Physics 1 Dynamics: Weight Normal Force and Tension (Single Block)

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Weight Normal Force and Tension (Single Block)

Study interactions between weight, normal force, and tension in this guide to force interactions through free body diagrams.

Equilibrium Situations (ΣF = 0N)

  • In equilibrium situations all forces are balanced and the net force on an object is zero.
  • An object is at rest or moving a constant velocity in a straight line.

Situations we will study here

  • A box on a surface
  • A box held in the air off the ground by a string
  • A box on a surface with tension in a rope attached above
Boxes with tension normal force and mAg

A Box on a Surface at Rest on a Horizontal Surface

Forces on box A with up being positive:

  • Fg: -mAg
  • +FN

ΣF = FN + Fg

  • ΣF = 0N in equilibrium

Substitute:

0 = FN – mAg

Rearranged gives you the final mathematical expression for normal force:

FN = mAg

Normal force is equal to the magnitude of box A's weight.

Normal Force and Weight on Box A

What is the normal force on an 8 kg box A on a horizontal surface?

(Use g = 10 m/s2)

FN = mAg

FN = (8)(10) = 80 N

A Box Hanging from a Rope off the Ground

Forces on box A with up being positive:

  • Fg: -mAg
  • +FT

ΣF = FT + Fg

  • ΣF = 0N in equilibrium

Substitute:

0 = FT – mAg

Rearranged gives you the final mathematical expression for tension force:

FT = mAg

Tension is equal to the magnitude of box A's weight.

Tension and weight on box A

What is the tension force on an 8 kg box A on a hanging from a rope?

(Use g = 10 m/s2)

FT = mAg

FT = (8)(10) = 80 N

A Box on a Surface with Tension in a Rope Attached Above

Forces on box A with up being positive:

  • Fg: -mAg
  • +FT
  • +FN

ΣF = FT + FN + Fg

  • ΣF = 0N in equilibrium

Substitute:

0 = FT + FN – mAg

Rearranged gives you the final mathematical expression for tension force and normal force:

FT = mAg – FN

Tension is equal to the magnitude of box A's weight minus the normal force the ground pushes up on box A.

FN = mAg - FT

Normal force is equal to the magnitude of box A's weight minus the tension in the rope above box A.

Tension Normal Force and weight on box A

What is the tension force on an 8 kg box A on a hanging from a rope that has 20N of normal force?

(Use g = 10 m/s2)

FT = mAg – FN

FT = (8)(10) – 20 = 60 N

What is the normal force on an 8 kg box A on a hanging from a rope that has 50N of tension force?

(Use g = 10 m/s2)

FN = mAg - FT

FN = (8)(10) – 50 = 30 N

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