Engineering Physics 131
Consolidated Final Examination
20 April 2002
9:00 PM - 11:30 AM
No notes of any kind or texts allowed.
Formula sheets are on the last two pages (may be removed).
Calculators allowed.
This exam has 6 questions. Attempt ALL questions.
The value of each question is indicated in the table below.
Budget your time accordingly.
Show all work in a neat and logical manner in the space provided.
Indicate clearly if you use the backs of the pages for material to be marked.
DO NOT SEPARATE the pages of the exam.
NAME:
_______________________________________________
ID #:
_______________________________________________
Circle your lecture section shown on the right - - - - - - - - - - - - - - - - –
Lecture
Instructor
Section
MWF 9:00 - 9:50
Isaac
B1
MWF 9:00 - 9:50
Sigurdson
B2
MWF 9:00 - 9:50
Koch
B3
MWF 3:00 - 3:50
Ropchan
B4
MWF 3:00 - 3:50
Grufman
B5
MWF 3:00 - 3:50
Abdelhadi
B6
DO NOT REMOVE THIS SHEET FROM
THE REST OF THIS EXAM.
Exam Marks
Question
Value
1a
3
1b
4
1c
5
1d
8
2
12
3
16
4
16
5
16
6
20
TOTAL:
Maximum:
100
Mark
Marks
3%
1 a) A block of mass m hangs from a string attached to a ceiling, as shown in the figure. An
identical string hangs down from the bottom of the block. Which string breaks first if:
(a) the lower string is pulled with a slowly increasing force? ______________________
(b) the lower string is jerked rapidly downward? _____________________________
Explain your answer.
4%
1 b) A small, initially stationary block is released on a frictionless ramp at a height of 3.0 m. Hill
heights along the ramp are as shown. The hills have identical circular tops (assume that the
block does not fly off any hill).
(a)
Which hill is the first the block cannot cross? _________________________________
(b)
What does it do after failing to cross that hill? ________________________________
(c)
On which hilltop is the centripetal acceleration of the block greatest? _____________
(d)
On which hilltop is the normal force on the block by the ramp least? ______________
5%
1 c) Each of the contacting cylinders A, B and C is free to rotate about an axis through its centre.
There is no slip between the cylinders. Cylinder C is given an angular velocity ω C . The
cylinders each have the same mass.
Fill in the table with: Asmallest@, Alargest@ or Asame@ as appropriate (some boxes could be left
blank):
Cylinder A
Cylinder B
Cylinder C
Angular velocity
Moment of inertia
Rotational kinetic energy
Speed of a point on the perimeter of
the cylinder
Speed of a point R/2 from the centre
of the cylinder
8%
1 d) A sphere rolls in a vertical plane without slip along a circular ramp to point C where it is
launched into the air (neglect air resistance at all times). Compare the values of the
horizontal and vertical components of momentum (px, py), rotational kinetic energy, and total
kinetic energy of the sphere at points B, C, D, and E to the values at point A (in the table
below indicate >, $, =, #, <, or insufficient info.). Use the coordinate system shown.
px
py
Rotational KE
Total KE
B
A
C
A
D
A
E
A
12%
2
A block of mass m1 = 2.0 kg slides along a frictionless table with a speed of 10 m/s.
Directly in front of it, and moving in the same direction, is a block of mass m2 = 5.0 kg
moving at 3.0 m/s. A massless spring with spring constant k = 1120 N/m is attached to the
near side of m2, as shown below. When the blocks collide, what is the maximum
compression of the spring?
16%
3
Sphere C of mass mc and block A of mass ma are both moving on a frictionless horizontal
surface to the left with speed ?o. Then the block is suddenly stopped by the wall in a
perfectly plastic collision.
Determine the smallest speed vo for which the sphere C will swing in a full circle about
pivot B:
a) if BC is a slender rod of negligible mass;
b) if BC is a cord.
The length of BC in both cases is R. Neglect the size of the sphere in your calculations.
16%
4
The crane shown in the drawing is lifting a 180-kg crate upward with an acceleration of 1.2
m/s2. The cable from the crate passes over a solid cylindrical pulley at the top of the boom.
The pulley has a mass of 130 kg. The cable is then wound onto a hollow cylindrical drum
with open ends that is mounted on the deck of the crane. The mass of the drum is 150 kg, and
its radius is 0.76 m. The engine applies a counterclockwise torque to the drum in order to
wind up the cable. What is the magnitude of this torque? Ignore the mass of the cable.
16%
5
In order to test the resistance of a chain to impact, the chain is suspended from a 100-kg
block supported by two columns. A rod attached to the last link of the inextensible chain is
then hit by a 25-kg cylinder dropped from a 1.5-m height. Determine the initial impulse
exerted on the chain, assuming that the impact has a coefficient of restitution e = o and that
the columns supporting the dead weight are either:
(a) perfectly rigid, or
(b) equivalent to two perfectly elastic springs. (Give answers for both cases.)
(c) Determine the kinetic energy change in the entire system, from just before the impact to
just after.
Assume the chain and rod have negligible mass.
20%
6
The 2-lb collar has a speed of 5 ft/s at A. The attached string has an unstretched length of 2 ft
and a stiffness of k = 10 lb/ft. If the collar moves over the smooth rod, when it reaches point
B (but has not impacted the base), determine:
a) its speed v,
b) the normal force of the rod on the collar N represented as a vector in the x – y coordinates,
and
c) the rate of decrease in its speed.