Work, energy, power tennis ball problem

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SUMMARY

The discussion centers on calculating the work done by a force on a tennis ball, described by the function F(x) = 2x + 5, as it moves from -2.5 m to 2.4 m. The correct approach involves integrating the force function over the specified distance, rather than simply multiplying force by distance. The integration from x = -2.5 to x = 2.4 is essential to accurately determine the work done, which was initially miscalculated by the user.

PREREQUISITES
  • Understanding of basic calculus, specifically integration.
  • Familiarity with Newton's laws of motion.
  • Knowledge of work-energy principles in physics.
  • Ability to interpret force functions and their graphical representations.
NEXT STEPS
  • Study the process of definite integration in calculus.
  • Learn about the work-energy theorem in physics.
  • Explore applications of force functions in real-world scenarios.
  • Practice problems involving integration of force functions to calculate work.
USEFUL FOR

Students studying physics, particularly those focusing on mechanics, as well as educators looking for examples of applying calculus to physical problems.

ferrariistheking
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Homework Statement


A force applied to a tennis ball is described by the function

F(x) = 2x + 5, with the force in Newtons and the position in meters.

How much work does the force do on a tennis ball as it moves from -2.5 m to a new position of 2.4 m?

Homework Equations


F(x)= 2x+5
force x distance= work

The Attempt at a Solution


I found the distance from -2.5m to 2.4m which is 4.9m.

Then I plugged -2.5m into x for the function which is 0.

I then plugged in 2.4m into the function which is 9.8.

With 9.8, I multiplied it by 4.9 m getting 48.02 which is incorrect

Can anybody find my error? Thanks!
 
Physics news on Phys.org
You need to integrate F(x) from x=-2.5 to x=2.4.
 
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Likes   Reactions: ferrariistheking
andrewkirk said:
You need to integrate F(x) from x=-2.5 to x=2.4.
ohhhh I see. Thanks for the help once again.
 

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