The work energy principle and power

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SUMMARY

The work-energy principle states that the net work done on an object equals its change in kinetic energy. In this discussion, a box with a mass of 25 kg is pulled 5 m across a smooth floor with a rope tension of 22 N at a 40-degree angle, facing a frictional force of 12 N. The calculated final speed using the formula $W_{net} = [22\cos(40) - 12]\cdot 5 = \dfrac{1}{2} \cdot 25 \cdot v_f^2$ yields a final speed of 1.39 m/s, which aligns with the textbook answer, correcting the initial miscalculation of 1.97 m/s.

PREREQUISITES
  • Understanding of the work-energy principle
  • Basic knowledge of trigonometry for resolving forces
  • Familiarity with Newton's laws of motion
  • Ability to perform calculations involving kinetic energy
NEXT STEPS
  • Study the derivation of the work-energy theorem
  • Learn how to resolve forces using trigonometric functions
  • Explore examples of frictional forces in physics problems
  • Practice calculating final velocities using different initial conditions
USEFUL FOR

Students studying physics, educators teaching mechanics, and anyone interested in understanding the application of the work-energy principle in real-world scenarios.

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A box of mass 25kg is pulled 5m across a smooth floor by rope with tension 22N. The rope is inclined at 40 degree to above the horizontal. There is a frictional force with average value 12N. The box starts from rest. Find the final speed.
Iam getting the ans 1.97m/s.
The textbook ans is 1.39 m/s
Pls help
 
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$W_{net} = [22\cos(40) - 12]\cdot 5 = \dfrac{1}{2} \cdot 25 \cdot v_f^2 \implies v_f = 1.39 \, m/s$
 
skeeter said:
$W_{net} = [22\cos(40) - 12]\cdot 5 = \dfrac{1}{2} \cdot 25 \cdot v_f^2 \implies v_f = 1.39 \, m/s$
Thank you!
 

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