This calculator estimates the constant-speed force and work required to move a mass uphill along a straight ramp using a user-entered Coulomb friction coefficient. It is a quasistatic free-body model, not a ramp or handling-system design.
Inclined Plane Interactive Calculator
Explore gravity and sliding-friction terms along a straight incline defined by rise and slope length.
Equation Used
- Straight rigid ramp with entered length measured along the slope and rise h not exceeding L.
- Mass moves uphill at constant speed with force parallel to the ramp.
- Coulomb sliding friction mu times normal force mg cos(theta).
- No acceleration, rolling, handle/rope angle, pulley/winch, load dimensions/centre of mass, tipping, ramp strength, surface failure, restraint, guarding or safety model.
The friction coefficient is a user assumption and may vary with materials, surface condition, contamination, speed and contact. The result excludes acceleration, wheels/rollers, handles, winches and safety factors.
Constant-speed incline force balance
For rise h and slope length L, sin(theta)=h/L. Gravity contributes mg sin(theta) downhill and modeled sliding friction contributes mu mg cos(theta), so an uphill parallel force must balance their sum at constant speed.
The drawing is a schematic block and ramp. Its displayed slope is fixed; the force results use the entered rise and ramp length.
Use as a preliminary free-body check
The result can compare ideal gravity and assumed sliding-friction work. It cannot determine whether a ramp, worker, cart, winch or anchorage is safe or compliant.
Force and path work
Fup=mg(sin theta+mu cos theta). Work along the uniform ramp is FupL=mgh+mu mgL cos theta. Ideal distance ratio L/h describes the frictionless force/travel exchange only.
The weight tile mg is a force magnitude, not the energy required for direct lifting.
Worked example
For m=100 kg, h=1 m, L=5 m and mu=0, sin(theta)=0.2, uphill constant-speed force is about 196.13 N, weight is 980.67 N, ideal distance ratio is 5 and ramp work is 980.67 J.
What a real ramp requires
A real ramp needs adequate structural capacity, stable load support and a way to control movement. Starting or stopping the load adds forces that this constant-speed calculation omits. Wheels, handles and pulling equipment also change the force balance; the sliding result does not determine safe human effort or equipment ratings.
Questions
Is L/h actual mechanical advantage with friction?
No. It is the ideal distance ratio; friction increases required force.
Does the model include starting force?
No. Static friction and acceleration are absent.
Can this approve a ramp?
No. Structural, stability and regulatory checks are not included.
References & Further Reading
- Wikipedia contributors. Inclined plane. Wikipedia
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