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HNRS 227 Lecture #2 Chapters 2 and 3. Motion and Patterns of Motion presented by Prof. Geller 29 August 2002. Recall from Chapter 1. Units of length, mass and time Metric Prefixes Density and its units The Scientific Method. Main Concepts for 2 & 3. Speed vs. Velocity Acceleration - PowerPoint PPT Presentation
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HNRS 227 Lecture #2Chapters 2 and 3
Motion and Patterns of Motionpresented by Prof. Geller29 August 2002
Recall from Chapter 1Units of length, mass and timeMetric PrefixesDensity and its unitsThe Scientific Method
Main Concepts for 2 & 3Speed vs. VelocityAccelerationForceFalling ObjectsNewton’s Laws of MotionMomentumCircular MotionUniversal Law of Gravity
Speed and VelocitySpeed
distance traveled in a unit of time a scalar quantity
Velocity speed and direction a vector quantity
Questions for ThoughtWhat is the difference between speed and
velocity?
Speed is a scalar, and velocity is a vector. Speed is the magnitude of the velocity vector.
Questions for ThoughtWhat is acceleration?
Acceleration is the ratio of the change in velocity per change in time.
Questions for ThoughtAn insect inside a bus flies from the back
toward the front at 5.0 miles/hour. The bus is moving in a straight line at 50 miles/hour. What is the speed of the insect?
The speed of the insect relative to the ground is the 50.0 mi/hr of the bus plus the 5.0 mi/hr of the insect relative to the bus for a total of 55 mi/hr. Relative to the bus alone the speed of the insect is 5.0 mi/hr.
ForceDefinition of force
something that causes a change in the motion of an objecta push or pullan electric, magnetic, gravitational effecta vector quantity
Net force - Resultant Force
InertiaDefining Inertia
tendency of an object to remain in its current state of motionthe more massive the more inertiathink of stopping a car vs. truck
Acceleration Due to GravityDirection of acceleration due to gravity
directed to center of EarthThink: scalar or vector?
a vector quantity
Why?
has magnitude and direction
Generalized MotionMotion can be viewed as a
combination of movements vertical component
typically gravitational acceleration horizontal component
some force from muscle, gunpowder, etc.
Question for ThoughtWhat happens to the velocity and acceleration
of an object in free fall?
Assuming a short free fall distance near the earth’s surface, the velocity increases downward as the acceleration remains constant.
Question for ThoughtIn the equation d=1/2*a*t2, if a is 9.8 meters
per second per second and t is in seconds, what is the unit of d?
Meters.
Question for ThoughtWhat is inertia?
Inertia is the property of matter that an object will remain in unchanging motion or at rest in the absence of an unbalanced force.
Question for ThoughtWhere does the unit s2 (or concept of “square
second”) come from?
Acceleration is change in velocity per change in time, with units of (m/s)/s. When the fraction is simplified, you get meters per second squared. The “seconds squared” indicates that something that changes in time is changing in time, that is, the ratio of change in distance per unit of time is changing in time.
Question for ThoughtNeglecting air resistance, what are the forces
acting on a bullet that has left the barrel of a rifle?
After it leaves the rifle barrel, the force of gravity acting straight down is the only force acting on the bullet.
Question for ThoughtHow does the force of gravity on a ball change
as a ball is thrown straight up in the air?
The force of gravity on the ball remains constant because the force of gravity is independent of the motion of the object near the surface of the earth.
Question B23 (p.46)An object falls from a bridge and hits
the water 2.5 seconds later. A) With what velocity did it strike the
water? B) What is the average velocity during
the fall? C) How high is the bridge?
Question B23 (p.46)23. These three questions are easily answered by using the three sets of relationships, or
equations, that were presented in this chapter:
(a) vf atvi
vf 9.8ms2
2.50s 0
ms
9.82.50 ms2 s
25m/s
(b) v vf vi
2
25m/s02
13ms
(c) v dt
d v t
d 13ms
2.50s
132.50 mss
33m
Newton’s Laws of MotionNewton’s First Law of Motion
body at rest tends to stay at rest and body in uniform motion will stay in straight line uniform motion unless acted upon by an outside force
Newton’s Second Law of Motion the acceleration of a body is
proportional to the force being applied•F = m*a
Newton’s Laws of MotionNewton’s Third Law of Motion
for every force there is an equal and opposite force (action and reaction)
Question for ThoughtHow can there ever be an unbalanced
force on an object if every action has an equal and opposite reaction?
The action and reaction forces are between two objects that are interacting. An unbalanced force occurs on a single object as the result of one or more interactions with other objects.
Question B 2 (page 65)What force would an asphalt road
have to be to give a 6,000 kilogram truck in order to accelerate it at 2.2 meters per second per second?
Question B 2 (page 65)
2 .F = m a
F 6 , 000 kg 2 . 2ms 2 1 . 3 10 4 N
MomentumBy definition momentum is the product
of mass and velocityConservation of momentum total momentum of a closed system remains constant
Question for ThoughtIs it possible for a small car to have the
same momentum as a large truck? Explain.
Yes, the small car would have to be moving with a much higher velocity, but it can have the same momentum since momentum is mass times velocity.
Question B 15 (p. 66)A 30.0 kilogram shell is fired from a
2,000 kilogram cannon with a velocity of 500 meters per second. What will be the velocity of the cannon?
B #15 page 66
15. Listing the known and unknown quantities:
Shell m = 30.0 kg Cannon m = 2,000 kgShell v = 500 m/s Cannon v = ? m/s
This is a conservation of momentum question, where the shell and cannon can be considered as a system of interacting objects:
Shell momentum = - Cannon momentummv s = - mv c
mv s - mv c = 0
30.0 kg 500 ms
2,000 kg vc 0
15,000 kg ms
2,000 kgvc 0
15,000 kgms
2,000 kgvc
vc 15,000 kg m
s2,000 kg
15,0002,000
kg1
1
kg
ms
7.5 ms
The cannon recoils with a velocity of 7.5 m/s.
Circular MotionCentripetal Force
usually gravity, but can be any force (such as the pull of a string) that forces an object into circular motion
Centrifugal Force a fictitious force, an apparent outward force
felt by an object in circular motionAcceleration in circular motion is a =
v2 / r therefore in circular motion F = mv2 / r
Question B 28 (page 66)What is the maximum speed at which
a 1000 kilogram car can move around a curve with a radius of 30.0 meters if the tires provide a maximum frictional force of 2700 Newtons? (1 Newton is a unit of force needed to accelerate a 1 kilogram mass 1 meter per second per second.)
Question B 28 (page 66)28.
F ma and a v2
r F m v2
r
v rF
m
v rFm
30.0m 2700.0N
1,000.0kg
9.00ms
or 32.4kmhr
Universal Law of GravityNewton’s Universal Law of
Gravitational Attraction every object is attracted to every other
object the force is proportional to masses and
inversely proportional to the distance squared
–F = (G*m*M) / r2
A Problem of Very Little AttractionWhat is the gravitational force
between two 100 kilogram people separated by 1 meter?
Really just a little
Use the formula for the force of gravity:F = G*m*M / r2
where G = 6.67 x 10-11 Nm2/kg2
and m = 100 kgand M = 100 kgand r = 1=======================ThenF = 6.67 x 10-11 Nm2/kg2 *100 kg*100 kg / (1 meter) 2
F = 6.67 x 10-7 N
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