A force F applied to an object of mass m1 produces an acceleration of 3.50 m/s.

Question

A force F applied to an object of mass m1 produces an acceleration of 3.50 m/s. The same force applied to a second object of mass m2 produces an acceleration of 1.50 m/s2 (a) What is the value of the ratio mi/m2? 0.42 (b) If m and m are combined into one object, find its acceleration under the action of the force F Write equations relating F, m, and a for the three cases (m, m and mum) and then manipulate the equation to determine the acceleration of the sum in terms of the other two accelerations. m/s

Explanation / Answer

According to the given problem,

a)Given,

F = m1(3.5) = 3.5m1----[1]

F = m2(1.50) = 1.5m2-----[2]

As force are equal, Equating eq1 and 2

m1/m2 = 1.5/3.5 = 0.428

b) We need,

F = (m1+m2)a----[3]

Modify equation [1] and [2] and add them.

F/3.5 = m1 and F/1.5 = m2

m1 + m2 = F[(1/3.5)+(1/1.5)] Substitute this equation in eq[3]

F = F[(1/3.5)+(1/1.5)]a ,

Now, F on both side cancel out and sen the numerical value to other side.

a = 1/[(1/3.5)+(1/1.5)]

a = 1/[20/21]

a = 21/20

a = 1.05 m/s2

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