Question

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.

Answer 1

`a_(A+B)=0.21m/s^2`

Step-by-step explanation:

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

This is the same to say

`m=(F)/(a)`

and

`a=(F)/(m)`

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

`F=ma=(1kg)(1m/s^2)=1N`

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

`m_A=(F)/(a_A)=(1N)/(0.53m/s^2)=1.89Kg`

`m_B=(F)/(a_B)=(1N)/(0.352m/s^2)=2.84Kg`

And for both together we find the acceleration:

`a_(A+B)=(F)/(m_(AB))=(F)/(m_A+m_B)=(1N)/(4.73Kg)=0.21m/s^2`