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Chapter 7: Problem 87

Within cells, small organelles containing newly synthesized proteins are transported along microtubules by tiny molecular motors called kinesins. What force does a kinesin molecule need to deliver in order to accelerate an organelle with mass \(0.01 \mathrm{pg}\left(10^{-17} \mathrm{kg}\right)\) from 0 to \(1 \mu \mathrm{m} / \mathrm{s}\) within a time of \(10 \mu \mathrm{s} ?\)

Short Answer

Expert verified
Answer: The force exerted by a kinesin molecule on the organelle is \(10^{-18}\,\mathrm{N}\).

Step by step solution

01

Identify the given values

The given values are: - Mass of the organelle (m): \(0.01\,\mathrm{pg} = 10^{-17}\,\mathrm{kg}\) - Initial velocity (v0): \(0\,\frac{\mu\mathrm{m}}{\mathrm{s}}\) - Final velocity (vf): \(1\,\frac{\mu\mathrm{m}}{\mathrm{s}} = 10^{-6}\,\frac{\mathrm{m}}{\mathrm{s}}\) - Time interval (t): \(10\,\mu\mathrm{s} = 10^{-5}\,\mathrm{s}\)
02

Calculate the acceleration

To find the acceleration (a), we can use the formula a = (vf - v0) / t. a = \(\frac{10^{-6}\,\frac{\mathrm{m}}{\mathrm{s}} - 0\,\frac{\mu\mathrm{m}}{\mathrm{s}}}{10^{-5}\,\mathrm{s}}\) a = \(10^{-1}\,\frac{\mathrm{m}}{\mathrm{s}^2}\)
03

Calculate the force

Now that we have the acceleration, we can use Newton's second law (F = m * a) to find the required force (F). F = \((10^{-17}\,\mathrm{kg})(10^{-1}\,\frac{\mathrm{m}}{\mathrm{s}^2})\) F = \(10^{-18}\,\mathrm{N}\) So, a kinesin molecule needs to deliver a force of \(10^{-18}\,\mathrm{N}\) in order to accelerate the organelle as described in the problem.

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