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2-D Dynamics
Definition: Dynamics - the study of the causes of motion; the relation between motion and forces
Definition: Force - a push or a pull; an action capable of accelerating a body
Newton's 3 Laws of Motion
1st Law: An object with no force acting on it remains at rest or will move with a constant velocity in a straight line.
-a.k.a "Law of Inertia"
Definition: Inertia - tendency for a body to not change its motion
-mass is a measure of inertia
2nd Law: The acceleration of a body is directly proportional to the net force on it and inversely proportional to its mass.
net force  resultant force (in 2-D)
-acceleration is always in the same direction as the net force causing it
-unit of force is Newton or N (kg.m/s2)
3rd Law: When one object exerts a force on a second object, the second exerts a force on the first that is equal in
magnitude and opposite in direction.
-action/reaction forces
Definition: Normal Force (FN) - force exerted by one surface, perpendicular (or orthogonal) to that surface, on another
surface
-often a reaction force due to a body's weight
FN = - Fw = -mg
Definition: Equilibrium - net sum of all forces = 0 N
Definition: Equilibriant Force - one that is equal in magnitude, but opposite in direction to the resultant
Definition: Free-Body Force Diagram (FBFD) - a diagram that shows ALL forces acting on a body
-when an object is supported by ropes at 0o, each rope exerts only 1/2 the
weight of the object
-as the angle between ropes increases, force exerted by each rope increases
Definition: Tension (FT) - the condition of a body subjected to equal but opposite
forces which tend to stretch it
-"pulls" exerted by strings, rods, wires, etc. on bodies to which they are attached
-act along the direction of the string or rod
-measured in Newtons
Definition: Friction - force created when two surfaces interact with one another
-always opposite to the applied force's direction
2 Types of Friction
 Static - friction at rest
 Sliding (or Kinetic) - friction of motion
- static friction > sliding friction
F f  FN
- µ is coefficient of friction ---> measures nature of contact surfaces
Definition: Air Resistance - force of air on objects moving throughout it
-a.k.a "drag force"
-a friction-like force
Problem-Solving Tips for 2-D Dynamics:
1. Draw one or more free body diagrams.
2. Use Newton's 2nd and 3rd Laws of Motion for success.
Inclined Plane Problems (most provincial exams have at least one of these problems!)
Example:
Key ideas required for this problem:
A 25 kg mass is placed on a rough board that is at an angle 1. Magnitudes of Ff and the component of Fw parallel to the
of 9o from the horizontal. At this angle the mass slides
incline are equal.
down the incline with constant speed. Using the given
2. Magnitudes of FN and the component of Fw perpendicular
information, calculate the force of friction, the normal force,
to the incline are equal.
the coefficient of kinetic friction and the force required to
3. Use ideas #1 and #2 to write down and solve equations
pull the mass up the incline at constant speed.
using Newton's 2nd Law and the friction equation.
Example:
Assume that the same mass in the previous example is
placed on another incline, but with less friction. If this mass
accelerates down the incline at 1.05 m/s2, calculate Ff and
the coefficient of kinetic friction.
Key ideas to solving this problem:
1. The component of the weight parallel to the incline is
greater than the force of friction.
The difference in these two magnitudes is the net force.
Use Newton's 2nd Law to find
the force of friction.
2. Once friction is calculated, determine normal force and
then coefficient of friction.
Atwood's Machine Problems
Example:
A mass of 25 kg is placed on a frictionless table top and is
connected by a massless string to a 5.0 kg mass, running
through a frictionless pulley. Determine the acceleration of
the system and the tension in the string.
Example:
A 5.0-kg mass on an inclined plane (30.0o to the horizontal)
is attached to a pulley at the top of the incline and a 4.2-kg
mass hanging over the pulley. The coefficient of friction
between the 5.0-kg mass and the plane is 0.10. What is
the acceleration of the 5.0-kg mass?
Key ideas:
1. Draw a free body diagram for the system as a WHOLE
and then determine the acceleration.
2. Draw a free body diagram for either mass to determine
tension (tension is the same
throughout the string!).
Key ideas:
1. Draw FBFD.
2. Problem combines inclined plane and Atwood’s
Machine.
Equilibrium
-think of a "balancing" of an object
-all forces vectors and torques add to 0
2 types of equilibrium:
1. Translational Equilibrium
2. Rotational Equilibrium
Translational Equilibrium
Definition: Static - not moving
Definition: Translate - to move through space without rotating
Definition: Translational Equilibrium - the condition where the vector sum of all forces acting on a body is 0 N or...
Definition: Statics - the branch of physics that deals with the calculation of forces acting on bodies which are in
equilibrium
Example: A 150-N weight is supported as shown in the diagram below.
Calculate the tension in each wire.
Method #1 (using vector addition)
Method #2 (using vector resolution)
Rotational Equilibrium
Definition: Torque ( ) - the product of the lever (or moment) arm and the applied force
Equation for torque...
F is the applied force
d is the distance from the rotation point to the point on the object where the force is applied
is the angle between the object and the line along which the force acts …
is measured in
-same unit as work but torque is not energy and therefore must remain as
Definition: lever arm - the perpendicular distance from the line along which the force acts to the point of rotation
Definition: moment - same as torque
Definition: moment arm - same as lever arm
Definition: fulcrum - the support about which a rigid object is free to rotate
Definition: center of gravity - the point in a rigid object where the force of gravity can be considered to act OR the point at
which the weight of a rigid object can be thought to be concentrated
Definition: Rotational Equilibrium - the condition where the vector sum of all torques acting on a rigid body is zero
Definition: Static Equilibrium - the condition where the vector sum of all forces AND torques acting on a rigid body are 0
-a body in static equilibrium is in both translational and rotational equilibrium
Example: A uniform metal rod 4.5 m long has a weight of 550 N and supports at the left hand end of 200 N and at the right
hand end a weight of 375 N. Where along the rod must a fulcrum be placed and what upward force must the fulcrum
provide if the rod is to be in static equilibrium?
Example: A uniform beam 6.0 m long, with a weight of 750 N, is supported by two pillars at each end. A weight of 920 N is
placed on the beam 4.5 m from the left hand end of the beam.
Calculate the force exerted on each pillar.
Example: A uniform bar 6.0 m long with a weight of 560 N is attached by a hinge to a wall at 30 o. The bar is free to rotate
about the hinge. The bar supports a 350 N weight which is attached 2.0 m from its end.
Calculate the tension in the supporting wire and the reaction force of the wall on the bar.