Download Day 3

Day 3
HW Problem 2-83
• Hot summer day. Swimmers jump from a
bridge into the river below. They hit the
water 1.5 s after they stepped off the bridge.
? How high was the bridge ?
? How fast were the swimmers moving when the
hit the water ?
? What would be swimmers’ drop time be if the
bridge were twice as high ?
HW Problem 2-87
• Standing at the edge of a cliff 32.5 m high, you
drop a ball. Later, you throw a second ball
downward with an initial speed of 11.0 m/s.
• (a) which ball has the greater increase in
speed when it reaches the base of the cliff, or
do both balls speed up by the same amount?
• (b) do the calculations.
HW Problem 2-90
• A hot-air balloon is descending at a rate of 2.0
m/s when a passenger drops a camera. If the
camera is 45 m above the ground when it is
dropped,
• (a) how long does it take for the camera to
reach the ground?
• (b) what is its velocity just before it lands?
HW Problem 2-102
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Drop Tower
2.2 second of free fall
? What is the drop distance of a 2.2-s tower?
? How fast are the experiments traveling when
they hit the air bags at the bottom of the tower?
? If the experimental package comes to rest over
a distance of 0.75 m upon hitting the air bags,
what is the average stopping acceleration?
HW Problem 3-10
• A lighthouse that rises 49 ft above the surface
of the water sits on a rocky cliff that extends
19 ft from its base. A sailor on the deck of a
ship sights the top of the lighthouse at an
angle of 30.0o above the horizontal. If the
sailor’s eye level is 14 ft above the water, how
far is the ship from the rocks?
HW Problem 3-24
• Vector A points in the negative x direction and
has a magnitude of 22 units. The vector B
points in the positive y direction.
• (a) Find the magnitude of vector B if the sum
of vector A and vector B has a magnitude of
37 units.
HW Problem 3-32
Unit vectors
Find the direction and the magnitude of
(a) Vector A = 25 m x direction, -12 m y direction
(b) Vector B = 2.0 m x direction, 15 m y direction
(c) Vector A + Vector B
HW 3-44
A skateboarder rolls from rest down an
inclined ramp that is 15.0 m long and inclines
above the horizontal at an angle of q = 20.0o.
When she reaches the bottom of the ramp
3.00 s later her speed is 10.0 m/s. Show that
the average acceleration of the skateboarder
is g sin q, where g = 9.81 m/s2.
HW Problem 3-51
As you hurry to catch your flight at the local
airport, you encounter a moving walkway that
is 85 m long and has a speed of 2.2 m/s
relative to the ground. If it takes you 68 s to
cover 85 m when walking on the ground, how
long will it take you to cover the same
distance on the walkway?
Assume that you walk with the same speed on
the walkway as you do on the ground.
HW Problem 3-82
• If the dragonfly approaches its prey with a
speed of 0.950 m/s, what angle q is required
to maintain a constant line of sight parallel to
the x axis?
• Assume the prey moves with a constant speed
of 0.750 m/s.
HW Problem 4-15
Playing shortstop, you pick up a ground ball
and throw it to second base. The ball is
thrown horizontally, with a speed of 22 m/s,
directly toward point A. When the ball
reached the second baseman 0.45 s later, it is
caught at point B.
(a) How far were you from the second baseman?
(b) What is the distance of vertical drop, AB?
HW Problem 4-19
In Denver, pumpkins are dropped from a
tower. Suppose the tower is 9.0 m high and
that the bull’s-eye is a horizontal distance of
3.5 m from the launch point. If the pumpkin
is thrown horizontally, what is the launch
speed needed to hit the bull’s-eye?
Section 4-4, General Launch Angle
y = yo + voyt - ½ ay t2
yo = altitude at the start
voyt = how much altitude gained at time t, “up”
½ ay t2 = how much altitude lost at time t,
“down”
ay usually = g
Example 4-5, “A Rough Shot”
Lovely picture of a clean parabola, a golf ball
as the “projectile,” illustrating one reason to
use a golf club with a large angle, for loft, for
getting over a tree. Howitzers and mortars
are used for the same reason, to shoot over
an obstacle.
Place Kicker
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Kick from surface
Distance to goal posts = 36.0 m
Height of crossbar = 3.05 m
Angle of kick above horizontal, q, =53o
Speed of kick = 20.0 m
• ? Does the kick clear the crossbar ?
Tiger Woods
• Shot hit at q of 26o
• Speed of ball off tee = 40.0 m/s?
• ? What are the components of his shot, voy
and vox ?
• ? What is the max height of the flight of the
ball ?
• ? What is the range of the shot ?
Max Height of Projectile
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Projectile of mass m
Launched at angle q with horizontal
Takes time t to get to max altitude h
If no gravity, it would reach altitude H
Use equations 2.12 and 2.9 to show that
h=H/2
Laws of Motion
• Newton #1: Object moves with a velocity
that is constant in magnitude and direction
unless acted on by a non-zero net force.
• Newton #2: The acceleration of an object is
proportional to the net force acting on the
object and inversely proportional to the
object’s mass.
• Unit of force is kg m / s2 = Newton “N”
Lab #2
• An object with a mass of 5.00 kg rests on a frictionless
horizontal table. It is connected to a cable that passes over a
pulley and is then fastened to a 10.0-kg hanging object.
• Find the acceleration of each object and the tension in the
cable.
Bullet in Rifle
• A 5.0-g bullet leaves the muzzle of a rifle with
a speed of 320 m/s.
• ? What force (assumed constant) is exerted on
the bullet while it is traveling down the 0.82m-long barrel of the rifle ?
Force during bounce
After falling from rest from a height of 30 m, a
0.50-kg ball rebounds upward, reaching a
height of 20 m.
? If the contact between ball and ground lasted
2.0 ms, what average force was exerted on the
ball ?
Free body diagrams
Sketch the object in its environment
Choose convenient coordinate system
Sketch all the forces
Resolve the forces into components
Apply Newton’s Laws along each coordinate
Forces add as Vectors
• N#2: total force = mass * acceleration
• Acceleration = sum of all forces / mass
Newton’s Third Law of Motion
N#3: For every force that acts on an object,
there is a reaction force acting on a different
object that is equal in magnitude and opposite
in direction.
You proved that this is true in Wednesday’s
lab, #3.
Pulling the car from the ditch
• Two forces are applied
to a car in an effort to
move it. (a) what is the
resultant of these two
forces?
• (b) If the car has a
mass of 3000 kg, what
acceleration does it
have?
• Ignore friction.
Runaway (sliding) car
Car of mass m
Slope of driveway q
? What is the acceleration of the car ?
Length of driveway, l, is 25.0 m
? What is time to slide to the bottom ?
? What is the velocity at the bottom ?
Lab for Newton’s #3
• Who wins tug of war?
• If fk(1) is greater than fk(2), rope will move
toward (1)
• Big guys in (1)
• Shoes with cleats in (1)
• Assume: Hands strong enough that the rope
doesn’t slip.