Derive the unit of force using the second law of motion. A force of 5 N produces an
acceleration of 8 m s–2 on a mass m1 and an acceleration of 24 m s–2 on a mass m2. What
acceleration would the same force provide if both the masses are tied together?
Answers
Given :
Force = 5N
In 1st case,
Acceleration = 8m/s²
Mass = m₁
In 2nd case,
Acceleration = 24m/s²
Mass = m₂
To find :
The acceleration then the same force provide if both the masses are tied together.
Solution :
Using second law of motion .i.e.,
» The rate of change of linear Momentum of a body with time is proportional to the net external force acting on it.
In order words,
F = ma
Where,
- F denotes force
- m denotes Mass
- a denotes accerlation
In 1st case,
acceleration is 8m/s² and mass = m₁ so,
➝ F = ma
➝ 5 = (m₁)(8)
➝ m₁ = 8/5
➝ m₁ = 1.6 kg
similarly,
In 2nd case,
acceleration is 24m/s² and mass = m₂ so,
➝ F = ma
➝ 24 = (m₂)(24)
➝ m₂ = 24/5
➝ m₂ = 4.8 kg
Now,we have to find acceleration when both the masses are tied together by applying Newton's second law of motion that is
➝ F = ma
➝ 5 = (m₁ + m₂) a
➝ 5 = (1.6 + 4.8)a
➝ 5 = 6.4a
➝ a = 5/6.4
➝ a = 0.7 m/s²
Thus, the acceleration then the same force provide if both the masses are tied together is 0.7 m/s².
Given :
Force = 5N
In 1st case,
Acceleration = 8m/s²
Mass = m₁
In 2nd case,
Acceleration = 24m/s²
Mass = m₂
To find :
The acceleration then the same force provide if both the masses are tied together.
Solution :
Using second law of motion .i.e.,
» The rate of change of linear Momentum of a body with time is proportional to the net external force acting on it.
In order words,
F = ma
Where,
F denotes force
m denotes Mass
a denotes accerlation
In 1st case,
acceleration is 8m/s² and mass = m₁ so,
➝ F = ma
➝ 5 = (m₁)(8)
➝ m₁ = 8/5
➝ m₁ = 1.6 kg
similarly,
In 2nd case,
acceleration is 24m/s² and mass = m₂ so,
➝ F = ma
➝ 24 = (m₂)(24)
➝ m₂ = 24/5
➝ m₂ = 4.8 kg
Now,we have to find acceleration when both the masses are tied together by applying Newton's second law of motion that is
➝ F = ma
➝ 5 = (m₁ + m₂) a
➝ 5 = (1.6 + 4.8)a
➝ 5 = 6.4a
➝ a = 5/6.4
➝ a = 0.7 m/s²
Thus, the acceleration then the same force provide if both the masses are tied together is 0.7 m/s².