91Ó°ÊÓ

A 22-caliber riffle bullet traveling at $\mathbf{350}\mathbf{m}\mathbf{/}\mathbf{s}$strikes a large tree and penetrates it to a depth of $\mathbf{0}\mathbf{.}\mathbf{130}\mathbf{m}$. The mass of the bullet is $\mathbf{1}\mathbf{.}\mathbf{80}\mathbf{g}$. Assume a constant retarding force. (a) How much time is required for the bullet to stop? (b) What force, in Newton, does the tree exert on the bullet?

In an experiment, one of the forces exerted on a proton is $\stackrel{\mathbf{→}}{\mathbf{F}}\mathbf{=}{\mathbf{Î\pm ³\ae }}^{\mathbf{2}}\mathbf{}\widehat{\mathbf{i}\mathbf{}}$, where $\mathbf{Î\pm }\mathbf{=}\mathbf{12}\mathbf{}\mathbf{N}\mathbf{/}{\mathbf{m}}^{\mathbf{2}}$. (a) How much work does $\stackrel{\mathbf{→}}{\mathbf{F}}$ do when the proton moves along the straight-line path from the point (0.10 m, 0) to the point (0.10 m, 0.40 m)? (b) Along the straight-line path from the point (0.10 m, 0) to the point (0.30 m, 0)? (c) Along the straight-line path from the point (0.30 m, 0) to the point (0.10 m, 0)? (d) Is the force $\stackrel{\mathbf{→}}{\mathbf{F}}$ conservative? Explain. If $\stackrel{\mathbf{→}}{\mathbf{F}}$is conservative, what is the potential-energy function for it? Let U = 0 when x = 0.

Let be the angle that the vectormakes with the +x-axis, measured counterclockwise from that axis. Find angle for a vector that has these components: (a) $A_x=2.00m,A_y=-1.00m$ ; (b$A_x=2.00m,A_y=1.00m$ ; (c) $A_x=-2.00m,A_y=1.00m$ ; (d) $A_x=-2.00m,A_y=-1.00m$

Let $\mathbf{θ}$ be the angle that the vector $\stackrel{\mathbf{→}}{\mathbf{A}}$makes with the +x-axis, measured counterclockwise from that axis. Find angle $\mathbf{θ}$ for a vector that has these components: (a)${\mathbf{A}}_{\mathbf{x}}\mathbf{=}\mathbf{2}\mathbf{.}\mathbf{00}\mathbf{}\mathbf{m}\mathbf{,}\mathbf{}{\mathbf{A}}_{\mathbf{y}}\mathbf{=}\mathbf{-}\mathbf{1}\mathbf{.}\mathbf{00}\mathbf{}\mathbf{m}$ ; (b)${\mathbf{A}}_{\mathbf{x}}\mathbf{=}\mathbf{2}\mathbf{.}\mathbf{00}\mathbf{}\mathbf{m}\mathbf{,}{\mathbf{A}}_{\mathbf{y}}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{00}\mathbf{}\mathbf{m}$ ; (c)${\mathbf{A}}_{\mathbf{x}}\mathbf{=}\mathbf{-}\mathbf{2}\mathbf{.}\mathbf{00}\mathbf{}\mathbf{m}\mathbf{,}{\mathbf{A}}_{\mathbf{y}}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{00}\mathbf{}\mathbf{m}$ ; (d) ${\mathbf{A}}_{\mathbf{x}}\mathbf{=}\mathbf{-}\mathbf{2}\mathbf{.}\mathbf{00}\mathbf{}\mathbf{m}\mathbf{,}{\mathbf{A}}_{\mathbf{y}}\mathbf{=}\mathbf{-}\mathbf{1}\mathbf{.}\mathbf{00}\mathbf{}\mathbf{m}$.

Question: A box of bananas weighing 40.0N rests on a horizontal surface. The coefficient of static friction between the box and the surface is 0.40, and the coefficient of kinetic friction is 0.20. (a) If no horizontal force is applied to the box and the box is at rest, how large is the friction force exerted on it? (b) What is the magnitude of the friction force if a monkey applies a horizontal force of 6.0N to the box and the box is initially at rest? (c) What minimum horizontal force must the monkey apply to start the box in motion? (d) What minimum horizontal force must the monkey apply to keep the box moving at constant velocity once it has been started? (e) If the monkey applies a horizontal force of 18.0N, what is the magnitude of the friction force and what is the box’s acceleration?

A nylon rope used by mountaineers elongates 1.10 m under the weight of a 65.0-kg climber. If the rope is 45.0 m in length and 7.0 mm in diameter, what is Young’s modulus for nylon?

Let $\mathbf{θ}$be the angle that the vector$\stackrel{\mathbf{→}}{\mathbf{A}}$makes with the +x-axis, measured counterclockwise from that axis. Find angle $\mathbf{θ}$for a vector that has these components: (a) ${\mathbf{θ´¡}}_{\mathbf{x}}\mathbf{=}\mathbf{-}\mathbf{2}\mathbf{.}\mathbf{00}\mathbf{}\mathbf{m}\mathbf{,}{\mathbf{A}}_{\mathbf{y}}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{00}\mathbf{}\mathbf{m}$; (b) ${\mathbf{A}}_{\mathbf{x}}\mathbf{=}\mathbf{2}\mathbf{.}\mathbf{00}\mathbf{}\mathbf{m}\mathbf{,}{\mathbf{A}}_{\mathbf{y}}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{00}\mathbf{}\mathbf{m}$; (c)${\mathbf{A}}_{\mathbf{x}}\mathbf{=}\mathbf{-}\mathbf{2}\mathbf{.}\mathbf{00}\mathbf{}\mathbf{m}\mathbf{,}{\mathbf{A}}_{\mathbf{y}}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{00}\mathbf{}\mathbf{m}$; (d)${\mathbf{A}}_{\mathbf{x}}\mathbf{=}\mathbf{-}\mathbf{2}\mathbf{.}\mathbf{00}\mathbf{ }\mathbf{m}\mathbf{,}\mathbf{ }{\mathbf{A}}_{\mathbf{y}}\mathbf{=}\mathbf{-}\mathbf{1}\mathbf{.}\mathbf{00}\mathbf{ }\mathbf{m}$

Four small spheres, each of which you can regard as a point of mass of 0.200 kg, are arranged in a square of 0.400 m on a side and connected by extremely light rods (Fig. E9.28). Find the moment of inertia of the system about an axis

through the center of the square, perpendicular to its plane (an axis through point O in the figure);

bisecting two opposite sides of the square (an axis along the line AB in the figure);

that passes through the centers of the upper left and lower right spheres and point O.

A playground marry-go-round has radius $2.40\mathrm{m}$ and moment of inertia $2100kg{m}^2$ about a vertical axle through its center, and it turns with negligible friction. (a) A child applies an $18.0-N$ force tangentially to the edge of the merry-go-round for $15.0s$. If the merry-go-round is initially at rest, what is its angular speed after this $15.0-s$ interval? (b) How much work did the child do on the merry-go-round? (c) What is the average power supplied by the child?

A gyroscope is precessing as in Fig. 10.32. What happens if you gently add some weight to the end of the flywheel axis farthest from the pivot?