Transcript Lecture 8: Forces & The Laws of Motion

Lecture 8:
Forces &
The Laws of Motion
Questions of Yesterday
1) You must apply a force F1 to begin pushing a crate from rest
across the floor, you must apply a force F2 to keep the crate
moving at a constant velocity once its in motion. Which statement
is true?
a) F1 = F2
b) F1 > F2
c) F1 < F2
2) When do action and reaction pairs of forces not cancel one another
out?
a) when one of the objects is accelerating
b) when both objects are accelerating
c) never
Newton’s Second Law
The acceleration a of an object is directly proportional
to the net force acting on it and inversely proportional
to its mass
a = F/m
SI Unit of force =
Newton
1 N = 1 kg*m/s2
F = ma
F and a are
vectors!
Vector equation!
Fx = max Fy = may Fz = maz
Free Body Diagrams
Diagram of a single object with all the forces acting ON it
DO NOT INCLUDE:
N
-Forces that the object
exerts on other objects
or the Earth
-Other objects that the
object is in contact with
N’
F
g
Fg’
Free Body Diagrams
Tennis ball undergoing projectile motion
F
g
Free Body Diagrams
Tennis ball while a tennis player is serving it.
The player swings his racket, hitting the 60 g tennis ball with a
force 60 N at an angle 30o with the horizontal.
FA
30o
What is the magnitude and
direction of the net force on
the ball?
F
g
What is the resultant acceleration?
Free Body Diagrams
A block sliding down a frictionless inclined plane.
N
q
q
F
Is the block accelerating?
In what direction?
g
Free Body Diagrams
A block sliding down a frictionless inclined plane.
N
q
q
F
g
Choose coordinate system to be in
direction of incline plane!
Fgx = Fgsinq
Fgy = Fgcosq
Free Body Diagrams
What is the acceleration of the block?
N
3 kg
30o
q
Fx = max Fy = may
F
Fy = may = 0
g
N - Fgy = 0
Fgx = Fgsinq
Fx = max
Fgy = Fgcosq
max = Fgx
FBDs and using Newton’s Laws
How much do you weigh in a moving elevator?
A 60-kg person stands on a scale in an
elevator
Draw a free body diagram for the person
What does the scale read when
the elevator is:
a) at rest?
b) Ascending with a speed of 2.0 m/s?
c) Descending with a speed of 2.0 m/s?
d) Ascending with an acceleration of 2.0 m/s2?
e) Ascending with an acceleration of 2.0 m/s2?
Practice Problem
A train has a mass of 5.0*106 kg and is moving at 90
km/h. The engineer applies the brakes, resulting in
a net backward force of 2.0*106 N on the train. The
brakes are held on for 30.0 s.
a) What is the final speed of the train?
b) How far does the train travel in this period?
Tension
Free Body Diagrams and Newton’s 2nd law only use forces
acting directly on an object
Draw a free body diagram for the block
What about the rope?
FA
a
Tension
Tension = force exerted along a rope
N
T’
FA
T
2nd law: ma = T’ + FA = 0
Fg
3rd law: T = -T’
Tension at one end of the rope is equal to the other
Tension is CONSTANT all along the rope
Applied force is acts “directly” on block through the rope
Tension: Practice Problem
5 kg
10 kg
Find the acceleration of each object and
the tension in the rope
Objects in Equilibrium
When is ∑F = 0?
When is a = 0?
An object at rest or moving with a constant velocity is in
EQUILIBRIUM
Conditions for equilibrium:
∑Fx = 0
∑Fy = 0
Objects in Equilibrium
Find the tension in the two wires that support the light
fixture
40o
Conditions
for
equilibrium:
∑Fx = 0
∑Fy = 0
40o
Questions of the Day
You must apply a force F to push your physics book across your desk at a
constant velocity.
1a) The net force acting on the book is…
a) F
b) between 0 and F
c) greater than F
d) 0
1b) Are other forces acting on the book in the horizontal direction?
a) YES
b) NO
c) not enough information to know
3) A large crate is at rest in the bed of a truck. As the truck accelerates the
crate remains at rest relative to the truck. In what direction is the net force
on the crate?
a) the same direction as the truck’s acceleration
b) opposite the direction of the truck’s acceleration
c) the net force is zero