What is the maximum spring stretch for a resting box on an inclined plank?

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SUMMARY

The maximum spring stretch for a resting box on an inclined plank can be determined using the principles of static friction and Hooke's Law. Given a mass of 2.12 kg, an incline angle of 64.5°, a spring constant of 15.2 N/m, and a coefficient of static friction of 0.243, the calculations involve balancing the forces acting on the box. The normal force is calculated as N = mg cos(θ), and the static friction force is Fs = usN. The correct application of these equations will yield the maximum stretch of the spring while keeping the box at rest.

PREREQUISITES
  • Understanding of Newton's laws of motion
  • Familiarity with Hooke's Law (F = -kx)
  • Knowledge of static friction and its coefficient
  • Basic trigonometry for resolving forces on an inclined plane
NEXT STEPS
  • Calculate the normal force using N = mg cos(θ)
  • Determine the static friction force with Fs = usN
  • Apply Hooke's Law to find the maximum stretch of the spring
  • Explore examples of inclined plane problems in physics for further practice
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and inclined planes, as well as educators looking for practical examples of static friction and spring dynamics.

Lnav1982
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I am having problems with this question:

An m = 2.12 kg box rests on a plank that is inclined at an angle of q = 64.5° above the horizontal. The upper end of the box is attached to a spring with a force constant of 15.2 N/m.

If the coefficient of static friction between the box and the plank is 0.243, what is the maximum amount the spring can be stretched and the box remain at rest?

Thank you
 
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You need to show some work or describe what you are thinking or where you are stuck.:wink:
 
Ok, well I tried using F=-Kx and solve for x but that didnt work because I didnt use the other values. Then using Fs=usN after finding N which I think was = mgcos(theta) to find Fs, then plug that into F=-kx. But this didnt work as well. What am I doing wrong? Thanks
 

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