Transcript Lectures 28-30

Physics 218: Mechanics
Instructor: Dr. Tatiana Erukhimova
Lectures 28-30
A block of mass m is moving along x axis
with a velocity of V0. It collides with a block
of mass M, initially at rest.
1) What is the change in kinetic energy of
the system of two balls:
a) if the collision is perfectly elastic;
b) if the collision is perfectly inelastic
(balls stick together after collision).
2) For m = M = m0, find the velocity of
each ball after a perfectly elastic
collision.
At the intersection of Texas Avenue and
University Drive, a blue, sub compact car with
mass 950 kg traveling east on University
collides with a maroon pickup truck with mass
1900 kg that is traveling north on Texas and
ran a red light. The two vehicles stick together
as a result of the collision and, after the
collision, the wreckage is sliding at 16.0 m/s in
the direction 24.0 degrees east of north.
Calculate the speed of each vehicle before the
collision. The collision occurs during a heavy
rainstorm; you can ignore friction forces
between the vehicles and the wet road.
Quiz 2
A block of mass m is sliding on a frictionless
table with velocity v0. It explodes into two
pieces, one with mass m/3. The light piece
flies off horizontally, perpendicular to the
original direction of motion, with velocity 2v0.
Find as many equations as you need to find
the velocity of the heavy piece.
Quiz 3
You are standing on a frictionless surface. Some
idiot throws a rock at you which you catch. In
terms of your mass, the rock’s mass and the
rock’s velocity find your position as a function of
time after you catch the rock.
Problem 2
A block of mass M is at rest on a frictionless
table. You can hit it with either a sticky block
which will stick to it or a very hard block for
which the collision will be perfectly elastic.
Both blocks have mass m and can be thrown
with velocity of magnitude V0 . Which way
will you get the block M moving fastest?
A small car weighing m1 is traveling due north
when it collides with a pick-up truck weighting
m2 which was traveling due east. After the
collision the two vehicles move off together at
an angle θ north of east. The driver of the car
claimed that the truck driver was at fault
because he was exceeding the speed limit,
going with a velocity v1. If this were true, what
was the car’s initial velocity?

Problem 4 p.200
In a nuclear collision an incoming proton has
initial velocity of magnitude 3.5 105 m/s. It
collides with another proton, initially at rest.
After the collision one proton goes off at 370 to
the x axis. If the collision is perfectly elastic,
find the velocities of the two protons after the
collision.
The ballistic pendulum
“Famous Problem” from the book
Impulse
 t2 


J   Fdt  p2  p1
t1
 dp
F
dt
Changes in a particle’s momentum are due to
impulse, which depends on the time over which
the net force acts.
Impulse
Suppose you throw a ball with a mass of 0.4
kg against a brick wall. It hits the wall moving
horizontally to the left at 30 m/s and rebounds
horizontally to the right at 20 m/s. a) Find the
impulse of the net force on the ball during its
collision with the wall. b) If the ball is in
contact with the wall for 0.010 s, find the
average horizontal force that the wall exerts
on the ball during the impact.
Polar coordinates
A ball of mass m is swung around a circle at the end
of a string of length L. The string will break if the
tension in it exceeds a critical value, Tc. What is the
largest constant angular velocity the ball can have
without breaking the string?
A ball of mass m is swung around a circle at the end
of a string of length L. What is the minimum  the
ball can have and still travel in a circle without string
becoming slack?