In three situations, a single force acts on a moving particle. Here are the velocities (at that instant) and the forces: (1) $\stackrel{\mathbf{\rightharpoonup }}{\mathbf{v}}\mathbf{}\mathbf{=}\left(-4\stackrel{⏜}{i}\right)\mathbf{m}\mathbf{/}\mathbf{s}\mathbf{,}\mathbf{}\overline{\mathbf{f}}\mathbf{}\mathbf{=}\left(6\stackrel{⏜}{i}-20\right)\mathbf{N}\mathbf{:}$ (2) $\stackrel{\mathbf{⏜}}{\mathbf{v}}\mathbf{=}\left(-3\stackrel{⏜}{i}+\stackrel{⏜}{j}\right)\mathbf{m}\mathbf{/}\mathbf{s}\mathbf{,}\mathbf{}\stackrel{\mathbf{\rightharpoonup }}{\mathbf{f}}\mathbf{=}\left(2\stackrel{⏜}{i}+6\stackrel{⏜}{j}\right)\mathbf{N}$(3) $\stackrel{\mathbf{\rightharpoonup }}{\mathbf{v}}\mathbf{=}\left(-3\stackrel{⏜}{i}+\stackrel{⏜}{j}\right)\mathbf{m}\mathbf{/}\mathbf{s}\mathbf{,}\stackrel{\mathbf{\rightharpoonup }}{\mathbf{f}}\mathbf{=}\left(2\stackrel{⏜}{i}+6\stackrel{⏜}{j}\right)\mathbf{N}$. Rank the situations according to the rate at which energy is being transferred, greatest transfer to the particle ranked first, greatest transfer from the particle ranked last.

A 2.0 kglunchbox is sent sliding over a frictionless surface, in the positive direction of an x axis along the surface. Beginning at time t=0, a steady wind pushes on the lunchbox in the negative direction of the x axis. Figure 7-51 shows the position x of the lunchbox as a function of time t as the wind pushes on the lunchbox. From the graph, estimate the kinetic energy of the lunchbox at (a) t=1.0 s and (b)t=5.0 s. (c) How much work does the force from the wind do on the lunchbox from t=1.0 s to t=5.0 s?

During spring semester at MIT, residents of the parallel buildings of the East Campus dorms battle one another with large catapults that are made with surgical hose mounted on a window frame. A balloon filled with dyed water is placed in a pouch attached to the hose, which is then stretched through the width of the room. Assume that the stretching of the hose obeys Hooke’s law with a spring constant of 100 N/m. If the hose is stretched by 5.00 m and then released, how much work does the force from the hose do on the balloon in the pouch by the time the hose reaches its relaxed length?

An explosion at ground level leaves a crater with a diameter that is proportional to the energy of the explosion raised to the $\frac{\mathbf{1}}{\mathbf{3}}$ power; an explosion of 1 megaton of TNT leaves a crater with a 1 km diameter. Below Lake Huron in Michigan there appears to be an ancient impact crater with a 50 km diameter. What was the kinetic energy associated with that impact, in terms of (a) megatons of TNT (1 megaton yields $\mathbf{4}\mathbf{.}\mathbf{2}\mathbf{\times }{\mathbf{10}}^{\mathbf{15}}\mathbf{}\mathbf{J}$) and (b) Hiroshima bomb equivalents (13 kilotons of TNT each)? (Ancient meteorite or comet impacts may have significantly altered the climate, killing off the dinosaurs and other life-forms.)

Figure 7-23 shows three arrangements of a block attached to identical springs that are in their relaxed state when the block is centered as shown. Rank the arrangements according to the magnitude of the net force on the block, largest first, when the block is displaced by distance d (a) to the right and (b) to the left. Rank the arrangements according to the work done on the block by the spring forces, greatest first, when the block is displaced by d (c) to the right and (d) to the left.

A glob of slime is launched or dropped from the edge of a cliff. Which of the graphs in figure 7-22 could possibly show how the kinetic energy of the glob changes during its flight?