Math Problem Statement

a box is being pushed to the right with the force of 10N. There is a frictional force of 4N on the box. The box gets pushed over a distance of 10m. Determine the work due to the person pushing.

Solution

To determine the work done by the person pushing the box, we can use the formula for work:

Work=Force×Distance×cos(θ)\text{Work} = \text{Force} \times \text{Distance} \times \cos(\theta)

where:

  • Force is the force applied by the person,
  • Distance is the distance over which the force is applied,
  • θ\theta is the angle between the force and the direction of motion.

In this problem:

  • The applied force is 10N10 \, \text{N},
  • The distance over which the box is pushed is 10m10 \, \text{m},
  • The angle θ\theta is 00^\circ because the force is applied in the direction of motion.

Since cos(0)=1\cos(0^\circ) = 1, the work done by the person is:

Work=10N×10m×1=100J\text{Work} = 10 \, \text{N} \times 10 \, \text{m} \times 1 = 100 \, \text{J}

Answer:

The work done by the person pushing the box is 100J100 \, \text{J}.

Would you like to explore more details about this solution or have any questions? Here are some related questions that might be helpful:

  1. How do you calculate the net work done on the box, taking friction into account?
  2. What is the significance of the angle θ\theta in calculating work?
  3. How does friction affect the net force on the box in this scenario?
  4. If the person applied a force at an angle, how would the work calculation change?
  5. What would happen to the work done if the distance was doubled?

Tip: When calculating work, always ensure that the force and distance are in the same direction, or consider the angle between them if they’re not.

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Math Problem Analysis

Mathematical Concepts

Physics
Work and Energy

Formulas

Work = Force × Distance × cos(θ)

Theorems

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Suitable Grade Level

Grades 9-12