# Chapter Study Guide; Chapter 4 by LeeGreenwood

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```									Chapter Study Guide; Chapter 4
Dynamics: Newton’s Laws of Motion

Chapter Goals
After studying the material of the chapter, the student should be able to:
 State Newton’s three laws of motion and give examples that illustrate each law.
 Explain what is meant by the term net force.
 Use the methods of vector algebra to determine the net force acting on an object.
 Define each of the following terms: mass and weight, and distinguish between mass and
weight.
 Identify the SI units for force, mass, and acceleration.
 Draw an accurate free body diagram locating each of the forces acting on an object or a
system of objects.
 Use free body diagrams and Newton’s laws of motion to solve word problems.

New Vocabulary

   Dynamics

   Net force

   Newton’s first law

   Newton’s second law

   Newton’s third law

   Weight

   Friction

   Coefficient of friction

   Normal Force
Principles of Physics

Newton’s Laws of Motion Newton’s three laws of motion describe the nature of forces and their effect on
mass. Forces are the pushes and pulls that are the cause for acceleration. Forces are vectors. As with 2D
motion, when forces act in two dimensions, the forces can be broken into perpendicular components and
the motion which results from the component forces can be studied separately. Forces add like vectors, and
the sum of all forces on an object is known as the net force.
The acceleration of an object is proportional to the net force and in the same direction as the net force. The
acceleration is inversely proportional to the mass of the object.
By their nature, forces are vectors that come in pairs. These paired forces act on different objects, point in
opposite directions, but have the same magnitude.
Force of Gravity The force of gravity which acts on an object near the surface of the Earth is also known
as the weight of the object. The force of gravity always acts to pull the object toward the center of the earth
and has a magnitude of 9.8m/s2 times the mass of the object.
Normal Force The normal force is an adaptive contact force that acts between two objects. The direction
of the normal force is perpendicular to the plane of contact and the magnitude can vary from zero to any
value depending on other forces acting perpendicular to the plane of contact.
Tension Forces Tension is a force transmitted by a rope. This force is like a contact force, but is a “pull”
rather than a “push”. If the rope is light enough to be considered massless, the tension is the same on both
sides of a rope.
Friction Forces Friction is a contact force that acts parallel to the surface of contact between two objects.
The magnitude of the force depends on the relative motion of the surfaces, the nature of the surfaces, and
the normal force between the surfaces. When the objects are at rest, static friction takes the appropriate
value to balance out other forces which act parallel to the surface of contact. If the sum of the other forces
exceeds a maximum value μS times FN, the force of static friction is overcome and the object will
accelerate. When the objects are in motion, kinetic friction takes a constant value of μ S times FN and points
opposite the direction of motion.

Equations

Formula                           Variables                Descriptions
Newton’s                        
first law         Net F  0 or  F  0
Newton’s               
second law       a  F /m                or
         
 F  m a
Newton’s                 
third law        F12   F 21
        
Weight
w  mg
F fr    F N
Force of
friction

Dimensional Analysis
Problem Solving Strategies

Free-body diagrams A free-body diagram is a sketch that
includes all of the forces acting on a single object to be
studied. The axes of the reference frame are included and any
vectors which do not point along the axes are broken into
components. A net force is typically included. Each object                                   FNet
being studied should have a separate free body diagram.

Solving for the net force If the magnitude and direction of all
forces acting on an object are known, the net force can be
found as the vector sum of all the forces. Break the vectors
into components along the appropriate axes, add the
components, and reconstruct the net force vector.

Solving for an adaptive force The normal force and the force of static friction are adaptive forces; they
can change their magnitude to maintain an object in its state of rest. To solve for the magnitude of this
force, find the total of all parallel (perpendicular) forces. The force of static friction (normal force) is the
opposite of this total.

Solving systems coupled by a string If two objects are connected by a string, they will have the same
acceleration. That is, the net force divided by the mass for each object must be the same.

Solving systems of equations If you have several unknown quantities that are related by a system of
equations, it is necessary to have an equal number of unknowns and equations. Isolate one unknown
quantity and substitute the expression into other equations to eliminate the unknown quantity. Repeat until
one unknown value is known.

Solving for the dynamics of a kinematics problem If a situation includes information about the motion
of an object and you wish to solve for the forces acting on an object, the way to relate kinematics (position,
velocity, acceleration) to dynamics (forces) is through Newton’s 2 nd law. The net force is proportional to
the acceleration.
Chapter Summary

(Use the space below to summarize the chapter.)
Sample Problems

1.   What average force is required to bring a 1500 kg car to rest from a speed of 100km/h within a
distance of 55m?

2.   A box of mass 10kg is resting on the smooth (frictionless) horizontal
surface of a table. (a) Determine the weight of the box and the
normal force exerted on it by the table. (b) Now your frident pushes
down on the box with a force of 40N. Again, determine the normal
force exerted on the box by the table. (c) If your pull upward on the
box with a force of 40n, what is the normal force?

3.   Calculate the sum of the two forces exerted on the boat by the
two workers?
4.   Two boxes, A and B, are connected by a cord and rest on a smooth (frictionless) table. The boxes
have masses of 12kg and 10kg. A horizontal force FP of 40N is applied to the 10kg box, as
shown. Find the acceleration of each box and the tension in the cord connecting the boxes.

5.   A mover is trying to lift a piano up to a second story apartment. He
is using a rope looped over two pulleys as shown. What force must
he exert on the rope to slowly lift the piano’s 2000N weight?

6.   A 10kg box rests on a horizontal floor. The coefficient of
static friction is 0.40 and the coefficient of kinetic friction is
0.30. Determine the force of friction acting on the box if a
horizontal external applied force FA is exerted on it of
magnitude (a) 0 (b) 10N (c) 20N, (d) 38N, and (E) 40 N.
What is the acceleration of the box in each case?
7. Two boxes are connected by a cord running over a
pulley. The coefficient of kinetic friction between box A
and the table is 0.20. We ignore the mass of the cord and
the pulley and any friction in the pulley, which means we
can assume that a force applied to one end of the cord will
have the same magnitude of the other end. We with to
find the acceleration of the system which will have the
same magnitude for both boxes assuming the cord doesn’t
stretch. As box B moves down, box A moves to the right.

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