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Question

Suppose that a constant force is applied to an object. Newton's Second Law of Motion states that the acceleration of the object varies inversely with its mass. A constant force acting upon an object with mass 2 kg produces an acceleration of 35 /ms2 . The acceleration of another object produced by the same force is 10 /ms2 . What is the mass of this object?

Answer 1

Hi Joshua,

 

For the first object, the force can be calculated by the formula F = ma.  You have a mass of 2 kg with an acceleration of 35 m/s².  So the force is:

 

F = ma

F = (2 kg)(35 m/s²)

F = 70 Newtons

 

Now if that 70 N force creates a 10 m/s² acceleration, then the mass must be

 

F = ma

70 N = m(10 m/s²)

70 N / 10 = m

7 kg = m

 

Hope this helps! :)

Answer 2

First object:

 

F = m₁a = (2 kg)(35 m/s²) = 70 N

 

Second object:

 

Same force, 

 

F = 70 N

 

m₂ = F/a₂ = (70 N)/(10 m/s²) = 7 kg