Normal Force Equation | Problems (With Solutions)

Normal Force Equation

For an object resting on the flat surface, the value of normal force (FN) is equal to its weight (mg). Using the equation of normal force: FN = mg, the value of normal force acting on an object can be calculated.

Here’s the equation of normal force:

  1. When an object is resting on the flat surface, FN = mg
  1. When an object is placed on an inclined surface, FN = mg × cos (α)
  1. When an external downward force is acting on an object, FN = mg + F sin (θ)
  1. When an external upward force is acting on an object, FN = mg – F sin (θ)

Where,

α = angle of an inclined surface, deg
F = external force acting on an object, N
θ = angle between horizontal surface and external force, deg

Let’s solve some problems based on these equations, so you’ll get a clear idea.

Normal Force Practice Problems

Problem 1: A flower pot of mass 2 kg is placed on the desk. Calculate the normal force acting on a flower pot. Take the value of gravitational acceleration, g = 9.81 m/s2.

Solution:

Given data:
Mass of a flower pot, m = 2 kg
Gravitational acceleration, g = 9.81 m/s2
Normal force acting on a flower pot, FN = ?

Using the equation of normal force, (when an object is resting on the flat surface)
FN = mg
FN = 2 × 9.81
FN = 19.62 N

Therefore, the normal force acting on a flower pot is 19.62 N.


Problem 2: Calculate the normal force acting on a 3 kg book which is placed on an inclined surface. Assume that the surface is inclined at 45° angle.

Solution:

Given data:
Mass of a book, m = 3 kg
Angle of an inclined surface, α = 45°
Normal force acting on a book, FN = ?

Using the equation of normal force, (when an object is placed on an inclined surface)
FN = mg × cos (α)
FN = 3 × 9.81 × cos (45°)
FN = 29.43 × 0.7071
FN = 20.8099 N

Therefore, the normal force acting on a book is 20.8099 N.


Problem 3: One wooden crate of mass 20 kg is resting on the ground. In order to move this crate, 8 N of external downward force is applied on it at 30° angle. Calculate the normal force acting on a wooden crate.

Solution:

Given data:
Mass of a wooden crate, m = 20 kg
External downward force applied on a wooden crate, F = 8 N
Angle between horizontal surface and external downward force, θ = 30°
Normal force acting on a wooden crate, FN = ?

Using the equation of force, (when an external downward force is acting on an object)

FN = mg + F sin (θ)
FN = [20 × 9.81] + [8 × sin (30°)]
FN = 196.2 + [8 × 0.5]
FN = 196.2 + 4
FN = 200.2 N

Therefore, the normal force acting on a wooden crate is 200.2 N.


Problem 4: Calculate the normal force acting on a 4 kg block, when it is pulled with an external upward force of 10 N at 45° angle.

Solution:

Given data:
Mass of a block, m = 4 kg
External upward force applied on a block, F = 10 N
Angle between horizontal surface and external upward force, θ = 45°
Normal force acting on a block, FN = ?

Using the equation of force, (when an external upward force is acting on an object)
FN = mg – F sin (θ)
FN = [4 × 9.81] – [10 × sin (45°)]
FN = 39.24 – [10 × 0.8509]
FN = 39.24 – 8.509
FN = 30.731 N

Therefore, the normal force acting on a block is 30.731 N.

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