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$$
\begin{array}{c}{\text { A. } 22 \text { rifle bullet, traveling at } 350 \mathrm{m} / \mathrm{s} \text { , strikes a large }} \\ {\text { tree, which it penetrates to a depth of } 0.130 \mathrm{m} \text { . The mass of the }} \\ {\text { bullet is } 1.80 \mathrm{g} \text { . Assume a constant retarding force. (a) How much }} \\ {\text { time is required for the bullet to stop?( b) What force, in newtons, }} \\ {\text { does the tree exert on the bullet? }}\end{array}
$$

$$
V_{0 x}=350 \mathrm{m/s}
$$

$$
V_{x}=0
$$

$$
x-x_{0}=0.13 \mathrm{m}
$$

$$
\left(x- x_{0}\right)=\left(\frac{v_{0 x}+v_{x}}{2}\right) t
$$

$$
t=\frac{2\left(x-x_{0}\right)}{V_{0 x}+V_{x}}=\frac{2(0.13)}{350}
$$

$$
=7.43 * 10^{-4} \mathrm{S}
$$

$$
\sum F_{x}=m a_ x
$$

$$
-F=ma_x \Rightarrow F=-ma_x
$$

$$
=-\left(1.8 * 10^{-3}\right)\left(a_{x}\right)
$$

$$
V_{x}^{2}=V_{0x}^{2}-2a_ x\left(x-x_{0}\right) \rightarrow a_{x}=\frac{\left(V_{x}^{2}-V_{0 x}^{2}\right)}{2\left(x+x_0\right)}=-4.71 \times 10^{5}m/s^2
$$

$$
F_{x}=848 N
$$

$$
\begin{array}{l}{\text { A chair of mass } 12.0 \mathrm{kg} \text { is sitting on the horizontal floor; }} \\ {\text { the floor is not frictionless. You push on the chair with a force }} \\ {F=40.0 \mathrm{N} \text { that is directed at an angle of } 37.0^{\circ} \text { below the horizon- }} \\ {\text { tal and the chair slides along the floor. (a) Draw a clearly labeled }} \\ {\text { free-body diagram for the chair. (b) Use your diagram and Newton's }} \\ {\text { laws to calculate the normal force that the floor exerts on the chair. }}\end{array}
$$

$$
a _y=Zero
$$

$$
\sum F_{y}=m g_{y}
$$

$$
\sum F_ y=0 \longrightarrow
$$

$$
n-m g-F \sin 37=0
$$

$$
n=m g+F \sin 37
$$

$$
n=(12)(9.8)+(40) \sin 37=142 \mathrm{N}
$$

\(∴ n=142 N \)

$$
\begin{array}{l}{\text { A skier of mass } 65.0 \mathrm{kg} \text { is pulled up a snow-covered slope }} \\ {\text { at constant speed by a tow rope that is parallel to the ground. The }} \\ {\text { ground slopes upward at a constant angle of } 26.0^{\circ} \text { above the hori- }} \\ {\text { zontal, and you can ignore friction. (a) Draw a clearly labeled free- }} \\ {\text { body diagram for the skier. (b) Calculate the tension in the tow rope. }}\end{array}
$$

$$
\sum F_{x}=ma_{x}
$$

$$
T-m g \sin \theta=0
$$

$$
T=m g \sin \theta
$$

$$
=(65)(9.8) \sin 26^{\circ}
$$

$$
=279 N
$$

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