A small bug is nestled between a 1-kg block and a 2-kg block on a frictionless table. A horizontal force can be applied to either of the blocks as shown in figure Q5.24 (i) In which situation illustrated in the figure (a) or (b), does the bug have a better chance of survival, or (c) does it make no difference? (ii) Consider the statement, "The force exerted by the larger block on the smaller one is larger in magnitude than the force exerted by the smaller block on the larger one." Is this statement true only in situation (a)? Only in situation (b)? Is it true (c) in both situations or (d) in neither? (iii) Consider the statment, "As the blocks move, the force exerted by the block in back on the block in front is stronger than the force exerted by the front block on the back one."Is this statement true only in situation (a), only in situation (b), in (c) both situations, or in (d) neither?
Go stand on some giant's shoulders. Only then will you see the answer.
(i) In situation (a), the bug has a better chance of survival. As the larger block is being pushed to the right, the bug will move with the smaller block and remain between the two blocks. In situation (b), the bug would be crushed between the two blocks as the smaller block is being pushed towards the larger block.
(ii) The statement "The force exerted by the larger block on the smaller one is larger in magnitude than the force exerted by the smaller block on the larger one" is true in situation (a). In this case, the force exerted by the larger block is equal to the applied force, whereas in situation (b), the force exerted by the smaller block is equal to the applied force.
(iii) The statement "As the blocks move, the force exerted by the block in back on the block in front is stronger than the force exerted by the front block on the back one" is true in situation (b). In this case, as the smaller block moves towards the larger block, it exerts a larger force on the back block than the force exerted by the front block on the back one. In situation (a), the forces are equal since both blocks have the same acceleration.
To determine the bug's chance of survival and evaluate the given statements, let's analyze the scenarios depicted in the figure:
(i) The bug's chance of survival:
To determine the bug's better chance of survival, we need to consider the forces acting on the bug in each situation. In both scenarios (a) and (b), the bug experiences the same forces because it is nestled between the two blocks.
However, in situation (a), if a horizontal force is applied to the smaller 1-kg block, it will accelerate, exerting a force on the bug. Meanwhile, the larger 2-kg block remains stationary. In contrast, in situation (b), if a horizontal force is applied to the larger 2-kg block, it will accelerate, pushing the smaller 1-kg block and subsequently the bug along with it. So, in situation (b), the bug has more chance of survival since it moves along with the blocks when a force is applied.
Therefore, the bug has a better chance of survival in situation (b).
(ii) The magnitude of forces between the blocks:
The statement "The force exerted by the larger block on the smaller one is larger in magnitude than the force exerted by the smaller block on the larger one" can be evaluated for both situations:
In situation (a), when a force is applied to the smaller block, it exerts an equal and opposite force on the larger block, as per Newton's third law. Therefore, the magnitudes of the forces between the blocks are the same.
In situation (b), when a force is applied to the larger block, it pushes the smaller block along with it, exerting a greater force on the smaller block than the force exerted by the smaller block on the larger one. Therefore, the statement is true in situation (b).
So, the statement is true in situation (b).
(iii) Forces between the blocks:
The statement "As the blocks move, the force exerted by the block in back on the block in front is stronger than the force exerted by the front block on the back one" needs to be examined for both situations:
In situation (a), the smaller block exerts an equal and opposite force on the larger block due to Newton's third law. So, the forces between the blocks are the same.
In situation (b), as the larger block accelerates, it pushes the smaller block along with it. Therefore, the force exerted by the back block (larger block) on the front block (smaller block) is stronger than the force exerted by the front block on the back one.
Thus, the statement is true in situation (b).
To summarize:
- The bug has a better chance of survival in situation (b).
- The statement "The force exerted by the larger block on the smaller one is larger in magnitude than the force exerted by the smaller block on the larger one" is true in situation (b).
- The statement "As the blocks move, the force exerted by the block in back on the block in front is stronger than the force exerted by the front block on the back one" is true in situation (b).