Physics for Scientists and Engineers with Modern Physics
Physics for Scientists and Engineers with Modern Physics
4th Edition
ISBN: 9780131495081
Author: Douglas C. Giancoli
Publisher: Addison-Wesley
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Chapter 7, Problem 90GP

Stretchable ropes ate used to safely arrest the fall of rock climbers. Suppose one end of a rope with unstretched length is anchored to a cliff and a climber of mass m is attached to the other end. When the climber is a height above the anchor point, he slips and falls under the influence of gravity for a distance 2, 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

x = m g k [ 1 + 1 + 4 k l m g ] .

(b) Assuming m = 85 kg, = 8.0 m and k = 850 N/m, determine x/ (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.

Chapter 7, Problem 90GP, Stretchable ropes ate used to safely arrest the fall of rock climbers. Suppose one end of a rope

FIGURE 7–33

Problem 90.

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Chapter 7 Solutions

Physics for Scientists and Engineers with Modern Physics

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 - Two bullets are fired at the same time with the...Ch. 7 - Does the net work done on a particle depend on the...Ch. 7 - A hand exerts a constant horizontal force on a...Ch. 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 - (II) Estimate the work you do to mow a lawn 10 m...Ch. 7 - (II) A lever such as that shown in Fig. 720 can be...Ch. 7 - (II) What is the minimum work needed to push a...Ch. 7 - (II) Eight books, each 4.0cm thick with mass 1.8...Ch. 7 - (II) A box of mass 6.0 kg is accelerated from rest...Ch. 7 - (II) (a) What magnitude force is required to give...Ch. 7 - (II) A 380-kg piano slides 3.9m down a 27 incline...Ch. 7 - (II) A gondola can carry 20 skiers, with a total...Ch. 7 - (II) A 17,000-kg jet takes off from an aircraft...Ch. 7 - (II) A 2200-N crate rests on the floor. How much...Ch. 7 - (II) A grocery cart with mass of 16 kg is being...Ch. 7 - (I) What is the dot product of...Ch. 7 - (I) For any vector V=Vxi+Vyj+Vzk show that...Ch. 7 - (I) Calculate the angle between the vectors:...Ch. 7 - Prob. 19PCh. 7 - (I) Vector V1 points along the z axis and has...Ch. 7 - (II) Given the vector A=3.0i+1.5j, find a vector...Ch. 7 - (II) A constant force F=(2.0i+4.0j)N acts on an...Ch. 7 - (II) If A=9.0i8.5j,B=8.0i+7.1j+4.2k,and...Ch. 7 - (II) Prove that AB=AxBx+AyBy+AzBz, starting from...Ch. 7 - (II) Given vectors A=4.8i+6.8jandB=9.6i+6.7j,...Ch. 7 - (II) Show that if two nonparallel vectors have the...Ch. 7 - (II) Let V=20.0i+22.0j14.0k. What angles does this...Ch. 7 - (II) Use the scalar product to prove the law of...Ch. 7 - (II) Vectors A and B are in the xy plane and their...Ch. 7 - (II) A and B are two vectors in the xy plane that...Ch. 7 - (II) Suppose A=1.0i+1.0j2.0k and B=1.0i+1.0j+2.0k,...Ch. 7 - (II) Find a vector of unit length in the xy plane...Ch. 7 - (III) Show that the scalar product of two vectors...Ch. 7 - (I) In pedaling a bicycle uphill, a cyclist exerts...Ch. 7 - (II) A spring has k = 65N/m. Draw a graph like...Ch. 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 - (II) If it requires 5.0 J of work to stretch a...Ch. 7 - (II) In Fig. 79 assume the distance axis is the x...Ch. 7 - (II) The force on a particle, acting along the x...Ch. 7 - (II) A child is pulling a wagon down the sidewalk....Ch. 7 - (II) The resistance of a packing material to a...Ch. 7 - (II) The force needed to hold a particular spring...Ch. 7 - (II) At the top of a pole vault, and athlete...Ch. 7 - (II) Consider a force F1=A/xwhich acts on an...Ch. 7 - (II) Assume that a force acting on an object is...Ch. 7 - (II) An object, moving along the circumference of...Ch. 7 - (III) A 2800-kg space vehicle, initially at rest,...Ch. 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 - (I) How much work is required to stop an electron...Ch. 7 - (I) How much work must be done to stop a 1300-kg...Ch. 7 - (II) Spiderman uses his spider webs to save a...Ch. 7 - (II) A baseball (m=145g) traveling 32mA moves a...Ch. 7 - (II) An 85-g arrow is fired from a bow whose...Ch. 7 - (II) A mass m is attached to a spring which is...Ch. 7 - (II) If the speed of a car is increased by 50%, by...Ch. 7 - (II) A 1200-kg car rolling on a horizontal surface...Ch. 7 - (II) One car has twice the mass of a second car,...Ch. 7 - (II) A 4.5-kg object moving in two dimensions...Ch. 7 - (II) A 265-kg load is lifted 23.0m vertically with...Ch. 7 - (II) (a) How much work is done by the horizontal...Ch. 7 - (II) (a) How much work is done by the horizontal...Ch. 7 - (II) At an accident scene on a level road,...Ch. 7 - (II) A 46.0-kg crate, starting from rest, is...Ch. 7 - (II) A train is moving along a track with constant...Ch. 7 - (III) We usually neglect the mass of a spring if...Ch. 7 - (III) An elevator cable breaks when a 925-kg...Ch. 7 - (a) A 3.0-g locust reaches a speed of 3.0m/s...Ch. 7 - In a certain library the first shelf is 12.0 cm...Ch. 7 - A 75-kg meteorite buries itself 5.0 m into soft...Ch. 7 - A 6.10-kg block is pushed 9.25 m up a smooth 37.0...Ch. 7 - Prob. 74GPCh. 7 - Two forces, F1=(1.50i0.80j+0.70k)Nand...Ch. 7 - The barrels of the 16-in, guns (bore diameter = 16...Ch. 7 - A varying force is given by F = Aekx, where x is...Ch. 7 - The force required to compress an imperfect...Ch. 7 - A force F=(10.0i+9.0j+12.0k)kNacts on a small...Ch. 7 - In the game of paintball, players use guns powered...Ch. 7 - A softball having a mass of 0.25 kg is pitched...Ch. 7 - An airplane pilot fell 370 m after jumping from an...Ch. 7 - Many cars have 5 mi/h (8 km/h) bumpers that are...Ch. 7 - What should be the spring constant k of a spring...Ch. 7 - Assume a cyclist of weight mg can exert a force on...Ch. 7 - A simple pendulum consists of a small object of...Ch. 7 - A car passenger buckles himself in with a seat...Ch. 7 - As an object moves along the x axis from x = 0.0 m...Ch. 7 - A cyclist starts from rest and coasts down a 4.0...Ch. 7 - Stretchable ropes ate used to safely arrest the...Ch. 7 - A small mass m hangs at rest from a vertical rope...Ch. 7 - (II) The net force along the linear path of a...Ch. 7 - (II) When different masses are suspended from a...
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