AP Physics C Mechanics 1.1 Vectors Overview

Distinguish scalar and vector quantities by whether a physical description requires magnitude alone or both magnitude and direction.

[Maximum number: 1]

A small sled slides across a rough horizontal table with an initial velocity $v_{0}$ . The coefficient of kinetic friction between the sled and the table is $\mu_{k}$ . A string connects the sled to a device on the ground. The device maintains constant tension $F_{T}$ in the string by unwinding the string as the sled slides to the right. The total mass of the sled is m. The string is attached to the device at x=0 and at a height of y, as shown in Figure 1. The horizontal position of the sled is represented by x, as shown in Figure 2. Express all algebraic answers in terms of $m, \mu_{k}$ , $F_{T}, x, y$ , and physical constants, as appropriate.

Determine an expression for the angle $\theta$ that the string makes with the vertical when the sled has traveled a horizontal distance x.

For any correct trigonometric expression for $\theta$ in terms of the given quantities 1 point

\sin \theta=\frac{x}{\sqrt{y^{2}+x^{2}}} \quad \therefore \theta=\sin ^{-1}\left(\frac{x}{\sqrt{y^{2}+x^{2}}}\right)

OR

\cos \theta=\frac{y}{\sqrt{y^{2}+x^{2}}} \quad \therefore \theta=\cos ^{-1} \frac{y}{\sqrt{y^{2}+x^{2}}}

OR

\tan \theta=\frac{x}{y} \quad \therefore \theta=\tan ^{-1} \frac{x}{y}

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Covered syllabus points

1.1 Scalars and Vectors question 1