Transcript ppt - MrMaloney.com

Solving Force
Probmems
Physics
Mr. Maloney
Objectives
You will be able to
 diagram Force problems
 use FBDs to analyze and solve force
problems.
© 2002 Mike Maloney
“Picturing Force”
Free-Body Diagrams
 Free
Body Diagrams are vector
diagrams.
 We use them to graphically depict what
is acting on an object.
 They represent the magnitude and
direction of all forces acting on an
object.
© 2002 Mike Maloney
Free Body
Diagrams
LET’S IDENTIFY SOME
 The
diagram at right
shows all the forces
acting on this object.
 Here we have Gravity, a Frictional
Force, an Applied Force, and a
Normal Force.
 Objects can have any number of
forces acting on them, depending on
the situation.
© 2002 Mike Maloney
Balanced Forces (Statics) (N1L)
 There
are often situations where a
number of forces are acting on something,
and the object has no motion –
it is STATIC or in EQUILIBRIUM.
 This means the NET FORCE on the object
is zero, or in other words the forces
balance each other out.
 What does this mean mathematically?
© 2002 Mike Maloney
unBalanced Forces
(Dynamics) (N2L)
 There
are other situations where all the
forces acting on something do not cancel
each other out completely.
 This means the NET FORCE on the object
is not zero, the object will change its motion
and accelerate proportional to the object’s
mass.
 F = m ∙ a
 Let’s try one of these.
© 2002 Mike Maloney
Solving Strategy
1.
2.
3.
4.
5.
6.
7.
Determine whether it is a static problem or a
dynamic problem if you can.
Sketch a Free Body diagram.
Draw and label vectors representing all forces.
Pick an “X” and “Y” direction. If there is any
motion, you should choose either X or Y to be in
the direction of motion.
Break forces into components if necessary
Sum the forces (F) in the X and Y directions, and
set them equal to either 0 or m∙a accordingly.
(If you are unsure, use m∙a)
Use the summation equations (F) you have
created to solve for unknown values.
Lets go back and try a few more.
© 2002 Mike Maloney
More Advanced Problems
 There
are usually many types of forces
acting on objects where friction and motion
is occurring.
 They can either be parallel to the motion,
or perpendicular to it.
 This next example has a block on a table
where there is friction and an applied force
at an angle.
© 2002 Mike Maloney
Advanced Problems
FN
Ff
surface

FAy
FAx
Fg
What forces are acting parallel to the surfaces?


block
FA
The horizontal (x) part of the Applied Force {FA}, and
the Friction Force {Ff}
What about Perpendicular?

The vertical (y) part of the Applied force {FA}, the
Weight {Fg} and the Normal force {FN}
© 2002 Mike Maloney
Advanced Problems
FN
Ff
surface
block
FA
FAy
FAx
Fg
 We
see that an applied force can be
applied at any angle. So it may act
perpendicular and/or parallel to the
motion.
© 2002 Mike Maloney
Advanced Problems
FN
Ff
surface
block
FA
FAy
FAx
Fg

However FN is always perpendicular to the
motion.
 Ff is always parallel to the motion.
By the Way, what
 On a flat surface Fg is perpendicular,
butis
we saw
how it can be both on an
incline.
wrong
with this Free
 Each problem has to be looked at and analyzed
Body Diagram?
individually.
 So lets try some.
© 2002 Mike Maloney
Block on hill
Let’s go back to a block just sitting on a track.
 What happens when I slant the track?
 The cart starts to move. I did not change any
of the forces acting on the cart … so what
changed?

© 2002 Mike Maloney
Objectives
Can you …
 diagram Force problems
 use FBDs to analyze and solve force
problems.
© 2002 Mike Maloney
APPENDIX
© 2002 Mike Maloney
Net Force

NET FORCE refers to the vector sum total
of all forces acting on an object. It is often
expressed as F
 For example, if there were two leftward forces
of 10 lb each, the NET FORCE would be 20
lb leftward.
 If there were one 10 lb rightward force and
one 8 lb leftward force, the NET FORCE
would be 2 lb rightward.
 What about if the forces were in X and Y?
 BACK
© 2002 Mike Maloney
Static problem
 Static
problems are associated with
Newton’s 1st Law.
 Static problems are problems in which
the net force is ZERO (0).
 In this case the sum of the forces in the
X-direction and the Y-direction are both
ZERO (0).
 BACK
© 2002 Mike Maloney
dynamic problem
 Dynamic
problems are associated
with Newton’s 2nd Law.
 Dynamic problems are problems in
which the net force is not ZERO.
 In this case the sum of the forces in the
X-direction and/or the Y-direction are
not always zero, and may result in some
acceleration.
 BACK
© 2002 Mike Maloney
x/y Components
 If
the forces are acting in more than 2
directions (i.e. applied force at an angle)
break all the forces down into vertical
and horizontal components or parallel
and perpendicular components using
vector rules (sine and cosine).
 Once they are broken up, you can Fx
and Fy to solve for the unknowns.
 BACK
© 2002 Mike Maloney
1.
A
book is at rest on a table top.
FN
Fg
BACK TO LECTURE
© 2002 Mike Maloney
2.
A
girl is suspended motionless in the air
by two ropes attached to her.
FT
FT
BACK TO LECTURE
Fg
© 2002 Mike Maloney
3.
 An
egg is free-falling from a nest in a
tree. Neglect air resistance.
Fg
BACK TO LECTURE
© 2002 Mike Maloney
4.
A
flying squirrel is gliding (no wing flaps)
from a tree to the ground at constant
velocity. Consider air resistance.
FAIR
BACK TO LECTURE
Fg
© 2002 Mike Maloney
5.

A rightward force is applied to a book in order
to move it across a desk with a rightward
acceleration. Consider frictional forces.
Neglect air resistance.
FN
FA
Ff
BACK TO LECTURE
Fg
© 2002 Mike Maloney
6.

A rightward force is applied to a book in order
to move it across a desk at constant velocity.
Consider frictional forces. Neglect air
resistance.
FN
FA
Ff
BACK TO LECTURE
Fg
© 2002 Mike Maloney
7.

A college student rests a backpack upon his
shoulder. The pack is suspended motionless
by one strap from one shoulder.
FA
BACK TO LECTURE
Fg
© 2002 Mike Maloney
8.
A
skydiver is descending with a
constant velocity. Consider air
resistance.
FAIR
Fg
BACK TO LECTURE
© 2002 Mike Maloney
9.
A
force is applied to the right to drag a
sled across loosely-packed snow with a
rightward acceleration.
FN
FA
Ff
BACK TO LECTURE
Fg
© 2002 Mike Maloney
10.
A
football is moving upwards towards its
peak after having been booted by the
punter. Neglect air resistance.
Fg
BACK TO LECTURE
© 2002 Mike Maloney
11.
Three smaller kids are pulling a rope against one
large kid.


A. They are at a stand still
B. The big kid is winning
BACK TO LECTURE
© 2002 Mike Maloney
11.
Three smaller kids are pulling a rope against one
large kid.


A. They are at a stand still
B. The big kid is winning
BACK TO LECTURE
© 2002 Mike Maloney
11.
Three smaller kids are pulling a rope against one
large kid.


A. They are at a stand still
B. The big kid is winning
BACK TO LECTURE
© 2002 Mike Maloney
12.
A
car is coasting to the right and
slowing down.
FN
Ff
BACK TO LECTURE
Fg
© 2002 Mike Maloney
13.
 Mr.
M is holding a book against a flat
wall.
Ff
FA
FN
Fg
BACK TO LECTURE
© 2002 Mike Maloney