University of Regina
Physics 109
Final Examination
December 16, 2008
Time: 3 hours
2008-30 Instructors: For section 001 Dr. P.-P. A. Ouimet and for section 002 Dr. M. Barbi.
Instructions
Please Read
Other than photo ID, pens, pencils, erasers and one calculator, you are not allowed to bring
any other materials, including cellphones and electronic translators, into the exam. A list of
equations and constants which you might find useful is attached.
The exam consists of two problem sets. Make sure you read carefully the instructions given
for each problem set. In problem set 1 you are to attempt all 5 problems. In problem set 2,
you are to choose and attempt three of the five problems.
Final note: The clarity and neatness of your solution is taken into account in the grading
process. Good luck to you all!
Problem Set 1
Complete all of the following five questions. Each completed problem is worth 10 marks.
1. A certain lens focuses light from an object 2.75 m away as an image 48.3 cm on the
other side of the lens. What type of lens is it and what is its focal length? is the image
real or virtual?
2. The magnification of a convex mirror is +0.65 for objects 2.2 m from the mirror. What
is the focal length of this mirror?
3. A 65.0 kg person stands on a scale in an elevator. What does the scale read (in N and
in kg) when the elevator is
(a) at rest,
(b) ascending at a constant speed of 2.5 m/s,
(c) accelerating upwards at 2.5 m/s2 ?
4. A projectile is fired at an upward angle of 45.0◦ from the top of a 265 m cliff with a
speed of 185 m/s. What will be its speed when it strikes the ground below? For full
marks you must use conservation of energy.
5. A rocket of total mass 3250 kg is traveling in outer space with a velocity of 156.0 m/s.
To alter its course by 30.0◦ , its rockets can be fired briefly in a direction perpendicular
to its original motion. If the rocket gases are expelled at a speed of 2450 m/s, how
much mass must be expelled?
1
Problem Set 2
Complete any three of the following five questions. Each completed problem is worth 10
marks.
6. A nonrotating cylindrical disk of moment of inertia I is dropped onto an identical disk
rotating at angular speed ω. Assuming no external torques, what is the final common
angular speed of the two disks?
7. In a “Rotor-ride” at a carnival, people are rotated in a cylindrically-walled “room” of
radius 5.0 m. After the ride has spun up to full speed, the floor of the “room” drops
out, but the people remain stuck with their backs to the wall.
(a) If the coefficient of static friction between a person and the wall is 0.5, what is
the minimum frequency of the rotor necessary for that person to remain in place?
(b) People on this ride say they where “pressed against the wall”. Is there really an
outward force pressing them against the wall? If so, what is its source? If not,
what is the proper description of their situation (besides “scary”)?
Note: Your solution must include a free-body diagram to receive full marks.
8. After a completely inelastic collision between two objects of equal mass, each having
initial speed v, the two move off together with speed v3 . What was the angle between
their initial directions?
9. An Atwood’s machine consists of two masses, m1 and m2 (m2 > m1 ), which are
connected by a massless inelastic cord that passes over a pulley, as shown in figure 1.
Model the pulley as a cylinder of unknown radius R and known mass M . Noting that
the tensions F~T 1 and F~T 2 are not equal, if the masses m1 , m2 and M are known, find
the acceleration of the system. Note: Your solution must include free body
diagrams to receive full marks.
Figure 1: Atwood’s machine for question 9.
2
10. A uniform ladder of mass m and length l leans at an angle θ against a frictionless wall,
see figure 2. If the coefficient of static friction between the ladder and the ground is µ,
determine a formula for the minimum angle at which the ladder will not slip.
Note: Your solution must include free body diagrams to receive full marks.
Figure 2: Ladder for question 10.
3