Transcript A ball of mass m is swung around a circle at the end of a string of

Physics 218: Mechanics
Instructor: Dr. Tatiana Erukhimova
Lectures 30, 31,
32
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?
A plane is flying in an arc at the speed of v0.
At the top of arc the passengers experience a
sense of weightlessness. What is the radius of
the arc?
A 3000 kg spacecraft is in a circular orbit 2000
km above the surface of Mars. How much
work must the spacecraft engines perform to
move the spacecraft to a circular orbit that is
4000 km above the surface?
Rotational Motion
r
N
Whirling Beaker of Water
r
mg

Fy  may
2
mV
N  mg 
R
mV 2
N
 mg
R
2
V
g
R

Platform rotates with angular acceleration (t)=t. A
man starts a distance L from the center and walks in
along a straight line painted on the platform towards
the center. He decreases his distance from the center
as a constant rate, vc. What force does the platform
exert on the man, as a function of his distance from
the center?
Conical pendulum
A race track designer wants to have the cars able to
maintain a speed vmax without skidding on a circular
track. If the track is flat with a coefficient of friction 
what does the radius have to be?
A frictionless track contains a circular section of radius
R as shown. What is the minimum height at which a
block must be started in order for it to go around the
loop without falling off the track?
H
R
Kinematics
Have a great day!
Reading: Chapter 12
Hw: All Chapters 12, 13 problems
and exercises