A solid rubber ball dropped from a certain height above a swimming pool takes 0.3 seconds to reach the surface of the water (stage 1). The ball enters the water and reaches its maximum depth after 0.2 seconds (stage 2). Air resistance is negligible. Which one of the following statements is TRUE? A. Both the mechanical energy and momentum of the ball are constant during both stages (0.5 seconds). B. Both the mechanical energy and momentum of the ball are constant during stage 1 (first 0.3 seconds). C. Only the mechanical energy of the ball remains constant during both stages (0.5 seconds).
Answer (2)
In both stages of the ball's motion, mechanical energy is not conserved due to the conversion into other forms, while momentum is conserved due to the lack of external forces. All provided statements in the question are false. The correct understanding is that mechanical energy changes while momentum remains constant in the defined system.
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To determine which statement is true, let's analyze each of the provided statements in relation to the conservation principles in physics.
Statement A: Both the mechanical energy and momentum of the ball are constant during both stages (0.5 seconds).
Mechanical Energy : In stage 1, as the ball falls towards the water, its potential energy converts into kinetic energy, keeping the total mechanical energy constant since air resistance is negligible. However, as it enters the water in stage 2, mechanical energy is not conserved because the water applies a force that does work on the ball, causing some of the ball's mechanical energy to convert into other forms of energy, like thermal energy and sound.
Momentum : Momentum is not conserved in either stage because external forces (like gravity in stage 1 and the force of water in stage 2) act on the ball.
Therefore, Statement A is not true.
Statement B: Both the mechanical energy and momentum of the ball are constant during stage 1 (first 0.3 seconds).
Mechanical Energy : As explained above, during free fall (stage 1), mechanical energy is conserved as potential energy converts to kinetic energy.
Momentum : While the momentum of the ball changes during the fall due to the increase in velocity from gravitational acceleration, without any external horizontal forces, the vertical component increases steadily.
Thus, Statement B is also not true because momentum changes.
Statement C: Only the mechanical energy of the ball remains constant during both stages (0.5 seconds).
In our analysis, mechanical energy is not conserved during stage 2 when the ball enters the water.
Hence, Statement C is not true either.
Therefore, the most accurate statement under the described conditions, although not perfectly fitting any choice, is closer to saying mechanical energy is conserved in stage 1, while neither momentum nor mechanical energy is conserved during the entire process. If interpreting in the context of the provided options, Statement B stating that mechanical energy is constant during the fall is partially accurate but reflects misunderstanding momentum conservation.
In conclusion, if strictly choosing only among these options, all given statements have inaccuracies due to not recognizing the forces at play during each stage.
