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Chapter 5, Problem 61P

In a loop-the-loop roller coaster, show that a car moving too slowly would leave the track at an angle ϕ given by cos ϕ = v2/rg, where ϕ is the angle made by a vertical line through the center of the circular track and a line from the center to the point where the car leaves the track.

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Chapter 5 Solutions

Essential University Physics: Volume 1; Mastering Physics with Pearson eText -- ValuePack Access Card -- for Essential University Physics (3rd Edition)

Ch. 5 - Gravity pulls a satellite toward Earths center. So...Ch. 5 - Explain why a car with ABS brakes can have a...Ch. 5 - A fishing line has a 20-lb breaking strength. Is...Ch. 5 - Two blocks rest on slopes of unequal angles,...Ch. 5 - Youre on a plane undergoing a banked turn, so...Ch. 5 - A backcountry skier weighing 700 N skis down a...Ch. 5 - Two forces, both in the x-y plane, act on a...Ch. 5 - Two forces act on a 3.1-kg mass that undergoes...Ch. 5 - At what angle should you tilt an air table to...Ch. 5 - A skier starts from rest at the top of a 24 slope...Ch. 5 - A tow truck is connected to a 1400-kg car by a...Ch. 5 - Studies of gymnasts show that their high rate of...Ch. 5 - Find the minimum slope angle for which the skier...Ch. 5 - Section 5.2 Multiple Objects Your 12-kg baby...Ch. 5 - If the left-hand slope in Fig. 5.30 makes a 60...Ch. 5 - Suppose the angles shown in Fig. 5.30 are 60 and...Ch. 5 - Two unfortunate climbers, roped together, are...Ch. 5 - Suppose the Moon were held in its orbit not by...Ch. 5 - Show that the force needed to keep a mass m in a...Ch. 5 - A 940-g rock is whirled in a horizontal circle at...Ch. 5 - Youre investigating a subway accident in which a...Ch. 5 - A tetherball on a 1.55-m rope is struck so that it...Ch. 5 - An airplane goes into a turn 3.6 km in radius. If...Ch. 5 - Movers slide a 73-kg file cabinet along a floor...Ch. 5 - A hockey puck is given an initial speed of 14 m/s....Ch. 5 - Starting from rest, a skier slides 100 m down a 28...Ch. 5 - A car moving at 40 km/h negotiates a 130-m-radius...Ch. 5 - Prob. 34PCh. 5 - A block is launched with initial speed 2.2 m/s up...Ch. 5 - In the process of mitosis (cell division), two...Ch. 5 - A 14.6-kg monkey hangs from the middle of a...Ch. 5 - A camper hangs a 26-kg pack between two trees...Ch. 5 - A mass m, undergoes circular motion of radius R on...Ch. 5 - Patients with severe leg breaks arc often placed...Ch. 5 - Riders on the Great American Revolution...Ch. 5 - A 45-kg skater rounds a 5.0-m-radius turn at 6.3...Ch. 5 - When a piano turns, it banks as shown in Fig. 5.35...Ch. 5 - You whirl a bucket of water in a vertical circle...Ch. 5 - A child sleds down an 8.5 slope at constant speed....Ch. 5 - The handle of a 22-kg lawnmower makes a 35 angle...Ch. 5 - Repeal Example 5.4, now assuming that the...Ch. 5 - A bat crashes into the vertical front of an...Ch. 5 - The coefficient of static friction between steel...Ch. 5 - A bug crawls outward from the center of a CD...Ch. 5 - A 310-g paperback book rests on a 1.2-kg textbook....Ch. 5 - Children sled down a41-m-long hill inclined at 25....Ch. 5 - In a typical front-wheel-drive car, 70% of the...Ch. 5 - A police officer investigating an accident...Ch. 5 - A slide inclined at 35 takes bathers into a...Ch. 5 - You try to move a heavy trunk, pushing down and...Ch. 5 - A block is shoved up a 22 slope with an initial...Ch. 5 - At the end of a factory production line, boxes...Ch. 5 - Youre in traffic court, arguing against a speeding...Ch. 5 - A space station is in the shape of a hollow ring,...Ch. 5 - In a loop-the-loop roller coaster, show that a car...Ch. 5 - Find an expression for the minimum frictional...Ch. 5 - An astronaut is training in an earthbound...Ch. 5 - You stand on a spring scale at the north pole and...Ch. 5 - Driving in thick fog on a horizontal road, you...Ch. 5 - A block is projected up an incline at angle . It...Ch. 5 - A 2.1-kg mass is connected to a spring with spring...Ch. 5 - Take k = 0.75 in Example 5.11, and plot the...Ch. 5 - Repeat the preceding problem for an arbitrary...Ch. 5 - Moving through a liquid, an object of mass m...Ch. 5 - Suppose the object in Problem 70 had an initial...Ch. 5 - A block is launched with speed v0 up a slope...Ch. 5 - A florist asks you to make a window display with...Ch. 5 - Youre al the state fair. A sideshow barker claims...Ch. 5 - One of the limiting factors in high-performance...Ch. 5 - Figure 5.39 shows an apparatus used to verify...Ch. 5 - A spiral is an ice-skating position in which the...Ch. 5 - A spiral is an ice-skating position in which the...Ch. 5 - A spiral is an ice-skating position in which the...Ch. 5 - A spiral is an ice-skating position in which the...
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