Math Problem Statement

Identify which of the objects do not have a net force acting on them based on the motion data collected for 9 different objects, including their positions, velocities, and accelerations.

Solution

The table in the image provides the motion data for nine different objects, including their positions, velocities, and accelerations over time. The problem asks to identify which of the objects do not have a net force acting on them. To determine this, we need to analyze the acceleration values of each object since Newton's second law states that an object with no net force has zero acceleration.

Analysis of Acceleration Columns:

  • Acceleration of object 7: 69 m/s² (non-zero, so there is a net force).
  • Acceleration of object 8: 0 m/s² (no net force since acceleration is zero).
  • Acceleration of object 9: Varies between -23 m/s² and -28 m/s² (non-zero, so there is a net force).

Thus, the only object that has no net force acting on it is object 8.

Would you like a detailed explanation of how I reached this conclusion, or do you have any additional questions?


Here are 5 related questions for further exploration:

  1. How does Newton's second law relate force, mass, and acceleration?
  2. How can you calculate net force from an object's acceleration and mass?
  3. Why is it significant that object 8 has zero acceleration?
  4. What is the difference between constant velocity and constant acceleration?
  5. How would the position of an object with zero acceleration change over time?

Tip: If an object has zero acceleration, it either remains at rest or moves with constant velocity, as there is no net force acting on it.

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Math Problem Analysis

Mathematical Concepts

Newton's Second Law
Acceleration
Net Force

Formulas

F = ma (Force = Mass * Acceleration)

Theorems

Newton's Second Law of Motion

Suitable Grade Level

Grades 9-12