Find the accelerations of each of the following three blocks:
2kg block, stacked on top of a 3kg block, stacked on top of a 7kg block
When a force of 10N is applied on the 2kg block.
Coefficient of friction between 2kg and 3kg block is 0.2, coefficient of friction between 3kg and 7kg block is 0.3, and surface between 7kg block and ground is smooth.
None needed or given, taking g=10
The Attempt at a Solution
It's a pretty straightforward question but I suddenly had a conceptual problem. First off, I check the maximum friction between the 2kg and 3kg block (uN), and I get that to be 4N. So obviously the the resultant force on the 2kg block is 6N, and by Newton's second law, acceleration of he 2kg block is 3m/s2.
Next up, the 3kg block. So we know that by Newton's third law, an equal and opposite force ( I.e 4N) will act on this 3kg block because of the friction between it and the 2kg. Upon checking the maximum frictional force between the 3kg and 7kg block, we find that it is a whopping 18N, so there will be no motion, (and another 4N will act on the 7kg block, quite obvious). THIS IS WHERE I HAVE A PROBLEM. According to my textbook, this means that the 3kg block will be at rest "with respect to the 7kg block", and hence acceleration of both 7kg and 3kg block will be the same, i.e 0.4 m/s2. Why do they say that it is at rest only w.r.t to the 7kg block? Since the net force acting on it is zero, shouldn't it just be at rest, and not move at all? And therefore shouldn't the 7kg block move with an acceleration of 4/7 m/s2? I'm thoroughly confused. By their logic, wouldn't that also mean that the 2kg block is accelerating with an acceleration of 3m/s2 w.r.t to 3kg block (not w.r.t the ground)? A detailed explanation would be appreciated, thanks all!