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Ask Your Teacher The same force that gives the standard 1 kg mass an acceleration of 1.00 m/s2 acts first on body A, producing an acceleration of 0.530 m/s2, and then on body B, producing an acceleration of 0.352 m/s2. Find the acceleration produced when A and B are attached and the same force is applied.

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AMB000

Answer:

[tex]a_{A+B}=0.21m/s^2[/tex]

Explanation:

We will use always Newton's 2nd Law F=ma.

This is the same to say

[tex]m=\frac{F}{a}[/tex]

and

[tex]a=\frac{F}{m}[/tex]

We use the information for the first object mentioned to calculate this force:

[tex]F=ma=(1kg)(1m/s^2)=1N[/tex]

We then calculate the masses of A and B, consdering the acceleration they experiment when the force F=1N is applied to them:

[tex]m_A=\frac{F}{a_A}=\frac{1N}{0.53m/s^2}=1.89Kg[/tex]

[tex]m_B=\frac{F}{a_B}=\frac{1N}{0.352m/s^2}=2.84Kg[/tex]

And for both together we find the acceleration:

[tex]a_{A+B}=\frac{F}{m_{AB}}=\frac{F}{m_A+m_B}=\frac{1N}{4.73Kg}=0.21m/s^2[/tex]

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