Math Problem Statement

A block is pulled by a force of 177 N directed at a 85.0° angle from the horizontal. What is the x-component of the force acting on the block?

Solution

To find the x-component of the force acting on the block, we can use the formula:

Fx=Fcos(θ)F_x = F \cdot \cos(\theta)

Where:

  • FxF_x is the x-component of the force,
  • F=177NF = 177 \, \text{N} is the total force applied,
  • θ=85\theta = 85^\circ is the angle between the force and the horizontal.

Now, I'll calculate the x-component.The x-component of the force acting on the block is approximately 15.43N15.43 \, \text{N}.

Would you like further details or have any questions?

Here are 5 related questions:

  1. What is the y-component of the force acting on the block?
  2. How would the x-component change if the angle were 60° instead of 85°?
  3. What is the resultant force on the block when considering both x and y components?
  4. How do friction forces impact the movement of the block in this situation?
  5. What if the block was pulled on an inclined plane—how would the components change?

Tip: Always use the cosine of the angle to calculate the horizontal (x) component and the sine for the vertical (y) component in force problems.

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Math Problem Analysis

Mathematical Concepts

Trigonometry
Vector Decomposition

Formulas

F_x = F * cos(θ)

Theorems

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Suitable Grade Level

High School