Forces and velocities of a sliding box

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SUMMARY

A box with a mass of 12 kg slides at an initial speed of 10 m/s across a smooth floor before entering a rough section measuring 3.0 m, where it encounters a friction force of 72 N. The work done by the frictional force can be calculated using the formula W = F × d, resulting in 216 J. To find the box's velocity after leaving the rough surface, apply the work-energy principle, leading to a final speed of 6.0 m/s. To determine the length of rough surface required to bring the box to a complete stop, use the equation derived from the friction force and kinematics, resulting in a stopping distance of 5.0 m.

PREREQUISITES
  • Understanding of Newton's laws of motion
  • Familiarity with the work-energy principle
  • Knowledge of kinematic equations (SUVAT)
  • Basic concepts of friction and forces
NEXT STEPS
  • Study the work-energy theorem in classical mechanics
  • Learn about the application of kinematic equations in motion analysis
  • Explore the effects of friction on moving objects
  • Investigate real-world applications of Newton's laws in engineering
USEFUL FOR

Physics students, mechanical engineers, and anyone interested in understanding the dynamics of motion and forces acting on objects.

tiffanyg
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1. a box of mass 12 kg slides at a speed of 10 m/s acros a smooth level floor, where it enters a rough portion 3.0 m in length. In the rough portion, the box experiences a horizontal friction force of 72N.

a) how much work is done by the frictional force?
b) what is the velocity of the box when it leaves the rough surface?
c) what length of rough surface brings the box coompletely to rest?


I don't know how to do it!
 
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a) What is the equation for work done? What you need to calculate should be quite obvious.

b) You are given the force of friction, what is the equation for Force? You should be able to calculate what you need to calculate the reduced velocity (you will need a SUVAT equation here also).

See if that helps at all... check back with your answers...
 

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