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 1An 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 3In 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?