A paddle boat is propelled to the left in the figure above by a wheel of nine flat blades that rotate about a central axis. Which of the following is correct?
A) the wheel should rotate in a counterclockwise (CW) direction because the force exerted on the water by the blade is in the direction opposite to the force exerted by the blade on the water
B) the wheel should rotate in a counterclockwise (CCW) direction because the force exerted on the water by the blade is in the direction opposite to the force exerted by the blade on the water.
C) the wheel should rotate in a counterclockwise (CCW) direction because the force exerted on the water by the blade is in the direction exerted by the blade on the water.
D) the wheel should rotate in a clockwise (CW) direction because the force exerted on the water by the blade is in the direction exerted by the blade on the water.
Hmm, let me think about this paddle boat conundrum for a moment. Ah, I've got it! The answer is D) the wheel should rotate in a clockwise (CW) direction because the force exerted on the water by the blade is in the same direction as the force exerted by the blade on the water. So, if you want that paddle boat to make some progress to the left, you better stick with the good old clockwise rotation. Happy paddling!
C) the wheel should rotate in a counterclockwise (CCW) direction because the force exerted on the water by the blade is in the direction exerted by the blade on the water.
To determine the correct answer, we need to understand the principle of action and reaction, which is described by Newton's third law of motion. According to Newton's third law, for every action, there is an equal and opposite reaction.
In the case of the paddle boat, when the blades push against the water, the water exerts an equal and opposite force on the blades. This force exerted by the water on the blade propels the paddle boat forward.
Now, let's analyze each option:
A) The option states that the wheel should rotate in a counterclockwise (CW) direction because the force exerted on the water by the blade is in the direction opposite to the force exerted by the blade on the water. This option contradicts Newton's third law because the reaction force should be in the direction opposite to the action force. Therefore, option A is incorrect.
B) The option states that the wheel should rotate in a counterclockwise (CCW) direction because the force exerted on the water by the blade is in the direction opposite to the force exerted by the blade on the water. This option correctly acknowledges Newton's third law by stating that the reaction force is in the opposite direction to the action force. Therefore, option B is a possible correct answer.
C) The option states that the wheel should rotate in a counterclockwise (CCW) direction because the force exerted on the water by the blade is in the direction exerted by the blade on the water. This option incorrectly assumes that the forces are in the same direction, which contradicts Newton's third law. Therefore, option C is incorrect.
D) The option states that the wheel should rotate in a clockwise (CW) direction because the force exerted on the water by the blade is in the direction exerted by the blade on the water. This option also incorrectly assumes that the forces are in the same direction, which contradicts Newton's third law. Therefore, option D is incorrect.
Based on our analysis, option B is the correct answer. The wheel should rotate in a counterclockwise (CCW) direction because the force exerted on the water by the blade is in the direction opposite to the force exerted by the blade on the water, according to Newton's third law.