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

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.

contact and non contact forces: 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.

contact and non contact forces: 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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