Download Quiz 1 Force and Vectors Static Equilibrium Problem Solving

Kinematics and Force
Problem Solving
8.01
W02D3
Next Reading Assignment:
W03D1
Young and Freedman: 4.1-4.6, 5.1-5.3
Today’s Reading Assignment:
W02D3
Young and Freedman: University Physics
(Review)5.1-5.3
Newton’s Second Law
Detailed Problem Solving
Strategy
Methodology for Newton’s 2nd Law
I.
Understand – get a conceptual grasp of the
problem
Sketch the system at some time when the system is in motion.
Draw free body diagrams for each body or composite
bodies:
Each force is represented by an arrow indicating the direction
of the force
Choose an appropriate symbol for the force
II. Devise a Plan
Choose a coordinate system:
•
Identify the position function of all objects and unit vectors.
•
Include the set of unit vectors on free body force diagram.
Apply vector decomposition to each force in the free body diagram:
Fi  ( Fx )i ˆi  ( Fy )i ˆj  ( Fz )i kˆ
Apply superposition principle to find total force in each direction:
ˆi : F total   F    F  
x
x 1
x 2
ˆj : F total   F    F  
y
y
y
1
2
kˆ : Fz total   Fz 1   Fz 2 
II. Devise a Plan:
Equations of Motion
• Application of Newton’s Second Law
F
total
 F1  F2   m a.
• This is a vector equality; the two sides are equal in
magnitude and direction.
ˆi :  F    F  
x 1
x 2
 m ax
ˆj :  F    F  
y
y
 m ay
kˆ :  Fz 1   Fz 2 
 m az
1
2
II. Devise a Plan (cont’d)
Analyze whether you can solve the system of
equations
•
Common problems and missing conditions.
•
Constraint conditions between the components of the
acceleration.
•
Action-reaction pairs.
•
Different bodies are not distinguished.
Design a strategy for solving the system of
equations.
III. Carry Out your Plan
Hints:
Use all your equations. Avoid thinking that
one equation alone will contain your
answer!
Solve your equations for the components of
the individual forces.
IV. Look Back
• Check your algebra
• Substitute in numbers
• Check your result
• Think about the result: Solved problems
become models for thinking about new
problems.
Group Problem: NonUniform Acceleration
An object has an acceleration given by
ax  b0  b1t
At t = 0 the object is located at x(t = 0)= x0 with a xcomponent of velocity v(t = 0) = v0. Find x(t).
Group Problem: Building 24
Elevator
A person of given mass m is standing on a scale in an elevator in Building 24.
Initially the elevator is at rest. The elevator then begins to ascend to the sixth
floor, which is a given distance h above the starting point. The elevator
undergoes an unknown constant acceleration of magnitude a for a known time
interval t1. Then the elevator moves at a constant velocity for a time interval 4t1 .
Finally the elevator brakes with a deceleration of the same magnitude as the
initial acceleration for a time interval t1 until stopping at the sixth floor. Assume
the gravitational constant is given as g. Find the magnitude of the acceleration.
Group Problem: Blocks and
Pulleys on Table
Two blocks rest on a frictionless horizontal surface. They are connected by 3
massless strings and 2 frictionless, massless pulleys as shown above. A force F
is applied to block 1. What is the resulting acceleration of block 1?
Next Reading Assignment:
W03D1
Young and Freedman: University Physics
(Review) 5.1-5.3
Experiment 1: Force and Motion