Math Problem Statement
The drawing shows a person, mass = 61 kg, doing push-ups. Draw a free-body-diagram and find the force exerted by the floor on each foot (in SI unit), assuming that the person holds this position. Enter only the number of your answer with 3 or more significant figures.
Solution
To solve this problem, let's break down the forces and solve for the force exerted by the floor on each foot:
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Understanding the setup: The person is in a static position, so the sum of the forces and torques must be zero.
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Free-Body Diagram:
- The person's weight () acts downward at the center of mass.
- There are reaction forces at the hands () and the feet ().
- Since the person is in static equilibrium, the upward forces () must balance the downward weight ().
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Setting up equations:
- Let be the distance from the feet to the hands.
- Let be the distance from the feet to the center of mass.
- Using torque equilibrium around the feet to eliminate , we get:
- Then using vertical force balance to find .
Let’s assume typical values for and , or if these are in the problem image, provide them for exact calculations.
After solving, let me know if you need a specific answer calculation or assumptions refinement.
Would you like the full step-by-step calculations, or do you have specific values from the diagram to share? Here are some further explorative questions to expand your understanding:
- How would changing the position of the hands affect the force distribution?
- What happens to the force on each foot if the person shifts their weight forward?
- How could this force analysis change for a heavier person?
- If friction at the hands is negligible, how does that impact equilibrium?
- Why does torque balance help us find individual forces in static equilibrium?
Tip: Always consider using torque equilibrium around one point to reduce unknowns when analyzing static systems.
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Math Problem Analysis
Mathematical Concepts
Static Equilibrium
Torque and Force Balance
Free-Body Diagrams
Formulas
Sum of forces in static equilibrium: ΣF = 0
Sum of torques in static equilibrium: Στ = 0
Weight force: W = mg
Theorems
Static Equilibrium Theorem
Suitable Grade Level
Grades 11-12
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