Math Problem Statement

You push a 200 kg boulder up a hill by applying a 90 N force up and to the left. Which of the following is the correct force diagram?

Solution

The problem states that you are pushing a 200 kg boulder up a hill with a force of 90 N applied up and to the left. Based on the question and the diagram choices:

  1. The correct diagram must depict a 90 N force applied at an angle up and to the left, rather than directly horizontal or vertical.
  2. The 200 kg label indicates the object's weight, which is not part of the force direction in this case but still represents its mass.

Correct Answer:

The middle diagram shows the force 90 N at an upward and leftward angle, which aligns with the problem's description.

Would you like a breakdown of why the other options are incorrect or more details about force diagrams? Here are five related questions to consider:

  1. How is the resultant force calculated when multiple forces act on an object at angles?
  2. How does the force of gravity factor into pushing an object up a slope?
  3. What additional forces (e.g., friction, normal force) might act on the boulder in this scenario?
  4. How do you calculate the acceleration of the boulder if only this 90 N force acts on it?
  5. What is the relationship between the angle of the applied force and its effectiveness in moving the boulder?

Tip: Always resolve forces into components (e.g., horizontal and vertical) when analyzing force diagrams!

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Math Problem Analysis

Mathematical Concepts

Force diagrams
Vector components
Newton's Laws of Motion

Formulas

Force components: F_x = F * cos(θ), F_y = F * sin(θ)
Newton's second law: F = ma

Theorems

Vector resolution theorem
Newton's second law of motion

Suitable Grade Level

Grades 9-12