Newton's Second Law for a System of Particles Calculator

The Newton's Second Law for a System of Particles Calculator will calculate:

Net Force acting on a system of particles (at maximum 3 particles)
Centre of mass of the system of particles
Acceleration of the system of particles

Newton's Second Law for a System of Particles Calculator
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Calculator Precision (Decimal Places)
mass of the first object (m₁) kg
mass of the second object (m₂) kg
mass of the third object (m₃) kg
x-position of the first object (x₁) m
x-position of the second object (x₂) m
x-position of the third object ( x₃) m
y-position of the first object (y₁) m
y-position of the second object (y₂) m
y-position of the third object (y₃) m
z-position of the first object (z₁) m
z-position of the second object ( z₂) m
z-position of the third object (z₃) m
x - component of force acting on the first object (F_1x) N
x - component of force acting on the second object (F_2x) N
x - component of force acting on the third object (F_3x) N
y - component of force acting on the first object (F_1y) N
y - component of force acting on the second object (F_2y) N
y - component of force acting on the third object (F_3y) N
z - component of force acting on the first object (F_1z) N
z - component of force acting on the second object (F_2z) N
z - component of force acting on the third object (F_3z) N

Newton's Second Law for a System of Particles Calculator Results (detailed calculations and formula below)
Magnitude of acceleration of the system of particles calculation
The magnitude of acceleration of the system of particles is m/s²
a = √b/√c/d a = √/√/ a = // a = / a =
Where b = (F_1x + F_2x + F_3x )² + (F_1y + F_2y + F_3y )² + (F_1z + F_2z + F_3z )² c = (x₁ × m₁ + x₂ × m₂ + x₃ × m₃ )² + (y₁ × m₁ + y₂ × m₂ + y₃ × m₃ )² + (z₁ × m₁ + z₂ × m₂ + z₃ × m₃ )² d = m₁ + m₂ + m₃
Newtons Second Law For A System Of Particles Calculator Input Values
Mass of the first object (m₁) kg
Mass of the second object (m₂) kg
Mass of the third object (m₃) kg
x-position of the first object (x₁) m
x-position of the second object (x₂) m
x-position of the third object ( x₃) m
y-position of the first object (y₁) m
y-position of the second object (y₂) m
y-position of the third object (y₃) m
z-position of the first object (z₁) m
z-position of the second object ( z₂) m
z-position of the third object (z₃) m
x - component of force acting on the first object (F_1x) N
x - component of force acting on the second object (F_2x) N
x - component of force acting on the third object (F_3x) N
y - component of force acting on the first object (F_1y) N
y - component of force acting on the second object (F_2y) N
y - component of force acting on the third object (F_3y) N
z - component of force acting on the first object (F_1z) N
z - component of force acting on the second object (F_2z) N
z - component of force acting on the third object (F_3z) N

Please note that the formula for each calculation along with detailed calculations are available below. As you enter the specific factors of each newtons second law for a system of particles calculation, the Newtons Second Law For A System Of Particles Calculator will automatically calculate the results and update the Physics formula elements with each element of the newtons second law for a system of particles calculation. You can then email or print this newtons second law for a system of particles calculation as required for later use.

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Magnitude of acceleration of the system of particles Formula and Calculation

a = √(F_1x + F_2x + F_3x )² + (F_1y + F_2y + F_3y )² + (F_1z + F_2z + F_3z )² / √(x₁ × m₁ + x₂ × m₂ + x₃ × m₃ )²
+ (y₁ × m₁ + y₂ × m₂ + y₃ × m₃ )²
+ (z₁ × m₁ + z₂ × m₂ + z₃ × m₃ )²/m₁ + m₂ + m₃

Using the Newton's Second Law for a System of Particles Calculator

If there are only two objects available, please leave the box of the third mass (i.e. m₃) empty.

If there are only two dimensions available, please leave the values of the third coordinate empty (i.e. z₁, z₂ and z₃).

If there is any missing components of force, please leave them empty.

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