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hysics of a Coin Drop in an Ascending Elevator
Chapter 5, Problem 46(choose chapter or problem)
An elevator cab is pulled upward by a cable. The cab and its single occupant have a combined mass of 2000 kg. When that occupant drops a coin, its acceleration relative to the cab is \(8.00 \mathrm{m} / \mathrm{s}^{2}\) downward. What is the tension in the cable?
Questions & Answers
QUESTION:
An elevator cab is pulled upward by a cable. The cab and its single occupant have a combined mass of 2000 kg. When that occupant drops a coin, its acceleration relative to the cab is \(8.00 \mathrm{m} / \mathrm{s}^{2}\) downward. What is the tension in the cable?
ANSWER:Step 1 of 3
The information in the question is given as follows.
The coin accelerates toward the floor of the elevator at a rate of \(a=8.00\dfrac{\text{m}}{{{\text{s}}^{\text{2}}}}\).
Since the coin is in free-fall it must be accelerating toward the surface of the earth at a rate of \(g=9.80\dfrac{\text{m}}{{{\text{s}}^{\text{2}}}}\).
That means that the elevator is an acceleration toward the surface of the earth at a rate of,
\(g-a =\left( 9.80-8.00 \right)\dfrac{\text{m}}{{{\text{s}}^{\text{2}}}}\)
\(=1.80\ m/s^2\)
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hysics of a Coin Drop in an Ascending Elevator
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In an elevator ascending, an occupant drops a coin, which accelerates at a different rate than expected. This reveals the elevator's own acceleration towards the Earth. By analyzing forces and tensions, we determine the cable's tension to be 16000 N.