F denotes field force
F denotes contact force
Fij is the force exerted by
object i on object j

F
 A  FBA+FEA
FAE
A
FEA
FBE
FEB
B
θ
Earth
FEB
FBE
F denotes field force
F denotes contact force
FEA

F
 A  FBA+FEA
Fij is the force exerted by
object i on object j
FEA
FEA
-FEA
A
270o
FAE
FEA
FBE
FEB
B
θ
FEA
θ
Earth
FEB
FBE
FEA=mA g
FBA = N (normal force)
Clicker
Consider two identical blocks,
one resting on a flat surface
and the other resting on an
a) case A
b) case B
incline. For which case is the
c) both the same (N = mg)
normal force greater?
d) both the same (0 < N < mg)
e) both the same (N = 0)
3
Weight is a non-intuitive and can be very tricky
Weight is the force exerted
on you by a bathroom scale.
Now we apply N2 to the
person
Which of the forces should
we consider?
Bathroom
Scale
What is her acceleration?
Your weight is exactly mg
4
Now I'm going to put you in an elevator while you are still
standing on the scales and accelerate you upwards
Motion of the
elevator
force exerted on you
by a bathroom scale.
Bathroom
Scale
5
You have gained weight
Acceleration is now downwards
Motion of the
elevator
force exerted on you
by a bathroom scale.
Bathroom
Scale
6
You have lost weight
A large man and a small boy stands facing each other on frictionless
ice. They put their hands together and push against each other so
they move apart. Who moves away with the higher acceleration?
a) Boy
b) Man
c) Same
7
A large man and a small boy stands facing each other on frictionless
ice. They put their hands together and push against each other so
they move apart. Who moves away with the higher acceleration?
a) Boy
b) Man
c) Same
8
Forces of Friction
•Friction has its basis in surfaces that are not
completely smooth
•When an object is in motion on a surface, there
will be a resistance to the motion.
•This resistance is called the force of friction.
•Friction is proportional to the normal force.
There are 2 type of friction: static and kinetic ƒs  µs N and ƒk= µk N
• μ is the coefficient of friction
For static friction, the equals sign is valid only at impeding
motion, the surfaces are on the verge of slipping.
Use the inequality for static friction if the surfaces are not on the verge of slipping.
•The coefficient of friction depends on the type surfaces in contact.
•The force of static friction is generally greater µs > µk
than the force of kinetic friction
•The direction of the kinetic frictional force exerted on the object is opposite the direction of motion and parallel to the surfaces in contact.
•The coefficients of friction are nearly independent of the area of contact.
A spring stretched or compressed by the amount x from its equilibrium
length exerts a force whose x component is given by
Fx  kx
(gives magnitude and direction)
If we are interested only in the magnitude of the force associated with
a given stretch or compression, we use the somewhat simpler form of
Hooke’s law:
F  kx
(gives magnitude and direction)
Hooke’s law for springs states that the
force exerted by the spring increases
with the amount the spring is stretched
or compressed:
F  kx
the restoring force of a spring is directly
proportional to a small displacement.
The constant k is called the spring
constant.
How to determine the k value of a spring? Suspend the spring from support mount with length scale. Attach a weight hanger on the bottom of the spring and systematically add mass to the hanger. Record mass versus displacement For each snapshot above the downward pull of gravity is balanced by the upward pull of the spring. A force or free‐body diagram of this is shown on the right‐hand side.
Note that the restoring spring force is given by Hooke's Law as kx.
This equilibrium can be expressed as W = kx
Mass (kg)
Displacement (m)
0.05
0.02
0.10
0.04
0.15
0.06
0.20
0.08
Raw data have been entered into the table to the left.
Weights are computed for the masses in the table above.
Yields a linear relationship with Force versus Distance
The fit is a least squares to a straight line. As shown, the intersect is very small meaning very little error in the data and the slope is the k value for the spring. F  kx
Same force and displacement relationship when compressing a spring, with the exception, the force is in opposite direction. The Force exerted by the spring is always toward the equilibrium position