Physics textbook answers & solutions

In the following problems, find the limit of the given sequence as $\mathit{n}\mathbf{\to }\mathbf{\infty }$.

1. $\frac{{\mathbf{n}}^{\mathbf{2}}\mathbf{+}\mathbf{5}{\mathbf{n}}^{\mathbf{3}}}{\mathbf{2}{\mathbf{n}}^{\mathbf{3}}\mathbf{+}\mathbf{3}\sqrt{\mathbf{4}\mathbf{+}{\mathbf{n}}^{\mathbf{6}}}}$

You observe three carts moving to the left. Cart A moves to the left at nearly constant speed. Cart B moves to the left, gradually speeding up. Cart C moves to the left, gradually slowing down. Which cart or carts, if any, experience a net force to the left?

Does a car speedometer measure speed, velocity, or both? Explain.

Suppose that the channel’s outgoing end is in the hydrogen $\mathcal{l}\mathbf{=}\mathbf{0}$ Stem-Gerlach apparatus of the figure. You place a second such apparatus whose channel is aligned with the first but rotated $\mathbf{90}\mathbf{°}$about the $\mathit{x}$-axis, so that its B –field lines point roughly in the $\mathit{y}$-direction instead of the. What would you see emerging at the end of your added apparatus? Consider the behavior of the spin-up and spin-down beams separately. Assume that when these beams are separated in the first apparatus, we can choose to block one or the other for study, but also assume that neither deviates too far from the center of the channel.

In Fig. 4-32, particle${}^{\mathbf{A}}$moves along the linelocalid="1654157716964" ${}^{\mathit{y}\mathbf{=}\mathbf{30}\mathbf{}\mathit{m}}$ with a constant velocitylocalid="1654157724548" $\stackrel{\mathbf{\rightharpoonup }}{\mathit{v}}$of magnitude localid="1654157733335" ${}^{\mathbf{3}\mathbf{.}\mathbf{0}\mathbf{}\mathit{m}\mathbf{/}\mathit{s}}$ and parallel to thelocalid="1654157740474" ${}^{\mathbf{x}}$ axis. At the instant particlelocalid="1654157754808" ${}^{\mathbf{A}}$ passes thelocalid="1654157747127" ${}^{\mathbf{y}}$ axis, particlelocalid="1654157760143" $\mathit{B}$ leaves the origin with a zero initial speed and a constant accelerationlocalid="1654157772700" ${}^{\mathit{a}}$ of magnitudelocalid="1654157766903" $\mathbf{0}\mathbf{.}\mathbf{40}\mathbf{}\mathit{m}\mathbf{/}{\mathit{s}}^{\mathbf{2}}$. What anglelocalid="1654157780936" ${}^{\mathbf{\theta }}$between $\overline{\mathbf{a}}$ and the positive direction of thelocalid="1654157787877" ${}^{\mathbf{y}}$axis would result in a collision?