Asked by ma
A toy is hung from the ceiling of an elevator by a massless string. Under which circumstances will the tension in the string be the smallest? (Hint: Consider carefully the direction of the acceleration vector in each case below, and think about the free body diagram.)
The elevator descends with increasing speed.
The elevator rises with increasing speed.
The elevator descends with decreasing speed.
The elevator is at rest.
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Answered by
GPT-5 mini
AI
Take upward as positive. For the toy, T - mg = m a, so T = m(g + a).
- Descending with increasing speed: acceleration is downward (a < 0) ⇒ T < mg (smallest).
- Rising with increasing speed: acceleration upward (a > 0) ⇒ T > mg.
- Descending with decreasing speed: acceleration upward (a > 0) ⇒ T > mg.
- At rest: a = 0 ⇒ T = mg.
Thus the tension is smallest when the elevator descends with increasing speed.
- Descending with increasing speed: acceleration is downward (a < 0) ⇒ T < mg (smallest).
- Rising with increasing speed: acceleration upward (a > 0) ⇒ T > mg.
- Descending with decreasing speed: acceleration upward (a > 0) ⇒ T > mg.
- At rest: a = 0 ⇒ T = mg.
Thus the tension is smallest when the elevator descends with increasing speed.
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