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Question

A force of 5N produces an acceleration of 8ms-2 on a mass m1 and an acceleration of 24ms-2 on a mass m2. What acceleration (in ms-2) would the same force provide if both the masses are tied together?


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Solution

Step1: Given data

A force of 5N produces an acceleration of 8ms-2 on a mass m1 and acceleration of 24ms-2 on a mass m2.

Step2: Formula used

F=m×a[whereF=force,m=mass,a=acceleration]

Step3: Calculating acceleration

Force is defined as the product of mass and acceleration. F=m×a

Here, the force applied is the same on masses m1andm2

Mass will be obtained by dividing the force with the acceleration produced by the mass. m=Fa

Mass m1 is obtained by dividing the force of 5N with the acceleration of 8ms-2

m1=Fa1m1=58kg[a1=8ms-2,F=5N]
Mass m2 is obtained by dividing the force of 5N with the acceleration of 24ms-2
m2=Fa2m2=524kg[a2=24ms-2,F=5N]

The resultant mass when both the masses are tied together will be
M=m1+m2M=58+524m1=58kg,m2=524kgM=2024M=56kg
The mass resulting when the two masses are combined is 56kg.
Acceleration (in ms-2 ) when both the masses are tied together is
a=Fma=556F=5N,m=56kga=6ms-2
Hence, the acceleration produced when the masses are tied together with the same force will be 6ms-2.


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