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SPH 3U
Day 8 – Newton’s Second Law of Motion (2.4)
Goal: To introduce Newton’s second law of motion, its equation, and how to solve problems
involving this law.
Part 1: History Leading to the Law
Recall Newton’s First Law – what is it? What does it mean?
History
* Newton spent many years of his life trying to understand the motion of objects. After many
experiments and a careful analysis of the ideas of Galileo, Descartes, and others, Newton
stated a simple mathematical relationship that models the motion of an object. The following
are some of the questions he wrestled with:

What happens to an object if the net force is not zero?

What is the relationship between the force applied and the acceleration of the object?

What is the relationship between acceleration and the mass of the object?
Relating Acceleration and Net Force
When a soccer player kicks a ball on the ground, the horizontal forces acting on the ball are the
applied push force, friction with the ground and air resistance. As long as the applied push
force is greater in magnitude than the sum of the forces of friction and air resistance acting on
the ball, the net force on the ball acts forward.
Also, the harder the kick, the greater will be the forward net force on the soccer ball and as a
result the acceleration of the ball will be greater.
Summary:
* If the net force is not zero, the object will accelerate in the direction of the net force.
* The greater the force, the greater the acceleration (a linear relationship).
Therefore, a  F net
Relating Acceleration and Mass
If you apply the same force to objects of different masses, how do their accelerations relate?
Think about kicking a soccer ball with the same force as kicking a medicine ball. Which ball
would accelerate faster?
Summary
Through experimentation, it can be shown that the magnitude of acceleration is inversely
proportional to the objects mass.
a
1
m
SPH 3U
Part 2: Newton’s Second Law
Newton’s Second Law of Motion
If the net external force on an object is not zero, the object accelerates in the direction of
the net force, with magnitude of acceleration proportional to the magnitude of the net force
and inversely proportional to the object’s mass.
What is the mathematical equation for Newton’s Second Law?
Combining the relationships listed earlier,
F net
m
So, F net  ma
a
Does this equation agree with Newton’s first law?
Part 3: Apply it!
Handout: Applying Newton’s Second Law
Example 5.1 pg. 134 Physics Source
A lacrosse player exerts an average net horizontal force of 2.8 N [forward] on a 0.15 kg
lacrosse ball while running with it in the net of his stick. Calculate the average horizontal
acceleration of the ball while in contact with the lacrosse net.
Example 5.2 pg. 136 Physics Source
Athlete A, who has a mass 70 kg, and athlete B, who has a mass of 75 kg, are racing in a canoe,
which has a mass of 20 kg. Using paddles, Athlete A exerts a force of 400 N [forward] and B
exerts a force of 420 N [forward] on the canoe. The magnitude of water resistance is 380 N.
Calculate the initial acceleration of the canoe.
HW – pg. 73 #1ac, 2ac, 3-6
SPH 3U
Applying Newton’s Second Law
Example 1:
A lacrosse player exerts an average net horizontal force of 2.8 N [forward] on a 0.15 kg
lacrosse ball while running with it in the net of his stick. Calculate the average horizontal
acceleration of the ball while in contact with the lacrosse net.
Example 2:
Athlete A, who has a mass of 70 kg, and athlete B, who has a mass of 75 kg, are racing in a
canoe, which has a mass of 20 kg. Using paddles, Athlete A exerts a force of 400 N [forward]
and B exerts a force of 420 N [forward] on the canoe. The magnitude of water resistance is
380 N. Draw a FBD and calculate the acceleration of the canoe.