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Surface Reaction with Applied Forces

Calculate surface reaction with applied forces with local equations, selectable units and supported inverse relationships.

  • Formula & worked example
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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

Private by default

Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

normal force = 98.0665. Values use the worked example unit selections.

Nincline = mg cos θ; Nhorizontal = mg ± F sin φ

Worked example

Enter these known values and leave the other values blank.

Surface
Horizontal
External Force
No
Mass
10 kg
Gravitational acceleration
9.80665 m/s²
Normal force
98.07 N

Assumptions and limitations

  • The body remains in contact with a stationary surface and has no acceleration normal to it. An upward force large enough to remove contact is outside the model. Incline and applied-force angles use the captured positive-angle branches.
  • Unit selectors convert known physical quantities. Leave a supported unknown blank; derived inverse branches are limited by the stated model and available captured equations.

Common questions

What does this calculation assume?

The body remains in contact with a stationary surface and has no acceleration normal to it. An upward force large enough to remove contact is outside the model. Incline and applied-force angles use the captured positive-angle branches.

Can I solve for an input?

Where the captured model supplies an inverse, leave that quantity blank and enter the remaining known quantities. A positive square-root or principal trigonometric inverse may represent only one of multiple mathematical branches.

Which unit should I use for the worked example?

The example uses the initial metric unit selection beside each field. Change a unit using its selector to convert the same known quantity; switching a unit does not change the underlying physical value.

References

Original accessible explanations preserve the captured diagram geometry, quantities and conditional variants without external image loading. Feet per second squared use exactly 0.3048 meters per second squared, replacing a rounded reciprocal factor.

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