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S2.6 Normal contact force

[A] About the force

The normal contact force FN is the repulsive force of interaction between two surfaces in contact, acting at right angles to the surfaces, and inhibiting closer contact.

  • otherwise known as: ‘normal force’, or ‘normal reaction’
  • each body experience force of same magnitude but opposite direction.
Graphic - No title - normalzero

[B] Example problem

Two bodies are free to move on a smooth horizontal surface under the action of a horizontal force of magnitude FA.
Graphic - No title - normalone

Determine the acceleration and the normal contact force between them.

Solution

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Solution

  • Let a be the acceleration to right (same for both bodies)
  • Choose a system comprising both masses.

    Apply 2nd law:

    FA=(m1+m2)a
    implying

    $$a = \frac{F_A}{m_1 +m_2}$$

    Graphic - No title - normaltwo
  • Choose a system comprising 2nd mass alone.
    Apply 2nd law:
    FN=m2a
    so
    \[ \xmlInlineElement[\xmlAttr{}{target}{slides}]{http://www.ph.ed.ac.uk/aardvark/NS/aardvark-latex}{aardvark:reveal}{a=\frac{F_N}{m_2}} \]
    Graphic - No title - normalthree
  • Eliminate a:

    \[ \frac{F_N}{m_2} =\frac{F_A}{m_1+m_2} \]

    Hence

    $$F_N= F_A \frac{m_2}{m_1 +m_2}$$

 

Results

acceleration:

\[ a = \frac{F_A}{m_1 +m_2} \]
magnitude of normal force
\[ F_N= F_A \frac{m_2}{m_1 +m_2} \]

Check It!
TBlock on a Table
TIn the lift
TPushing two boxes
MBlock on a Frictionless Plane

Learning Resources

Textbook: HRW Chapter 5.7,5.9
Course Questions:
Self-Test Questions: