Force and Motion
Learning Goals:
-Differentiate between scalars (distance, speed) and vectors
(displacement, velocity)
-Explain the relationship between acceleration and velocity
-Define g, the acceleration due to gravity
-Describe and understand centripetal acceleration
-Understand projectile motion
-Understand and apply the three laws of Newton and the
law of Universal gravitation
-Explain the conditions for the conservations of linear and
angular momenta
Motion
• To describe completely the motion of an
object you need to know three things
– Position (at one single time)
• Cartesian coordinates
• Needs a reference point
– Velocity
• Speed (scalar) AND direction → VECTOR
– Acceleration
• Magnitude (scalar) AND direction → VECTOR
Scalar VS Vector
• Scalar: magnitude (and units, of course!)
– Ex.: your mass, the temperature, SPEED,
distance, etc.
• Vector: magnitude (and units) AND
DIRECTION!
– Ex.: velocity, force, displacement, etc.
– Are represented by arrows
• Length proportional to the magnitude
• Arrowhead indicates the direction
Moving from place to place
• Speed: SCALAR
d
– Average speed = Distance Traveled/time to travel OR v 
t
• Ex.: 2h to go to L.A. (180km), 4h to come back
Average Speed = (180[km]+180[km])/(2[h] + 4[h]) = 60 [km/h]
– Instantaneous Speed: speedometer reading
• Velocity: VECTOR
– Average velocity = displacement / time to travel
• Displacement: straight line distance between starting and ending point,
with direction pointing towards the end point.
• Ex.: 2h to go to L.A. (180km), 4h to come back
Average velocity = 0[km] / (2[h]+ 4[h]) = 0 [km/h] !!!
– Instantaneous velocity = speedometer reading + direction!!!
Displacement is a vector quantity between two points.
Distance is the actual path traveled.
Special Case: Constant Velocity
• If the velocity is constant then
– The speed is not changing
– The direction is not changing (i.e. straight line motion!)
• We choose one direction to be +, the other to be –
Ex. At a track meet, a runner runs the 100.m dash in 15s.
What was the runner’s average speed? Average
velocity?
d 100.[m]
v 
 6.7[m/s]
t
15[s]
Acceleration
• If the velocity changes, there is acceleration
– Change in MAGNITUDE and/or the DIRECTION
– Ex. : car slowing down or speeding up, the Earth around the
Sun, a ball falling down
• Average acceleration = change in velocity/ time for change
v v f  vo

= a
t
t
vo = starting velocity
vf = ending velocity
The UNITS of acceleration are (m/s)/s = m/s2
Acceleration (cont’d)
• Acceleration is a vector
– Magnitude: rate at which the velocity is changing
– Direction: how is the velocity changing
• If velocity and acceleration are in the same direction,
the speed INCREASES
• If velocity and acceleration are in opposite direction,
the speed DECREASES
Which of these car is accelerating?
A. A car on a circular race track going at a
constant speed
B. A car coasting to a stop
C. A and B
D. None of these car is accelerating.
Special Case: gravitational
acceleration g
• Objects falling at the surface of the Earth ALL fall
with the same acceleration
g=9.80m/s2, down
• Without the effect of AIR resistance = free fall
• Dropping:
Distance fallen =
• t = time for falling
1 2
d  gt
2
A ball is dropped
from a tall building.
How far does the
ball drop in 0.50 s?
1 2
d  gt
2
d

1
2
9.80[m/s 2 ]  0.50[s]
2
d  1.2[m]

Throwing a ball up, letting it fall
down…
• There is gravitational
acceleration (ALWAYS
DOWN) when the ball
goes up as well as when
it comes down
– Way Up: acceleration
opposite velocity so
SLOWING DOWN
– Way Down: acceleration
same direction as
velocity so SPEEDING
UP
Uniform Circular Motion
• Constant speed BUT direction is changing all the
time!
– There is an ACCELERATION!!!
– Points towards the center of the circular path
– Called Centripetal Acceleration ac
v2
– ac=
r
– v = speed, r = radius of the circular path
If you cut the string, the ball will
continue in a straight line.
The string keeps the ball in circular
motion.
Uniform Circular Motion (cont’d)
Ex.: A person drives a car around a circular racetrack
with a radius of 70.m at 10.m/s. What is the
acceleration of the car?
2
v
ac 
r
2
(10.[m/s ])
2
ac 
 1.4[m/s ]
70.[m]
Projectile Motion
• Any object thrown by some means
– Golf ball, tennis ball, football, bullet, etc.
• The HORIZONTAL (parallel to the ground)
and VERTICAL (perpendicular to the
ground) motions are INDEPENDANT
Gravity with high speed
A zookeeper wants to feed a banana
to the monkey with his cannon. The
monkey always let go of the branch
when the banana is shot. Where
should he aim:
above, below or on???
If there were no gravity
Gravity with slow speed
Aiming above the monkey’s head
Forces and Net Force
• Forces are CAPABLE of producing a
change in velocity.
– ONLY if the force is unbalanced
– Forces are VECTORS
• If there is a net, or unbalanced, force: the
motion will CHANGE!
– There will be an acceleration
Laws of Newton
1. An object will remain at rest or in uniform
motion in a straight line unless acted on by an
external, unbalanced force.
•
•
The greater the mass of an object, the harder it is to
change its motion : INERTIA
An object doesn’t need a force to keep on moving!!!
•
Examples of forces?
•
Apart from gravity, in your daily lives, force is transmitted
through contact
An elevator is being lifted up an elevator shaft
at a constant speed by a steel cable. Forces
on the elevator are such that:
A. The upward force by the cable is greater than the
downward force of gravity
B. The upward force by the cable is equal to the
downward force of gravity
C. The upward force by the cable is smaller than the
downward force of gravity
D. None of the above.
An object keeps on moving the way it was UNLESS a force acts on it…
Explain those Examples using Newton’s first law:
1. Blood rushes from your head to your feet while quickly stopping
when riding on a descending elevator.
2. The head of a hammer can be tightened onto the wooden handle by
banging the bottom of the handle against a hard surface.
3. To dislodge ketchup from the bottom of a ketchup bottle, it is often
turned upside down and thrusted downward at high speeds and then
abruptly halted.
4. Headrests are placed in cars to prevent whiplash injuries during
rear-end collisions.
5. While riding a skateboard (or wagon or bicycle), you fly forward off
the board when hitting a curb or rock or other object which abruptly
halts the motion of the skateboard.
2.
Fnet = ma
•
Unbalanced Force = mass × acceleration
OR
Unbalanced force
accelerati on 
mass
•
•
•
For the same force acting on difference object, the
heavier the object, the smaller the acceleration.
For a given object, the larger the force acting on it, the
larger the acceleration.
Different objects will have the same acceleration if a
force proportional to their mass is applied on them…
A net external force of 21 N is applied
to a mass of 3.0 kg. From Newton’s 2nd
law, what will be the resulting
acceleration?
A.
B.
C.
D.
63 m/s2
21 m/s2
7.0 m/s2
Zero.
Centripetal Acceleration: caused by
a FORCE!
3. For every action there is an equal and
opposite reaction.
•
Force always come in pair, acting between two
different object!!!
— The Earth attracts you towards it by gravity, you attract
it towards YOU with the same force.
— When a train and a Beetle collide, the train AND the
Beetle will have the same force hitting them.
— When you walk, you push on the ground BACK and
the ground reacts by pushing you FORWARD with the
same force.
— Recoil from a fired riffle: the bullet is pushed forward
with the same force that pushes back on the riffle.
— If you are stranded in space with nothing… you are
dooooomed!
A large truck breaks down out on the road and
receives a push back into town by a small
compact car.
1. While the car, still pushing the truck, is
speeding up to get up to cruising speed:
A. The amount of force with which the car pushes on
the truck is equal to that with which the truck pushes
back on the car
B. The amount of force with which the car pushes on
the truck is smaller than that with which the truck
pushes back on the car.
C. The amount of force with which the car pushes on
the truck is greater than that with which the truck
pushes back on the car
D. Neither the car nor the truck exert any force on the
other.
A large truck breaks down out on the road and
receives a push back into town by a small compact
car.
2. After the car reaches the constant cruising speed at
which its driver wishes to push the truck:
A. The amount of force with which the car pushes on the
truck is equal to that with which the truck pushes back on
the car.
B. The amount of force with which the car pushes on the
truck is smaller than that with which the truck pushes back
on the car.
C. The amount of force with which the car pushes on the
truck is greater than that with which the truck pushes back
on the car.
D. Neither the car nor the truck exert any force on the other.
Newton’s Law of Gravitation
Gm1m2
FG 
r2
• FG = Force of gravity
• G = 6.67x10-11 Nm2/kg2
• m1 and m2: the TWO masses that are
attracting each other
• r: the distance between their centers
What would the force of gravity be between:
1.
the Earth and an apple of 0.25kg on a table?
2.5N
2.
the Earth and a football player of 85kg on a
football field?
830N
3.
the Earth and a 1250kg elephant at the Wild
Animal Park?
12300N
4.
The Earth and a 85kg astronaut in the Space
Station 400km above ground?
740N
Gm1m2 G  mE  m?
m
FG 

 9.81 2   m?
2
2
r
RE
s 
Linear and Angular momenta
• Linear momentum p = mv → vector!
– m: mass, v: velocity
• Angular momentum L = mvr → vector!
– m: mass, v: velocity, r: separation with center
These two quantities will remain constant for a
group of objects UNLESS an EXTERNAL
UNBALANCED force is applied to them.
Linear momentum
• Pi = Pf = 0 (for man and boat)
• When the man jumps out of the
boat he has momentum in one
direction and, therefore, so does
the boat, but in the opposite
direction.
• Their momenta must cancel out!
(= 0)
Angular Momentum
• force that can create rotation: force that can generate torque
• If there are no torques acting on an object, the angular
momentum is conserved (L doesn’t change).
L = mrv
• Planets are in elliptical motion around the Sun
• Sometimes they are closer (r gets smaller) and
sometimes they are further (r gets larger) from
the Sun.
L = mrv
Homework
• Chapter 2
– Short-answer questions
• 4, 7, 10, 18
– Exercises
• 2
• Chapter 3
– Short-answer questions
• 1, 8, 9, 20
– Exercises
• 2, 4