Chapter 1: Mechanics

A rigid, lighter-than-air dirigible filled with helium cannot continue to rise indefinitely. Why? What determines the maximum height it can attain?

Can you have zero displacement and nonzero average velocity? Zero displacement and nonzero velocity? Illustrate your answers on an x-t graph.

projectile is fired upward at an angle$\mathit{\theta }$above the horizontal with an initial speed${\mathit{v}}_{\mathbf{0}}$. At its maximum height, what are its velocity vector, its speed, and its acceleration vector?

You make two versions of the same object out of the same material having uniform density. For one version, all the dimensions are exactly twice as great as for the other one. If the same torque acts on both versions, giving the smaller version angular acceleration$\mathbf{\alpha }$, what will be the angular acceleration of the larger version in terms of$\mathbf{\alpha }$?

A force$\overrightarrow{\mathbf{F}}$ is in the x-direction and has a magnitude that depends on x. Sketch a possible graph of F versus x such that the force does zero work on an object that moves from${\mathit{x}}_{\mathbf{1}}$ to ${\mathit{x}}_{\mathbf{2}}$, even though the force magnitude is not zero at all x in this range.

In a completely inelastic collision between two objects,wherethe objects stick together after the collision, is it possiblefor the final kinetic energy of the system to be zero? If so, givean example in which this would occur. If the final kinetic energyis zero, what must the initial momentum of the system be? Is theinitial kinetic energy of the system zero? Explain.

(a) A book is lifted upward a vertical distance of 0.800 m. During this displacement, does the gravitational force acting on the book do positive work or negative work? Does the gravitational potential energy of the book increase or decrease? (b) A can of beans is released from rest and falls downward a vertical distance of 2.00 m. During this displacement, does the gravitational force acting on the can do positive work or negative work? Does the gravitational potential energy of the can increase or decrease?

The system shown in Fig. 14.17 is mounted in an elevator. What happens to the period of the motion (does it increase, decrease, or remain the same) if the elevator (a) accelerates upward at$\mathbf{5}\mathbf{.}\mathbf{0}\mathbf{}\mathbf{m}\mathbf{/}{\mathbf{s}}^{\mathbf{2}}$ ; (b) moves upward at a steady $\mathbf{5}\mathbf{.}\mathbf{0}\mathbf{}\mathbf{m}\mathbf{/}\mathbf{s}$; (c) accelerates downward at $\mathbf{5}\mathbf{.}\mathbf{0}\mathbf{}\mathbf{m}\mathbf{/}{\mathbf{s}}^{\mathbf{2}}$? Justify your answers.

The sun pulls on the moon with a force that is more than twice the magnitude of the force with which the earth attracts the moon. Why, then, doesn’t the sun take the moon away from the earth?

Three archers each fire four arrows at a target. Joe’s four arrows hit at points$10cm$above,$10cm$below,$10cm$to the left, and$10cm$ to the right of the centre of the target. All four of Moe’s arrows hit within $1\mathrm{cm}$ of a point $20cm$ from the centre, and Flo’s four arrows hit within localid="1664338672895" $1cm$of the centre. The contest judge says that one of the archers is precise but not accurate, another archer is accurate but not precise, and the third archer is both accurate and precise. Which description applies to which archer? Explain.