Question

Assume that block A is accelerating with block B at a rate of 0.800 m/s2 along a frictionless surface. What is the mass of both A and B?

A. 145 kg

B. 120 kg

C. 105 kg

D. 125 kg

Answer 1

The mass of A and B together is 125kg

Step-by-step explanation:

To solve this problem, we set up the equations expressing the net force acting on A and B (forces acting to the right are +, those acting to the left are -):

`m_B\cdot a_B=F - F_(fr)\\m_A\cdot a_A = F_(fr)\\a_A = a_B`

The net force acting on B is due to the acting pull force 100N less friction force caused by A. The net force on A is due to the friction force caused by the block B. Since we know both blocks accelerate at the same rate, the system can be solved easily:

`(m_B+m_A)\cdot a_B=F\\(m_B+m_A)\cdot 0.800 (m)/(s^2)=100N\implies\\m_B+m_A = (100N)/(0.800(m)/(s^2))kg= 125kg`

Of course, alternatively, in this very simple case you could consider A+B a single object being pulled with 100N, and obtain the same results by diving the pull force by the acceleration.