The landing distance of each cube.
Answer to Problem 29P
The landing distance of cube is
The landing distance of small cube is
Explanation of Solution
Given:
The mass of the cube is
The mass of small cube is
The height of the incline is
The height of the table from the floor is
Formula used:
The expression for the speed of the sliding cube is,
Here, g is the acceleration due to gravity and h is the height of sliding.
The expression for relative velocity is,
Here,
The expression for law of conservation of momentum is,
Here,
The expression for falling time is,
Here,
The expression for landing distance is,
Here, v is the speed and t is the time.
Calculation:
Consider the acceleration due to gravity as
The initial speed of the cube is,
The initial speed of the small cube is,
The relative velocity is,
The speed of each object using the relation of conservation of momentum is,
The speed of the cube after sliding using equation (1) is,
The time of fall is,
The landing distance of cube is,
The landing distance of small cube is,
Conclusion:
Thus, the landing distance of cube is
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