PHY131H1S – Class 16
Today:
• Energy in Collisions
• Work
Quick true or false question..
•
True or false: “I am sure I learned in high
school that the normal force on an object of
mass m is given by n = mg.”
A. True
B. False
Problem Set 6 on
MasteringPhysics
due Friday at
11:59PM
Normal Force is a self-adjusting force like static friction,
usuallyrfound by drawing a free body diagram, then
r
using F = ma
net
Help the Force find its Equation!
Tension
Spring force
• mg (on Earth’s surface), or
Gm1m2/r2 (in general)
• None. It can’t be negative.
Gravity
• None. It must be directed
away from the surface.
Kinetic Friction
• μkn, directed opposite the
motion.
Normal
• None. It can’t exceed μsn.
Drag
• kx (towards equilibrium of
spring where x=0)
Static Friction
• 0.5Av2, directed opposite the
motion.
• Test marks are posted
on portal.
• The tests will be
returned to you in
Practicals this week;
please have a look over
the marking and get
back to me if there were
any issues with the
marking before Mar.20.
• 3.5 points were added to all students marks, so that the
average is 65%.
• Top mark was 29.5, which was increased to 33/30.
• The top 5 marks were all above 98%.
• 17.5 out of 30 corresponds to a B- on the test; 39 students
got 17.5 or better.
A small child slides down the four frictionless slides
A–D. Each has the same height. Rank in order, from
largest to smallest, her speeds vA to vD at the bottom.
A. vC > vA = vB > vD
B. vC > vB > vA > vD
C. vD > vA > vB > vC
D. vA = vB = vC = vD
E. vD > vA = vB > vC
•
A.
B.
C.
D.
A perfectly elastic collision conserves
Momentum p=mv
Kinetic energy E = ½ mv2
Both
Neither
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Elastic Collisions
•
A.
B.
C.
D.
An inelastic collision conserves
Momentum p=mv
Kinetic energy E = ½ mv2
Both
Neither
• All collisions conserve momentum.
• Energy can sometimes be lost if the objects
that collide are deformed or create heat in
some way.
Elastic Collisions
Elastic Collisions
Consider a head-on, perfectly elastic collision of a ball of
mass m1 having initial velocity (vix)1, with a ball of mass m2
that is initially at rest.
There are two equations, and two unknowns. The solution,
worked out in the text on page 285, is
The balls’ velocities after the collision are (vfx)1 and (vfx)2.
Work Done by a Constant Force
Work
Consider a force acting on a particle as the particle
moves along the s-axis from si to sf.
The force component Fs parallel to the s-axis causes
the particle to speed up or slow down, thus transferring
energy to or from the particle.
We say that the force does work on the particle:
The unit of work is J, or Joules.
Consider a particle which experiences a constant force
which makes an angle θ with respect to the particle’s
displacement.
The work done on the particle is
Both F and θ are constant, so they can be taken outside the
integral. Thus
or:
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Example 1
• Adeel is doing a bench press, and he
holds the bar above him for 10 seconds
while pushing upwards on the bar with a
force of 200 N. The bar does not move.
• During this 10 seconds, how much work
does Adeel do on the bar?
Example 2
• Adeel is doing a bench press, and he slowly
pushes the bar up a distance of 30 cm while
pushing upwards on the bar with a force of 200 N.
The bar moves with a constant velocity during this
time.
• During the upward push, how much work does
Adeel do on the bar?
Example 3
Example 4: quiz
• Adeel is doing a bench press, and he slowly
lowers the bar down a distance of 30 cm while
pushing upwards on the bar with a force of 200 N.
The bar moves with a constant velocity during this
time.
• During the downward lowering, how much work
does Adeel do on the bar?
• Adeel is doing a bench press, and he slowly
lowers the bar down a distance of 30 cm while
pushing upwards on the bar with a force of 200 N.
He then pushes it up slowly the same distance of
30 cm back to its starting position, also pushing
upwards on the bar with a force of 200 N.
• During the complete downward and upward
motion, how much total work does Adeel do on the
bar?
A. 60 J
B. 120 J
C. 0 J
D. -60 J
E. -120 J
W > 0: The environment does work on the system and the
system’s energy increases.
W < 0: The system does work on the environment and the
system’s energy decreases.
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