Pearson eText -- Physics for Scientists and Engineers with Modern Physics -- Instant Access (Pearson+)
5th Edition
ISBN: 9780137488179
Author: Douglas Giancoli
Publisher: PEARSON+
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Chapter 7, Problem 99GP
Stretchable ropes ate used to safely arrest the fall of rock climbers. Suppose one end of a rope with unstretched length ℓ is anchored to a cliff and a climber of mass m is attached to the other end. When the climber is a height ℓ above the anchor point, he slips and falls under the influence of gravity for a distance 2ℓ, after which the rope becomes taut and stretches a distance x as it stops the climber (see Fig. 7–33). Assume a stretchy rope behaves as a spring with spring constant k. (a) Applying the work-energy principle, show that
(b) Assuming m = 85 kg, ℓ = 8.0 m and k = 850 N/m, determine x/ℓ (the fractional stretch of the rope) and kx/mg (the force that the rope exerts on the climber compared to his own weight) at the moment the climber’s fall has been stopped.
FIGURE 7–33
Problem 90.
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Chapter 7 Solutions
Pearson eText -- Physics for Scientists and Engineers with Modern Physics -- Instant Access (Pearson+)
Ch. 7.1 - A box is dragged a distance d across a floor by a...Ch. 7.1 - Return to the Chapter-Opening Question, page 163,...Ch. 7.4 - (a) Make a guess: will the work needed to...Ch. 7.4 - Can kinetic energy ever be negative?Ch. 7.4 - Prob. 1EECh. 7 - In what ways is the word work as used in everyday...Ch. 7 - A woman swimming upstream is not moving with...Ch. 7 - Can a centripetal force ever do work on an object?...Ch. 7 - Why is it tiring to push hard against a solid wall...Ch. 7 - Does the scalar product of two vectors depend on...
Ch. 7 - Can a dot product ever he negative? If yes, under...Ch. 7 - Prob. 7QCh. 7 - Does the dot product of two vectors have direction...Ch. 7 - Can the normal force on an object ever do work?...Ch. 7 - You have two springs that are identical except...Ch. 7 - Prob. 11QCh. 7 - In Example 710, it was stated that the block...Ch. 7 - Does the net work done on a particle depend on the...Ch. 7 - Prob. 2MCQCh. 7 - Prob. 3MCQCh. 7 - Prob. 5MCQCh. 7 - Prob. 7MCQCh. 7 - Prob. 8MCQCh. 7 - Prob. 9MCQCh. 7 - Prob. 10MCQCh. 7 - Prob. 12MCQCh. 7 - Prob. 13MCQCh. 7 - Prob. 14MCQCh. 7 - (I) How much work is done by the gravitational...Ch. 7 - (I) How high will a 1.85-kg rock go if thrown...Ch. 7 - (I) A 75.0-kg firefighter climbs a flight of...Ch. 7 - (I) A hammerhead with a mass of 2.0 kg is allowed...Ch. 7 - Prob. 5PCh. 7 - Prob. 6PCh. 7 - Prob. 7PCh. 7 - Prob. 8PCh. 7 - (II) Estimate the work you do to mow a lawn 10 m...Ch. 7 - Prob. 10PCh. 7 - (II) A lever such as that shown in Fig. 720 can be...Ch. 7 - Prob. 12PCh. 7 - Prob. 13PCh. 7 - Prob. 14PCh. 7 - Prob. 15PCh. 7 - Prob. 16PCh. 7 - Prob. 17PCh. 7 - Prob. 18PCh. 7 - (I) For any vector V=Vxi+Vyj+Vzk show that...Ch. 7 - Prob. 20PCh. 7 - Prob. 21PCh. 7 - Prob. 22PCh. 7 - Prob. 23PCh. 7 - (II) A constant force F=(2.0i+4.0j)N acts on an...Ch. 7 - Prob. 25PCh. 7 - Prob. 26PCh. 7 - (II) Show that if two nonparallel vectors have the...Ch. 7 - Prob. 28PCh. 7 - Prob. 29PCh. 7 - Prob. 30PCh. 7 - Prob. 31PCh. 7 - Prob. 32PCh. 7 - Prob. 33PCh. 7 - Prob. 34PCh. 7 - Prob. 35PCh. 7 - Prob. 36PCh. 7 - Prob. 37PCh. 7 - (II) If the hill in Example 72 (Fig. 74) was not...Ch. 7 - (II) The net force exerted on a particle acts in...Ch. 7 - Prob. 40PCh. 7 - (II) The force on a particle, acting along the x...Ch. 7 - Prob. 42PCh. 7 - Prob. 43PCh. 7 - (II) At the top of a pole vault, and athlete...Ch. 7 - Prob. 45PCh. 7 - Prob. 46PCh. 7 - (II) If it requires 5.0 J of work to stretch a...Ch. 7 - (II) An object, moving along the circumference of...Ch. 7 - Prob. 49PCh. 7 - Prob. 50PCh. 7 - Prob. 51PCh. 7 - Prob. 52PCh. 7 - (III) A 3.0-m-long steel chain is stretched out...Ch. 7 - (I) At room temperature, an oxygen molecule, with...Ch. 7 - (I) (a) If the kinetic energy of a particle is...Ch. 7 - Prob. 56PCh. 7 - Prob. 57PCh. 7 - Prob. 58PCh. 7 - Prob. 59PCh. 7 - (II) An 85-g arrow is fired from a bow whose...Ch. 7 - (II) If the speed of a car is increased by 50%, by...Ch. 7 - Prob. 62PCh. 7 - Prob. 63PCh. 7 - Prob. 64PCh. 7 - Prob. 65PCh. 7 - (II) (a) How much work is done by the horizontal...Ch. 7 - Prob. 67PCh. 7 - Prob. 68PCh. 7 - (II) A train is moving along a track with constant...Ch. 7 - Prob. 70PCh. 7 - Prob. 71PCh. 7 - Prob. 72PCh. 7 - Prob. 73PCh. 7 - Prob. 74GPCh. 7 - Prob. 75GPCh. 7 - Prob. 76GPCh. 7 - Prob. 77GPCh. 7 - Prob. 78GPCh. 7 - A varying force is given by F = Aekx, where x is...Ch. 7 - Prob. 80GPCh. 7 - A force F=(10.0i+9.0j+12.0k)kNacts on a small...Ch. 7 - Prob. 82GPCh. 7 - Prob. 83GPCh. 7 - Prob. 84GPCh. 7 - (III) We usually neglect the mass of a spring if...Ch. 7 - Prob. 86GPCh. 7 - Prob. 87GPCh. 7 - Prob. 88GPCh. 7 - Prob. 89GPCh. 7 - Prob. 90GPCh. 7 - Prob. 91GPCh. 7 - Assume a cyclist of weight mg can exert a force on...Ch. 7 - A car passenger buckles himself in with a seat...Ch. 7 - A simple pendulum consists of a small object of...Ch. 7 - Prob. 95GPCh. 7 - A small mass m hangs at rest from a vertical rope...Ch. 7 - Prob. 97GPCh. 7 - Prob. 98GPCh. 7 - Stretchable ropes ate used to safely arrest the...Ch. 7 - Prob. 100GP
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