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Dynamics – Newton’s 2nd Law
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Unit #3 Dynamics

Objectives and Learning Targets
 Verify Newton’s Second Law for linear
motion.
 Describe how mass and weight are related.
Unit #3 Dynamics
Newton’s 2nd Law
 Newton’s 2nd Law of Motion may be the most important
principle in all of modern-day physics because it explains exactly
how an object’s velocity is changed by a net force. In words,
Newton’s 2nd Law states that “the acceleration of an object is
directly proportional to the net force applied, and inversely
proportional to the object’s mass.”
 In equation form, you can express Newton’s 2nd Law as:
Unit #3 Dynamics
Newton’s 2nd Law
 It’s important to remember that both force and acceleration are
vectors. Therefore, the direction of the acceleration, or the
change in velocity, will be in the same direction as the net
force. You can also look at this equation from the opposite
perspective. A net force applied to an object changes an
object’s velocity (produces an acceleration), and is frequently
written as:
Unit #3 Dynamics
Newton’s 2nd Law Steps
You can analyze many situations involving both balanced and
unbalanced forces on an object using the same basic steps.
1. Draw a free body diagram.
2. For any forces that don’t line up with the x- or y-axes, break
those forces up into components that do lie on the x- or y-axis.
3. Write expressions for the net force in x- and y- directions. Set the
net force equal to ma, since Newton’s 2nd Law tells us that Fnet=ma.
4. Solve the resulting equations.
Unit #3 Dynamics
Sample Problem #1
Question: A force of 25 newtons east and a force of 25
newtons west act concurrently on a 5-kilogram cart.
Find the acceleration of the cart.
Step 1: Draw a free-body diagram (FBD).
Step 2: All forces line up with x-axis. Define east as
positive. Step 3: Fnet = 25N − 25N = ma Step 4: 0 = ma
⇒ a=0
Answer: The acceleration must be 0 m/s2.
Unit #3 Dynamics
Sample Problem #2
Question: A 0.15-kilogram baseball moving at 20
m/s is stopped by a catcher in 0.010 seconds. Find
the average force stopping the ball.
Answer: First write down what information is
given and what you’re asked to find. Define the
initial direction of the baseball as positive.
Unit #3 Dynamics
Sample Problem #2
Use kinematics to find acceleration.
The negative acceleration indicates the
acceleration is in the direction opposite that of
the initial velocity of the baseball. Now that you
know acceleration, you can solve for force using
Newton’s 2nd Law.
Unit #3 Dynamics
Sample Problem #3
 Question: What is the weight of a 2.00-
kilogram object on the surface of Earth?
 Answer: Weight is the force of gravity on an
object. From Newton’s 2nd Law, the force of
gravity on an object (Fg), is equal to the mass
of the object times its acceleration, the
acceleration due to gravity (9.81 m/s2),
which you can abbreviate as g.
Unit #3 Dynamics
Sample Problem #4
 Question: A 25-newton horizontal force
northward and a 35-newton horizontal force
southward act concurrently on a 15-kilogram
object on a frictionless surface. What is the
magnitude of the object’s acceleration?
 Answer:
Unit #3 Dynamics
Newton’s 2nd Law (Bad Idea)
Unit #3 Dynamics