How to Calculate the Minimum Force Needed to Move a Box on a Ramp with Friction?

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SUMMARY

The minimum force required to move a 3.00 kg box on a ramp inclined at 20 degrees with a coefficient of static friction of 0.700 can be calculated using physics principles. For part (a), when the force is applied perpendicular to the slope, the formula involves the gravitational force components and the frictional force. For part (b), applying force horizontally requires a different approach, factoring in the angle of the ramp and the static friction. The gravitational acceleration is taken as 9.80 m/s².

PREREQUISITES
  • Understanding of Newton's laws of motion
  • Basic knowledge of friction and its coefficients
  • Ability to resolve forces into components
  • Familiarity with trigonometric functions related to angles
NEXT STEPS
  • Calculate the normal force acting on the box on the ramp
  • Learn about static friction and its role in motion
  • Study the effects of angle on force components in inclined planes
  • Explore dynamics of forces applied at different angles
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Physics students, engineers, and anyone interested in mechanics and force calculations on inclined planes.

darlafelicity
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A box with a mass of 3.00 kg is at rest on a ramp that is at an angle of 20 degrees with the horizontal. The coefficient of static friction between the box and the ramp is 0.700. Use g = 9.80 m/s2. You now want to make the box move by applying a force. To start the box moving, what is the minimum force you need to apply if your force is directed ...

(a) perpendicular to the slope?

(b) horizontally?
 
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i got part (a) but I'm not sure why it works. mgcos20(mgsin20/static coefficient)

i still don't know how to do part (b) though.
 

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