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 LawI. 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:

Apply superposition principle to find total force in each direction:

ˆ ˆ ˆ( ) ( ) ( )i x i y i z iF F F= + +F i j kr

( ) ( )( ) ( )( ) ( )

total

1 2

total

1 2

total

1 2

ˆ :

ˆ :

ˆ :

x x x

y y y

z z z

F F F

F F F

F F F

= + +

= + +

= + +

i

j

k

L

L

L

II. Devise a Plan: Equations of Motion

• Application of Newton’s Second Law

• This is a vector equality; the two sides are equal in magnitude and direction.

total1 2 .m= + +⋅⋅⋅=F F F a

r r r r

( ) ( )( ) ( )( ) ( )

1 2

1 2

1 2

ˆ :

ˆ :

ˆ :

x x x

y y y

z z z

F F ma

F F ma

F F ma

+ + =

+ + =

+ + =

i

j

k

L

L

L

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: Non-Uniform Acceleration

An object has an acceleration given by

 

  At t = 0 the object is located at x(t = 0)= x0 with a x-component of velocity v(t = 0) = v0. Find x(t).

 

 

0 1xa b b 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