![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgo3EhsWx4n7zT2PdgKDN2ORlQL_8IHpsZ4rZGjb34DM7CJLb6xQg-RLUG4Np5r71rUzeY8siHXpVZzGY-XdGs2fm0Xh8vFjpBF7D_13xb65iawAwRbYYTSG6W0Inq4566NvQtv2emEvohE/s400/1.81_fig1.JPG)
In the system, as body 1 moves backwards, body 2 will slide down along the inclined plane. Let the acceleration of body 1 be
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjE9f-lJ0kP9peFK3BHZYBW7AMF4AXbKJVTu0WQpKifYXsf5DaYqD8_khcvJN5ZIzigc0Qbof4pNImK0qvB2aDB9OhL9xUJVptwxd0hqq-Dj2Coupax_g3ecbIIfjM1n1Aw0tNHJORMLi0o/s400/1.80_1.JPG)
and let the acceleration of body 2 with respect to an observer on body 1 be
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh2udjvw-LcOw1VF39R5T8wLjA2gfkCzPlyLbdWLZOVpIPDAV4vcBJrrynbGammyRaPBzXup2Ro_YP8_GRv832FXyT7N3dfpwc1nQcgaiHPGm-kG4FGpUnogVhyphenhyphenlOpxPg3Txu6JzximeeFq/s400/1.80_2.JPG)
along the direction down the inclined plane. Further let the normal reaction between the two bodies be
N.
Forces acting on body 2 : We shall resolve all forces in directions parallel and perpendicular to the incline of body 1. There are two forces acting on this body in the perpendicular direction.
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhA1oDQowPtXJLtbiZnTa1XFoiUgEljf62IgAhXZ2EE5EbViq0krjjhx1K8jwMIHvy1ke1l8AHwBzV-xnuwEFOS1hVvnTG3L1oSvppR8s4YiAGSeQLKbNRQCwQnIIR7Bat9rCg1ddQtuM6T/s400/1.81_fig2.JPG)
i) the component of force of gravity
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEizATRxv6-uVtF2Vu83w5OW_w9IlS7HstsvenQ3rTEsEI2AaT6-TL4ev5Op_Ju_acRBrjfDjSpVbtrLRsqO67TCOgCjXXlSDjPYXPhMNWwp0-j8EWkaBNblzoZYny9seN7PZasJuZTY9aTm/s400/1.80_3.JPG)
and ii) the normal reaction
N between the surfaces. The only acceleration experienced by the body in this direction is the component of its acceleration as it rides on body 1 -
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhUJjJNrXtJHlxhPMthb4JIGRcudfDKVU2ErN3E4bz9KSmWUgqYzzD294gqntxoesHsGRb-IyEeqPTTRGRxCPm1wiQuMFf49Xam-jklUcrSYpVhIWdBsiH1evTUEu3BbCyxtXvYBWWeIkHB/s400/1.80_6.JPG)
as shown in the figure. Thus, we have,
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEihLGkAILxHhtkQeLkKMnyiLiBLkexilv9CI4rNCuAgEwUsYqwi8ZmfX0Ry2Ekdziswoa_7n21M8bDmJfG4F4xpi-lu40R5WyG6UIjKp2ZfeGxV4oUrDZ1sNbiVVCYKE8sJGv9-ZHCP46Do/s400/1.80_5.JPG)
In the direction parallel to the inclined plane, there is only one force acting on the body - the component of force of gravity that's pulling it down the inclined plane,
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEghGBxtfHXIsdNiEC-oAvmjbAc1P8qGA1TxbJ0LfwPJY6Hk5sPLQZOAuBJpDTdbArSmWXJQRHdwLdxPKClhHzf-et6XqUyHdxDhfxXkwsm-APrl0ksgzB-Axe0ttfGlmUZfPexL4j97qpeH/s400/1.80_7.JPG)
. The net acceleration of the body along this direction is sum of two accelerations it is being subject to, i) its acceleration as it rides on body 1 -
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhnEfSeJ1Xsr1nCeJNfdPvHOoGg6zE05_UsQl-aLEXfTOF7Pm-RjsX64lslPaosuGzvagFFcNsC6a5HXZw3ExW7NWb_WyqNcdJI1KFu_zCt3DHqkkkzdD1o-vHvEBboTy4FoGcaQgIszJ8B/s400/1.81_8.JPG)
and ii) its acceleration relative to an observer on body 1 along the inclined plane
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEidLw6KM8rFamh6efkfzo7nryHCNWPSkKHfkKgg2c6FRmD7Oe6JLPf3iQpCm5cj3MUYdCUkJQJexSDylJO96tYTkXXVankEFsVVgzi7vea3LSx0-KKgf3kRLcmCN2RHL3MhB3jkUCImDuNJ/s400/1.81_9.JPG)
. Thus, we have,
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjw4Wn7tOn0wuS6C51xRjFQjn1PySYOaxj8Glzww9bZNKet6q7qTRG7XQg6DpTvf8aJdrH1WNcph7odTd-kas-fpUGbPJ-t33E2eLRXVWSbMtv5CjBpxw7n5xB1n-_h42nbTXwZyrWP9mjM/s400/1.81_10.JPG)
Forces acting on body 1: We shall consider only the horizontal direction for this part. There is only one force acting on the body - the component of normal reaction
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgqZAYQsmieGicm4Nda5Z4mr5kM_yOf_PB6JkZ3HA4bGHmaOfqed37kfKmauN1_W8gdMxsmw6zD4wbq3JXG5NNIj4gT8Kgejc49vWtRdIPd-JFVxMWi7jFec-dvv3xKChloaRkmcgrlEhYz/s400/1.81_11.JPG)
that is responsible to accelerate the body at a rate
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjE9f-lJ0kP9peFK3BHZYBW7AMF4AXbKJVTu0WQpKifYXsf5DaYqD8_khcvJN5ZIzigc0Qbof4pNImK0qvB2aDB9OhL9xUJVptwxd0hqq-Dj2Coupax_g3ecbIIfjM1n1Aw0tNHJORMLi0o/s400/1.80_1.JPG)
. Thus, we have,
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEieM-cAMlsEiaTqNj6xPHjlE_gPO7jN1X-2sTzYYeOopVTogFmAUDFev3vb1Bo86MWo_bj5_UxF3zJTaItYXSdl6EDSzVX7_w4AhwNn9PfBlNKtqDjO3q3MJ24GcUT07Wp3-cNZsd3SszCZ/s400/1.81_12.JPG)
From
(1) and
(3)
3 comments:
Thanks for such beautiful solutions.
sir yu have such a great art to solve a very much complicated problem so much easily thks sir 1000 times you had really inspired me now i will try to solve irodov on my own
This Cleared my concept
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