Question

Hi everyone,
I have a problem understanding the solutions of challenge problems 5,6,7 on Application of Newton's Second Law. In problem 5 they use the "kinetic constraint" that the cart and the block have same magnitude of acceleration, in the problem 6 they use it again. I would like to know if in the problem 7 it is possible to say that the three blocks have same magnitude of acceleration. Thanks a lot.

Answer 1

Can you post the section you are working on? A link is useful, but section number is important..

Answer 2

Okay it's in the challenge problems of the section 8.
Here is the link :
http://ocw.mit.edu/courses/physics/8-01sc-physics-i-classical-mechanics-fall-2010/applications-of-newtons-second-law/MIT8_01SC_problems08.pdf
Thanks,

Answer 3

No, it is not possible to say that these three blocks have the same magnitude of acceleration! Each block will have a different acceleration due to its mass. This is because:\[F = ma\]
If we ignore the friction for a moment we will see that each block has the same force applied to it by the tension of the cable. Therefore each block will have a different acceleration.

Let me know if you need a better explanation, or a different solution from the answer key. I have found the answer keys to be quite cryptic sometimes...

Answer 4

I understand now that the accelerations cannot be equal.
But the magnitudes of the acceleration can maybe be equal.
When I think about it intuitively, it is possible that because the two objects are attached the magnitudes of the acceleration of each objects are equal.
And in the solutions of the exercise 5 point 5.5 in the section 8 they use this and call it the kinematic constraint. I would like to know how to justify this "correctly," with a good reasoning.
Thanks,

Answer 5

When I am discussing acceleration in my previous answer I am talking about both magnitude and direction. For problem 7 you have 3 different objects that are attached. This allows them to move with different accelerations.

In problems 5 and 6 only two objects are attached so they cannot move independently.

To visualize this imagine attaching a cable attaching a tissue box and a car. If the car drives the tissue box must move with the same speed and acceleration of the car(assuming it only drives forwards). This is like problems 5 and 6. Now imagine pushing on the center of the cable while the car and tissue box are resting on the tar . The tissue box will move thus have an acceleration. The car however will likely not move and if it did it would be with a much smaller acceleration than the tissue box.