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Curvature also plays a key role in physics. The magnitude of a force required to move an object at constant speed along a curved path is, according to Newton's laws, a constant multiple of the curvature of the trajectories. Use |F| = m|a| IF|=m|a| and the decomposition of acceleration into tangential and normal components to choose the answer choice below that correctly expresses the above statement as a mathematical equation.

Curvature also plays a key role in physics. The magnitude of a force required to move an object at constant speed along a curved path is, according to Newton's laws, a constant multiple of the curvature of the trajectories. Use |F| = m|a| IF|=m|a| and the decomposition of acceleration into tangential and normal components to choose the answer choice below that correctly expresses the above statement as a mathematical equation.

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**Homework 13.4 (page 10 of 10)** The following is a quotation from an article in The American Mathematical Monthly, titled "Curvature in the Eighties" by Robert Osserman (October 1990, page 731): "Curvature also plays a key role in physics. The magnitude of a force required to move an object at constant speed along a curved path is, according to Newton's laws, a constant multiple of the curvature of the trajectories." Use \(|\mathbf{F}| = m|a|\), \(|\mathbf{F}| = m|a|\), and the decomposition of acceleration into tangential and normal components to choose the answer choice below that correctly expresses the above statement as a mathematical equation. **Select one:** a. \(|\mathbf{F}| = 2m^2v\kappa\) b. \(|\mathbf{F}| = \frac{1}{2}mv^2\kappa\) c. \(|\mathbf{F}| = \frac{1}{2}mv\kappa\) d. \(|\mathbf{F}| = mv^2\kappa\) e. \(|\mathbf{F}| = m^2v^2\kappa\)
Transcribed Image Text:**Homework 13.4 (page 10 of 10)** The following is a quotation from an article in The American Mathematical Monthly, titled "Curvature in the Eighties" by Robert Osserman (October 1990, page 731): "Curvature also plays a key role in physics. The magnitude of a force required to move an object at constant speed along a curved path is, according to Newton's laws, a constant multiple of the curvature of the trajectories." Use \(|\mathbf{F}| = m|a|\), \(|\mathbf{F}| = m|a|\), and the decomposition of acceleration into tangential and normal components to choose the answer choice below that correctly expresses the above statement as a mathematical equation. **Select one:** a. \(|\mathbf{F}| = 2m^2v\kappa\) b. \(|\mathbf{F}| = \frac{1}{2}mv^2\kappa\) c. \(|\mathbf{F}| = \frac{1}{2}mv\kappa\) d. \(|\mathbf{F}| = mv^2\kappa\) e. \(|\mathbf{F}| = m^2v^2\kappa\)
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