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:
where:
- Force is the force applied by the person,
- Distance is the distance over which the force is applied,
- is the angle between the force and the direction of motion.
In this problem:
- The applied force is ,
- The distance over which the box is pushed is ,
- The angle is because the force is applied in the direction of motion.
Since , the work done by the person is:
Answer:
The work done by the person pushing the box is .
Would you like to explore more details about this solution or have any questions? Here are some related questions that might be helpful:
- How do you calculate the net work done on the box, taking friction into account?
- What is the significance of the angle in calculating work?
- How does friction affect the net force on the box in this scenario?
- If the person applied a force at an angle, how would the work calculation change?
- 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
-
Suitable Grade Level
Grades 9-12