Applying Newton's Laws - Notes

Applying Newton's Laws

Solving a System

  • Focusing on multiple objects:

  • When dealing with multiple objects in a system, we apply a series of steps to analyze the forces acting on each object effectively.

Steps to Solve a Multiple Object Problem

  1. Draw Free Body Diagrams (FBDs):

  • Create an individual FBD for each object in the system. This helps visualize the forces acting on each object.

  1. Connect Individual FBDs:

  • Connect the individual FBDs to represent the system.

  • If the objects are connected by ropes or strings, ensure that tensions are indicated between them, possibly requiring rotation of the FBD for clarity.

  1. Net Force Equation:

  • Construct a net force equation to assess if there is an overall net force acting on the system, which can lead to acceleration.

  1. Solve for Unknowns:

  • After determining the net force, return to the individual FBDs to solve for any unknown variables, such as tension or acceleration.

Example Problems

Example 1

  • Given:

  • Mass M = 5.0 kg, mass m = 1.0 kg

  • External force = 80.0 N

  • Friction assumed to be negligible

  • Tasks:
    a) Calculate the acceleration of the system.
    b) Determine the tension between M and m.

Example 2

  • Conditions:

  • Add third mass N = 3.0 kg to the previous setup.

  • Tasks:
    a) Find the acceleration of the system.
    b) Calculate tensions between M and m, and between m and N.

Practice Problem 1

  • Setup:

  • M = 5.0 kg, m = 1.0 kg, N = 3.0 kg

  • External force = 75.0 N

  • Friction on N = 8.2 N, friction on m = 4.1 N

  • Tasks:
    a) What is the acceleration of the system?
    b) What are the tensions between M and m, and between N and m?

Example 3

  • Given:

  • m1 = 8.0 kg, m2 = 14.0 kg

  • No friction between m1 and the surface

  • Tasks:
    a) Determine the acceleration of the system.
    b) Find the tension in the rope.

Example 4

  • Conditions:

  • m1 = 7.5 kg, m2 = 12.0 kg

  • Friction force = 22 N between m1 and the surface

  • Task:
    a) Find the acceleration of the system.
    b) Calculate the tension in the rope.

Practice Problem 2

  • Scenario:

  • Two blocks connected by a string over a frictionless pulley:

  • Block A experiences kinetic friction of 5.4 N

  • Masses m1 = 2.3 kg, m2 = 3.5 kg

  • Tasks:
    a) Calculate the magnitude of the acceleration of the blocks.
    b) Calculate the magnitude of the tension in the string.