In the image below, a combination of gears (1-5), pulley (6), weight (W), belts (connecting 1&2, 4&6)and a shaft drive is shown. The shaft rotates in the direction of the arrow without any horizontal translation. Which of the following statement(s) is/are CORRECT?
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Work through this gear train one connection at a time from the shaft to the weight, using two simple rules, meshed teeth always reverse the direction, while a belt always keeps the same direction on both wheels. Do not try to judge the whole picture at once, follow the chain link by link and you will get the direction of every single gear and the pulley without guessing. Once you know which way the pulley turns, look carefully at which side of the pulley the cord hangs from to work out whether the weight goes up or down.
Step 1: Understanding the gear system and motion.
In this system, gears 1 to 5 interact with each other, and the pulley is connected to the weight (W). The movement of these gears transfers motion to the weight, which moves vertically. Step 2: Analyzing the options. (A) 5 rotates clockwise and W moves upwards: This is correct because the rotation of gear 5 will transfer motion to the weight (W), causing it to move upwards. (B) 4 rotates anticlockwise and W moves downwards: This is incorrect because gear 4 does not rotate in the specified direction, and the movement of W does not match this behavior. (C) 5 and 4 rotate in opposite directions: This is correct as gears 5 and 4 will rotate in opposite directions due to the interconnection of gears. (D) 1 and 4 rotate in opposite directions: This is incorrect because gears 1 and 4 rotate in the same direction in this system. Step 3: Conclusion.
The correct answers are (A) and (C) based on the interactions of the gears and the movement of the weight.
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Approach Solution -2
Concept:
In any gear train, two gears whose teeth touch each other always spin in opposite directions, while two wheels joined by a belt always spin in the same direction. Following the direction of rotation link by link, from the shaft all the way to the weight, tells us the direction of every single gear without guessing.
Step 1: Start at the shaft and move through the meshed gears one link at a time.
The shaft drives gear 5 directly using the worm thread wound around it. Take gear 5 to turn clockwise, matching the arrow on the shaft. Gear 5 has its teeth touching the next gear in the chain, so that gear turns anticlockwise, opposite to gear 5. That gear then has its teeth touching gear 3, so gear 3 turns clockwise again, opposite to it. Gear 3 has its teeth touching gear 4, so gear 4 turns anticlockwise, opposite to gear 3, and therefore opposite to gear 5 as well.
Step 2: Apply the belt rule wherever a belt connects two wheels.
Gear 4 is joined to pulley 6 by a belt, and a belt always keeps both wheels turning the same way, so pulley 6 also turns anticlockwise, the same direction as gear 4. In the same way, gear 1 is joined by a belt to the gear right after gear 5 in the chain, so gear 1 turns in the same direction as that gear, anticlockwise.
Step 3: Read off the direction of the weight from the pulley, and check each statement.
Since pulley 6 turns anticlockwise in this setup, the cord winds onto the pulley on the side shown in the figure, lifting the weight W upward rather than lowering it. Statement one, gear 5 clockwise with W moving upward, matches this directly. Statement three, gear 5 and gear 4 turning in opposite directions, also matches Step 1. Statement two is wrong because W actually moves upward, not downward. Statement four is wrong because gear 1 and gear 4 both came out anticlockwise in Steps 1 and 2, the same direction, not opposite.
Final Answer: Gear 5 rotates clockwise and W moves upward; gear 5 and gear 4 rotate in opposite directions
