Applying
Newton’s Laws
of Motion
Solving Dynamics
Problems
1. Read the problem carefully and check the
definitions of any unfamiliar words.
2. Draw a system diagram. Label all relevant
information, including any numerical quantities
given. (For simple situation, you can omit this
step.)
3. Draw a FBD of the object (or group of objects) and
label all the forces. Choose the +x and +y
directions. (Try to choose one of these directions
as the direction of the acceleration.)
Solving Dynamics
Problems
4. Calculate the label and x- and y- components of all the
forces on the FBD.
5. Write the second-law equation(s), ΣFx=max
and/or ΣFy=may, and substitute for the variables on
both sides of the equation(s).
6. Repeat steps 3 to 5 for any other objects as required.
7. Solve the resulting equation(s) algebraically.
8. Check to see if your answers have appropriate units, a
reasonable magnitude, a logical direction (if required),
and the correct number of significant digits.
Objects in Equilibrium
• Equilibrium is a state in which an object has
no net force acting on (ie. At rest or a
constant velocity with no acceleration).
• Mathematically, an object is equilibrium
when ∑F = 0, or, when you break down the
forces down into their components, both
∑Fx = 0 and ∑Fy = 0
Accelerating Objects
• An object that is not in equilibrium
accelerates in some direction according to
Newton’s second law.
∑F = ma
Example 1
An astronaut on the surface of Mars finds that
a rock accelerates at 3.6 m/s2 when dropped.
The astronaut also finds that a force scale
reads 260 N when the astronaut steps on it.
a) What is the astronaut’s mass as
determined on the surface of Mars?
b) What would the force scale read if the
astronaut stepped on it on Earth?
Example 2
An 8.0 kg mass on a frictionless table is accelerated by a
2.0 kg mass hanging from the table as shown.
(a) Draw a FBD for each mass with properly labeled
forces
(b) Calculate the acceleration of the blocks.
(c) Calculate the tension in the rope
Example 3
In a tug-of-war match, you can pull on a rope with a
maximum force of 2.00 x 102 N. Your opponent can pull
with a force of 2.80 x 102 N. You are allowed to use one
pulley and one fixed support, set up as shown. What is
the maximum angle you can use that well allow you to at
least tie?