An object of mass \(200 \mathrm{~kg}\) hangs at the end of a rope. Find its acceleration when the tension in the rope is \(2000 \mathrm{~N}\).
A. \(20 \mathrm{~m} / \mathrm{s}^2\)
B. \(0.2 \mathrm{~m} / \mathrm{s}^2\)
C. \(2 \mathrm{~m} / \mathrm{s}^2\)
D. \(25 \mathrm{~m} / \mathrm{s}^2\)
Correct Answer: B
Explanation
|\mathrm{W}-\mathrm{T}|=\mathrm{ma} \\
|200 \times 9.8-2000|=200 \mathrm{a} \\
\mathrm{a}=\frac{|1960-2000|}{200} \\
\mathrm{a}=\frac{40}{200}=0.2 \mathrm{~m} / \mathrm{s}^2, \text { B } \\
\text { Note: if we use } \mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2, \text { we obtain } \\
\mathrm{W}-\mathrm{T}=\mathrm{ma} \\
\mathrm{mg}-\mathrm{T}=\mathrm{ma} \\
200 \times 10-2000=\mathrm{ma} \\
0=200 \mathrm{a} \\
\mathrm{a}=0 \mathrm{~m} / \mathrm{s}^2
\end{array}
