Normal Force Equation | Problems (With Solutions)

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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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