Unbalanced Forces
Acceleration Lab I:
• How does the acceleration of a system depend
on the mass of the system?
–Acceleration is inversely
proportional to
mass
𝑎 ∝
1
𝑚
Acceleration Lab II:
• How does the acceleration of a system depend
on the force applied to the system?
–Acceleration is directly proportional
the force applied
𝑎 ∝𝐹
Combining the results…
𝐹
𝑎=
𝑚
This equation incorporates both of the previous
relationships in one expression.
- greater force  larger acceleration
- greater mass  less acceleration
Newton’s Second Law
• The acceleration of an object is directly
proportional to the magnitude of the net
force, in the same direction as the net force,
and inversely proportional to the mass of the
object.
𝑎=
𝐹
𝑚
A conceptual comparison of the 1st
and 2nd laws of Newton…
Newton’s First Law
Newton’s Second Law
Elevator Lab summary
• Upward acceleration
occurs when…
• Downward acceleration
occurs when…
– Moving upwards and
speeding up (leaving a
lower floor going up)
– Moving downwards
speeding up (leaving a
higher floor going down)
– Moving downwards and
slowing down (stopping at
a lower floor)
– Moving upwards and
slowing down (stopping at
a higher floor)
*Scales read more than
normal weight
*Scales read less than
normal weight
Problem solving with unbalanced
forces
• Draw a force diagram to represent the situation
• Use your force diagram as a guide for writing
force equations…pay close attention to the
directions of forces (F = ma)
• Remember that acceleration is also a vector
quantity…it has direction too!
Example
• A 25 kg bucket is lifted by a rope with an
upwards acceleration of 1.5 m/s2. Find the
tension in the rope.
Example
• A 50 kg girl in an elevator accelerates
downward at a rate of 3.0 m/s2. How much
force does the floor exert on the girl?
Example – forces
at angles
A 15 kg lawn mower is pushed with a force of 100.0N
directed along the handle at 40° to the horizontal.
a) If the frictional force on the mower is 30 N,
determine the acceleration.
b) Calculate the normal force on the mower
Friction
• Friction is a force that opposes the motion, or
tendency of motion, of an object.
• Friction is caused mostly by the
electromagnetic interactions of particles
within molecules at the surfaces of objects in
contact.
Two Basic Types of Friction
– Static friction
• exists between the surfaces of non-moving objects that
are trying to move
• Maximum static friction refers to the most force that
can be applied before the object starts to move
– Kinetic friction (also called sliding friction)
• Exists between the surfaces of objects when there is
relative motion between the objects
Coefficient of Friction
• The coefficient of friction is the slope of a
friction vs. normal force graph for two given
surfaces
– It is the ratio of the magnitudes of frictional force
to the normal force acting between two surfaces.
μ = f/FN
• Since this is a ratio of force to force, there are
no units for the coefficient of friction
• This is an experimentally determined value for
any two surface combinations.
Coefficient of Friction
• The coefficient for static friction (μs) is generally
larger than that of kinetic friction (μk) between
surfaces.
• A common substitution to be made in problem
solving will be f = μFN.
– If working with static friction, this equation represents a
maximum possible value.
Example – kinetic, constant speed
• The coefficient of friction between a 12 kg
wooden crate and the floor is 0.32. How
much force is needed to push this crate across
the floor at a constant speed?
Example – accelerated motion
• A 5.0 kg box is pushed horizontally across the
floor with a force of 25.0 N. If the coefficient
of kinetic friction is 0.24, what is the
acceleration of the box?