Problem 23
Is it possible to swing a mass attached to a string in a perfectly horizontal circle (with the mass and the string parallel to the ground)?
Problem 25
Suppose you are riding on a roller coaster, which moves through a vertical circular loop. Show that your apparent weight at the bottom of the loop is six times your weight when you experience weightlessness at the top, independent of the size of the loop. Assume that friction is negligible.
Problem 28
Assuming that the Earth is spherical and recalling that latitudes range from \(0^{\circ}\) at the Equator to \(90^{\circ} \mathrm{N}\) at the North Pole, how far apart, measured on the Earth's surface, are Dubuque, Iowa \(\left(42.50^{\circ} \mathrm{N}\right.\) latitude \()\), and Guatemala City \(\left(14.62^{\circ} \mathrm{N}\right.\) latitude \() ?\) The two cities lie on approximately the same longitude. Do not neglect the curvature of the Earth in determining this distance.
Problem 30
A typical Major League fastball is thrown at approximately \(88 \mathrm{mph}\) and with a spin rate of \(110 \mathrm{rpm} .\) If the distance between the pitcher's point of release and the catcher's glove is exactly \(60.5 \mathrm{ft},\) how many full turns does the ball make between release and catch? Neglect any effect of gravity or air resistance on the ball's flight.
Problem 34
Mars orbits the Sun at a mean distance of 228 million \(\mathrm{km},\) in a period of 687 days. The Earth orbits at a mean distance of 149.6 million \(\mathrm{km},\) in a period of 365.26 days. a) Suppose Earth and Mars are positioned such that Earth lies on a straight line between Mars and the Sun. Exactly 365.26 days later, when the Earth has completed one orbit, what is the angle between the Earth-Sun line and the Mars-Sun line? b) The initial situation in part (a) is a closest approach of Mars to Earth. What is the time, in days, between two closest approaches? Assume constant speed and circular orbits for both Mars and Earth. c) Another way of expressing the answer to part (b) is in terms of the angle between the lines drawn through the Sun, Earth, and Mars in the two closest approach situations. What is that angle?
Problem 36
What is the centripetal acceleration of the Moon? The period of the Moon's orbit about the Earth is 27.3 days, measured with respect to the fixed stars. The radius of the Moon's orbit is \(R_{M}=3.85 \cdot 10^{8} \mathrm{~m}\).
Problem 37
You are holding the axle of a bicycle wheel with radius \(35.0 \mathrm{~cm}\) and mass \(1.00 \mathrm{~kg}\). You get the wheel spinning at a rate of 75.0 rpm and then stop it by pressing the tire against the pavement. You notice that it takes \(1.20 \mathrm{~s}\) for the wheel to come to a complete stop. What is the angular acceleration of the wheel?
Problem 38
Life scientists use ultracentrifuges to separate biological components or to remove molecules from suspension. Samples in a symmetric array of containers are spun rapidly about a central axis. The centrifugal acceleration they experience in their moving reference frame acts as "artificial gravity" to effect a rapid separation. If the sample containers are \(10.0 \mathrm{~cm}\) from the rotation axis, what rotation frequency is required to produce an acceleration of \(1.00 \cdot 10^{5} g ?\)
Problem 39
A centrifuge in a medical laboratory rotates at an angular speed of 3600 rpm (revolutions per minute). When switched off, it rotates 60.0 times before coming to rest. Find the constant angular acceleration of the centrifuge.
Problem 40
A discus thrower (with arm length of \(1.2 \mathrm{~m}\) ) starts from rest and begins to rotate counterclockwise with an angular acceleration of \(2.5 \mathrm{rad} / \mathrm{s}^{2}\) a) How long does it take the discus thrower's speed to get to \(4.7 \mathrm{rad} / \mathrm{s} ?\) b) How many revolutions does the thrower make to reach the speed of \(4.7 \mathrm{rad} / \mathrm{s} ?\) c) What is the linear speed of the discus at \(4.7 \mathrm{rad} / \mathrm{s} ?\) d) What is the linear acceleration of the discus thrower at this point? e) What is the magnitude of the centripetal acceleration of the discus thrown? f) What is the magnitude of the discus's total acceleration?
