A proposed space station consists of a circular tube that will rotate about its centre (like a tubular bicycle tire), Fig. 5-44. The circle formed by the tube has a diameter of about $1.1 \mathrm{~km}$. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth $(1.0 \mathrm{~g})$ is to be felt?

Is it possible to whirl a bucket of water fast enough in a vertical circle so the water won't fall out? If so, what is the minimum speed?

At what minimum speed must a roller coaster be traveling when upside down at the top of a circle so that the passengers will not fall out? Assume a radius of curvature of 7.4 m.

$\mathbf{A}$ jet pilot takes his aircraft in a vertical loop (Fig. 5-43). Estimate the $78-\mathrm{kg}$ pilot's effective weight (the force with which the seat pushes up on him) at the bottom of the circle, and $(c)$ at the top of the circle (assume the same speed).

A $1050 \mathrm{~kg}$ car rounds a curve of radius $72 \mathrm{~m}$ banked at an angle of $14^{\circ}$. If the car is traveling at $85 \mathrm{~km} / \mathrm{h}$, will a friction force be required? If so, how much and in what direction?

How many revolutions per minute would a $15$-m-diameter Ferris wheel need to make for the passengers to feel "weightless" at the topmost point of the trip?

A jet pilot takes his aircraft in a vertical loop (Fig. 5-46). If the jet is moving at a speed of $1200 \mathrm{~km} / \mathrm{h}$ at the lowest point of the loop, estimate the $78\,\text{kg}$ pilot's effective weight (the force with which the seat pushes up on him) at the bottom of the circle.

A child slides down a slide with a $34^{\circ}$ incline, and at the bottom her speed is precisely half what it would have been if the slide had been frictionless. Estimate the coefficient of kinetic friction between the slide and the child.

Two masses $m_{\mathrm{A}}=2.0 \mathrm{~kg}$ and $m_{\mathrm{B}}=5.0 \mathrm{~kg}$ are on inclines and are connected together by a string as shown in Fig. $5-38$. The coefficient of kinetic friction between each mass and its incline is $\mu_{\mathrm{k}}=0.30$. If $m_{\mathrm{A}}$ moves up, and $m_{\mathrm{B}}$ moves down, determine their acceleration. Ignore the masses of the cord and the pulley (assume frictionless).

A system consists of three particles with these masses and velocities: mass 3.0 kg, moving north at 3.0 m/s; mass 4.0 kg, moving sooth at 5.0 m/s; and mass 7.0 kg, moving north at 2.0 m/s. What is the total momentum of the system?

A jet pilot takes his aircraft in a vertical loop (Fig. 5-46). If the jet is moving at a speed of $1200 \mathrm{~km} / \mathrm{h}$ at the lowest point of the loop, find the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed $5.0 \mathrm{~g}$'s.

A crate is given an initial speed of $3.0 \mathrm{~m} / \mathrm{s}$ up the $25.0^{\circ}$ plane shown in Fig. 5-35. How much time elapses before it returns to its starting point? Assume $\mu_{\mathrm{k}}=0.17$.

A crate is given an initial speed of $3.0 \mathrm{~m} / \mathrm{s}$ up the $25.0^{\circ}$ plane shown in Fig. 5-35. How far up the plane will it go?

A package of mass $m$ is dropped vertically onto a horizontal conveyor belt whose speed is $v=1.5 \mathrm{~m} / \mathrm{s}$, and the coefficient of kinetic friction between the package and the belt is $\mu_{\mathrm{k}}=0.70$. For how much time does the package slide on the belt (until it is at rest relative to the belt)?