gravitational potential energy and elastic potential energy
d) all forces
4.) What is the unit for energy?
a) Watt
b) Joule
c) Newton
d) Energy unit
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.) For constant speed, the acceleration is
a) zero
b) velocity over time
c) change in distance
d) always negative
Midterm, November 2nd 2009 --- 1206EL Dr. Christine Kraus
7.) For a stone thrown horizontally from a building with height h, the vertical
component can be treated
a) the same as the horizontal
e) as accelerated motion, but the horizontal part has to be accounted for
f) independently from the horizontal and has no acceleration
g) independently from the horizontal and has acceleration
8.) An empty and full cylinder made from the same material roll down an incline.
The solid cylinder is
a) slower
b) same speed
c) faster
d) twice as fast
9.) Torque depends on the lever arm mathematically
a) quadratic
b) linear
c) not at all
d) linear but like 1/x
10.) When a leave falls off a tree, the speed will be influenced by
a) the time of the year
b) gravity and movement of the air
c) movement of the air
d) gravity only
SHORT QUESTIONS (1 POINT each, unless otherwise noted)
Answer the following question 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 first law in your own words!
12.) Draw a free body diagram for a book resting on a table.
13.) Describe potential gravitational energy in words and write as a formula.
14.) Explain the work-energy theorem in your own words. (2 points)
Midterm, November 2nd 2009 --- 1206EL Dr. Christine Kraus
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.) Give an example for conservation of angular momentum. (2 points)
17.) What do we mean, when we talk about the center of mass - describe in your own
words.
18.) Two objects collide head on - what can you say about the momentum of the system
before and after the collision?
19.) If the gravitational acceleration on Jupiter is larger than on earth, what does that
mean for the weight of a person? (2 points)
20.) How is the normal force defined? How is the friction force defined? (2 points)
SHORT QUESTIONS (3 points each, unless otherwise noted)
21.) What is the connection between gravity and tides? Describe in two sentences.
22.) Three springs of the same relaxed length (original equilibrium position) have spring
constants k1 > k2 > k3. The springs are suspended from the ceiling and identical
masses are then hung on each of the springs. In response to these identical stretching
forces, the springs stretch amounts x1, x2 and x3, respectively. What is the relation
between the amounts stretched x1 ? x2 ?x3 for the given relation of the spring
constants? (4 points)
23.) A force of 10 N works on a ball over a distance of 5 m. The force is perpendicular to
the displacement of the ball. What is the total work done by the force?
24.) How is kinetic energy proportional to velocity?
25.) Describe under which conditions the center of mass of a system is located in the
center of the system.
Midterm, November 2nd 2009 --- 1206EL Dr. Christine Kraus
PROBLEMS
A.) Elevator at a mine (could be here in Sudbury)
30 Points
The elevator going down the shaft in a mine is called a cage and consists of two cabins
on top of each other, where each one is 5 m long, 3 m wide and 8 m high. The cabins
have a total mass of 5.0 tonnes. The cage is held by 1 cable (made of stainless steel)
with 2.5 cm diameter and it is 2.2 km long. Each cabin can hold 40 people and we will
assume an average mass of 80.0 kg per person.
a) Calculate the volume of one of the cabins as well as the volume of both of them.
b) The stainless steel cable has a density of 4000 kg/m3. What is the mass of the cable?
c) If the engine of the system has to lift the cable and cabins full of people with
v = 3.6 m/s, how much power is needed?
d) If the cable slips and the cage falls, what would be the work done by gravity?
e) In free fall, how much kinetic energy would the cage system have at the moment
when it passes the 6800 feet level - assuming that it started at surface?
f) The cage is moving up with v = 3.6 m/s. When it passes the 3600 feet level, the cable
disconnects from the cage (just on top of the cage) and it starts free falling. What is
its velocity when it passes the 6000 feet level?
a) 3 points
b) 3 points
c) 6 points
d) 5 points
e) 7 points
f) 6 points
B.) A ship (Grace) approaches an island from the west. The island has one big mountain
in the center. The island forms a perfect circle and the mountain is 1500 m high. The
diameter of the island is 7.0 km. On the east side of the island is another ship. In order
to communicate with the other ship (Wildthing) the captain of the Grace wants to use a
canon to shoot over a message. But he doesnʼt know which angle above the horizon to
point the canon at, so that he reaches his goal. He knows that the velocity of the
message once it leaves the canon is 250 m/s. He is still one km from the island and so
is the other ship. Can you help him? (Make a drawing first including all the important
information and comment on your calculations along the way)
(15 points)
C.) Two ice skaters have masses m1 and m2 and are initially stationary. Their skates are
identical. They push against each other and move in opposite directions with different
speeds. While they are pushing against each other, any kinetic frictional forces acting
on their skates can be ignored. However, once the skaters separate, kinetic frictional
forces eventually bring them to a halt. As they glide to a halt, the magnitudes of their
accelerations are equal, and skater 1 glides twice as far as skater 2. What is the ratio
m1/m2 of their masses?
i) make a drawing (before and after)
(3 points)
ii) write down reasoning
(5 points)
iii) solve problem
(7 points)