Solving the Stopping Force of an Arrow Shot into Hay

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SUMMARY

The discussion focuses on calculating the average stopping force acting on an arrow of mass 20 grams shot horizontally into a bale of hay at a velocity of 60 m/s, which penetrates 20 cm before stopping. The correct average stopping force is determined to be 180 N, achieved through the application of Newton's second law (F = ma) rather than work-energy principles. The initial miscalculation of 360 N stemmed from a misunderstanding of the work done by the stopping force.

PREREQUISITES
  • Understanding of Newton's second law (F = ma)
  • Basic knowledge of kinematics and motion equations
  • Familiarity with units of mass and force (grams to kilograms, Newtons)
  • Concept of work and energy in physics
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  • Review the principles of Newton's laws of motion
  • Study kinematic equations and their applications in solving motion problems
  • Learn about the conversion of units, particularly mass from grams to kilograms
  • Explore the concept of work-energy theorem and its implications in physics
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This discussion is beneficial for physics students, educators, and anyone interested in understanding the dynamics of projectile motion and force calculations.

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An arrow of mass 20 grams is shot horizontally into a bale of hay with a velocity of 60 m/s. It penetrates a debpt of 20 CM before stopping.

What is the average stopping force acting on the arrow?


I've been doing

W = -F*D
W = -(ma)*d

I'm finding a by using a kinematic equation, v (final ) ^2 = v (initial ) ^ 2 + 2 a (delta) x.

The answer I'm getting is 360 N, but that is not the correct answer. Any ideas?
 
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I'm an idiot. Never mind. I misread to work done by the stopping force. 180 is the right answer for those that care. There is no need for work at all, just a simple F = ma problem.
 
If misreading the question makes one an idiot, I'm an idiot many times over for trasngressions as an undergrad :(
 

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