Normal Force and Gravitational Force Calculations

Drawing and Calculating Normal Force

Finding g from Fg and m

• Use the formula: $g = \frac{Fg}{m}$

• Example: On a certain planet, an object has a weight of $240 N$ and a mass of $10 Kg$. Find the gravitational acceleration, $g$.

  • Given: $Fg = 240 N$, $m = 10 kg$

  • $g = \frac{Fg}{m} = \frac{240 N}{10 Kg} = 24 \frac{m}{s^2}$ or $24 \frac{N}{Kg}$

Mass on Different Planets

• Mass remains constant regardless of the planet.

• Weight changes depending on the gravitational acceleration of the planet.

• Example:

  • On Earth, $g = 10 \frac{m}{s^2}$

  • On the Moon, $g ≈ 1.6 \frac{m}{s^2}$

• Calculating Gravitational Force:

  • On Earth: $Fg = m \times 10$

  • On the Moon: $Fg = m \times 1.6$

What is Normal Force?

• Normal Force ($Fn$): The perpendicular support force exerted by a surface on an object.

• On a flat, horizontal surface, the normal force is equal to the gravitational force: $Fn = Fg$

$Fn$ on Horizontal Surface

• For an object at rest on a horizontal surface: $Fn = m \times g$

• Example: If an object has a mass of $m = 4 kg$, then

  • $Fn = 4 \times 10 = 40 N$

Fn > Fg: Object Pushed Down

• When an object is pushed down, the added force increases the normal force.

• $Fn = Fg + F_{push}$

Fn < Fg: Object Pulled Up

• When an object is pulled up, the added force decreases the normal force.

• $Fn = Fg - F_{pull}$

Equilibrium Conditions

• The sum of all forces acting on an object is zero.

• All forces are balanced, meaning $Fn = Fg$.

• As a result, the object has zero acceleration and constant velocity along a straight path.

What Happens If…

• What happens to $Fn$ if the object is lifted?

• What happens to $Fn$ if the object is pushed down?

• Predict and justify your answers based on the principles discussed.