Which Mass Travels Further When Stopped by the Same Force?

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SUMMARY

The discussion centers on the physics problem of determining which mass, a 4.0 kg object moving at 2.0 m/s or a 1.0 kg object moving at 4.0 m/s, travels further when subjected to the same constant braking force. The conclusion is that both masses travel the same distance before stopping, as derived from the equation D = (Vf^2 - Vi^2)M/(2F). This formula shows that the distance D is directly proportional to mass M and inversely proportional to the braking force F, leading to the same stopping distance for both objects due to their equal kinetic energy when the braking force is applied.

PREREQUISITES
  • Understanding of Newton's laws of motion
  • Familiarity with kinetic energy concepts
  • Knowledge of basic algebra for rearranging equations
  • Proficiency in applying the equations of motion, specifically Vf^2 = Vi^2 + 2AD
NEXT STEPS
  • Study the principles of kinetic energy and its relation to work done by forces
  • Learn about the equations of motion and their applications in physics problems
  • Explore the concept of braking force and its impact on different masses
  • Investigate real-world applications of these principles in vehicle dynamics
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Students of physics, educators teaching mechanics, and anyone interested in understanding the principles of motion and forces in practical scenarios.

astro_kat
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Forces velocity & position?!?

A 4.0 kg mass is moving with speed 2.0 m/s A 1.0 kg mass is moving with a speed of 4.0 m/s. Both objects encounter the same constant breaking force, and are brought to rest. Which object travels the greater distance before stopping?

A. the 1.0 kg mass
B. the 4.0 kg mass
C. Both travel the same distance
D. Cannot be determined

*answer is C, why?!?*
 
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ok you know the equation Vf^2 = Vi^2 +2AD. Rearrange it to solve for D

D = (Vf^2 - Vi^2)/(2A)
And A (acceleration) = F/M

So D = (Vf^2 - Vi^2)M/(2F)

Plug in the givens for Vi and M, (F is constant) and you'll get D = -8F for both
 
The kinetic energy is equal to the braking force times the distance travelled. They both have the same kinetic energy.
 

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