Explanation 1) Concept: If we know the U(x) for a system, we can find the force acting on the system|F(x)| by differentiating the potential energy with respect to distance.Mechanical energy of an isolated system is equal to the kinetic energy + potential energy 2) Formula: i) F = - d U x d x ii) ∆ E m e c = ∆ k + ∆ U 3) Given: i) Mass of the particle m = 2.0 k g ii) At x = 2.0 m, v = - 1.5 m / s From graph iii) A t x = 2.0 m U ( x ) = - 8 J iv) A t x = 7.0 m U ( x ) = - 16 J 4) Calculations: a) The force at x = 2.0 m is, We can take a slope of this graph between the region x= 1 m to x = 4 m F = - d U x d x F = U ( x = 4 m ) - U ( x = 1 m ) 4 m - 1 m F = - 17.5 - - 2.8 3 m F = 4.9 N b) Since slope is negative, the force would be in positive x direction. c) At x = 2.0 m we can find potential energy, as U x = 2.0 m = U x = 1.0 m + - 4.9 J m 1.0 = - 7.7 J … … … … … … … … … … … … … … ( 1 ) ∆ k = 1 2 × m v 2 ∆ k = 1 2 × - 1.5 2 × 2 k = 2.25 J … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … ( 2 ) So the total mechanical energy is, ∆ E m e c = ∆ k + ∆ U … … … … … … … … … … … … … … … … … … … … … … … … … … … … …

11th Edition

ISBN: 9781119459132

Author: Halliday

Publisher: WILEY

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Question

Chapter 8, Problem 77P

To determine

To find:

a) Magnitude of force |F(x)|

b) Directionof force |F(x)|

c) Position of the particle to the left x(left)

d) Position of the particle to the right, x(right)

e) particles speed at x = 7.0 m, V(7)

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Chapter 8, Problem 76P

Chapter 8, Problem 78P

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Chapter 8 Solutions

FUNDAMENTALS OF PHYSICS (LLF)+WILEYPLUS

Ch. 8 - In Fig. 8-18, a horizontally moving block can take...Ch. 8 - Figure 8-19 gives the potential energy function of...Ch. 8 - Figure 8-20 shows one direct path and four...Ch. 8 - In Fig. 8-21, a small, initially stationary block...Ch. 8 - In Fig. 8-22, a block slides from A to C along a...Ch. 8 - In Fig. 8-23a, you pull upward on a rope that is...Ch. 8 - The arrangement shown in Fig. 8-24 is similar to...Ch. 8 - In Fig. 8-25, a block slides along a track that...Ch. 8 - Figure 8-26 shows three situations involving a...Ch. 8 - Figure 8-27 shows three plums that are launched...

Ch. 8 - When a particle moves from f to i and from j to i...Ch. 8 - SSM What is the spring constant of a spring that...Ch. 8 - In Fig. 8-29, a single frictionless roller-coaster...Ch. 8 - You drop a 2.00 kg book to a friend who stands on...Ch. 8 - Figure 8-31 shows a ball with mass m = 0.341 kg...Ch. 8 - SSM In Fig. 8-32, a 2.00 g ice flake is released...Ch. 8 - In Fig. 8-33, a small block of mass m = 0.032 kg...Ch. 8 - Figure 8-34 shows a thin rod, of length L = 2.00 m...Ch. 8 - A 1.50 kg snowball is fired from a cliff 12.5 m...Ch. 8 - GO In Problem 2, what is the speed of the car at a...Ch. 8 - a In Problem 3, what is the speed of the book when...Ch. 8 - SSM WWW a In Problem 5, what is the speed of the...Ch. 8 - a In Problem 8, using energy techniques rather...Ch. 8 - SSM A 5.0 g marble is fired vertically upward...Ch. 8 - a In Problem 4, what initial speed must be given...Ch. 8 - SSM In Fig. 8-35, a runaway truck with failed...Ch. 8 - A 700 g block is released from rest at height h0...Ch. 8 - In Problem 6, what are the magnitudes of a the...Ch. 8 - a In Problem 7, what is the speed of the ball at...Ch. 8 - GO Figure 8-36 shows an 8.00 kg stone at rest on a...Ch. 8 - GO A pendulum consists of a 2.0 kg stone swinging...Ch. 8 - Figure 8-34 shows a pendulum of length L = 1.25 m....Ch. 8 - A 60 kg skier starts from rest at height H = 20 m...Ch. 8 - ILW The string in Fig. 8-38 is L = 120 cm long,...Ch. 8 - A block of mass m = 2.0 kg is dropped from height...Ch. 8 - At t = 0 a 1.0 kg ball is thrown from a tall tower...Ch. 8 - A conservative force F=(6.0x12)i N, where x is in...Ch. 8 - Tarzan, who weighs 688 N, swings from a cliff at...Ch. 8 - Figure 8-41a applies to the spring in a cork gun...Ch. 8 - SSM WWW In Fig. 8-42, a block of mass m = 12 kg is...Ch. 8 - GO A 2.0 kg breadbox on a frictionless incline of...Ch. 8 - ILW A block with mass m = 2.00 kg is placed...Ch. 8 - In Fig. 8-45, a chain is held on a frictionless...Ch. 8 - GO In Fig. 8-46, a spring with k = 170 N/m is at...Ch. 8 - GO A boy is initially seated on the top of a...Ch. 8 - GO In Fig. 8-42, a block of mass m = 3.20 kg...Ch. 8 - GO Two children are playing a game in which they...Ch. 8 - A uniform cord of length 25 cm and mass 15 g is...Ch. 8 - Figure 8-49 shows a plot of potential energy U...Ch. 8 - GO Figure 8-50 shows a plot of potential energy U...Ch. 8 - The potential energy of a diatomic molecule a...Ch. 8 - A single conservative force Fx acts on a 1.0 kg...Ch. 8 - A worker pushed a 27 kg block 9.2 m along a level...Ch. 8 - A collie drags its bed box across a floor by...Ch. 8 - A horizontal force of magnitude 35.0 N pushes a...Ch. 8 - SSM A rope is used to pull a 3.57 kg block at...Ch. 8 - An outfielder throws a baseball with an initial...Ch. 8 - A 75 g Frisbee is thrown from a point 1.1 m above...Ch. 8 - In Fig. 8-51, a block slides down an incline. As...Ch. 8 - SSM ILW A 25 kg bear slides, from rest, 12 m down...Ch. 8 - A 60 kg skier leaves the end of a ski-jump ramp...Ch. 8 - During a rockslide, a 520 kg rock slides from rest...Ch. 8 - A large fake cookie sliding on a horizontal...Ch. 8 - GO In Fig. 8-52, a 3.5 kg block is accelerated...Ch. 8 - A child whose weight is 267 N slides down a 6.1 m...Ch. 8 - ILW In Fig. 8-53, a block of mass m = 2.5 kg...Ch. 8 - You push a 2.0 kg block against a horizontal...Ch. 8 - GO In Fig. 8-54, a block slides along a track from...Ch. 8 - A cookie jar is moving up a 40 incline. At a point...Ch. 8 - A stone with a weight of 5.29 N is launched...Ch. 8 - Prob. 60P Ch. 8 - When a click beetle is upside down on its back, it...Ch. 8 - GO In Fig. 8-55, a block slides along a path that...Ch. 8 - The cable of the 1800 kg elevator cab in Fig. 8-56...Ch. 8 - GO In Fig. 8-57, a block is released from rest at...Ch. 8 - GO A particle can slide along a track with...Ch. 8 - A 3.2 kg sloth hangs 3.0 m above the ground. a...Ch. 8 - SSM A spring k = 200 N/m is fixed at the top of a...Ch. 8 - From the edge of a cliff, a 0.55 kg projectile is...Ch. 8 - SSM In Fig. 8-60, the pulley has negligible mass,...Ch. 8 - GO In Fig. 8-38, the string is L = 120 cm long,...Ch. 8 - SSM In Fig. 8-51, a block is sent sliding down a...Ch. 8 - Two snowy peaks are at heights H = 850 m and h =...Ch. 8 - SSM The temperature of a plastic cube is monitored...Ch. 8 - A skier weighing 600 N goes over a frictionless...Ch. 8 - SSM To form a pendulum, a 0.092 kg ball is...Ch. 8 - Prob. 76P Ch. 8 - Prob. 77P Ch. 8 - At a certain factory, 300 kg crates are dropped...Ch. 8 - SSM A 1500 kg car begins sliding down a 5.0...Ch. 8 - In Fig. 8-65, a 1400 kg block of granite is pulled...Ch. 8 - A particle can move along only an x axis, where...Ch. 8 - For the arrangement of forces in Problem 81, a...Ch. 8 - SSM A 15 kg block is accelerated at 2.0 m/s2 along...Ch. 8 - A certain spring is found not to conform to Hookes...Ch. 8 - SSM Each second, 1200 m3 of water passes over a...Ch. 8 - GO In Fig. 8-67, a small block is sent through...Ch. 8 - SSM A massless rigid rod of length L has a ball of...Ch. 8 - A 1.50 kg water balloon is shot straight up with...Ch. 8 - A 2.50 kg beverage can is thrown directly downward...Ch. 8 - A constant horizontal force moves a 50 kg trunk...Ch. 8 - GO Two blocks, of masses M = 2.0 kg and 2M, are...Ch. 8 - A volcanic ash flow is moving across horizontal...Ch. 8 - A playground slide is in the form of an arc of a...Ch. 8 - The luxury liner Queen Elizabeth 2 has a...Ch. 8 - A factory worker accidentally releases a 180 kg...Ch. 8 - If a 70 kg baseball player steals home by sliding...Ch. 8 - A 0.50 kg banana is thrown directly upward with an...Ch. 8 - A metal tool is sharpened by being held against...Ch. 8 - A swimmer moves through the water at an average...Ch. 8 - An automobile with passengers has weight 16 400 N...Ch. 8 - A 0.63 kg ball thrown directly upward with an...Ch. 8 - The summit of Mount Everest is 8850 m above sea...Ch. 8 - A sprinter who weighs 670 N runs the first 7.0 m...Ch. 8 - A 20 kg object is acted on by a conservative force...Ch. 8 - A machine pulls a 40 kg trunk 2.0 m up a 40 ramp...Ch. 8 - Prob. 106P Ch. 8 - The only force acting on a particle is...Ch. 8 - In 1981, Daniel Goodwin climbed 443 m up the...Ch. 8 - A 60.0 kg circus performer slides 4.00 m down a...Ch. 8 - A 5.0 kg block is projected at 5.0 m/s up a plane...Ch. 8 - A 9.40 kg projectile is fired vertically upward....Ch. 8 - A 70.0 kg man jumping from a window lands in an...Ch. 8 - A 30 g bullet moving a horizontal velocity of 500...Ch. 8 - A 1500 kg car starts from rest on a horizontal...Ch. 8 - A 1.50 kg snowball is shot upward at an angle of...Ch. 8 - A 68 kg sky diver falls at a constant terminal...Ch. 8 - A 20 kg block on a horizontal surface is attached...Ch. 8 - Resistance to the motion of an automobile consists...Ch. 8 - SSM A 50 g ball is thrown from a window with an...Ch. 8 - A spring with a spring constant of 3200 N/m is...Ch. 8 - A locomotive with a power capability of 1.5 MW can...Ch. 8 - SSM A 0.42 kg shuffleboard disk is initially at...Ch. 8 - A river descends 15 m through rapids. The speed of...Ch. 8 - The magnitude of the gravitational force between a...Ch. 8 - Approximately 5.5 106 kg of water falls 50 m over...Ch. 8 - To make a pendulum, a 300 g ball is attached to...Ch. 8 - In a circus act, a 60 kg clown is shot from a...Ch. 8 - A 70 kg firefighter slides, from rest, 4.3 m down...Ch. 8 - The surface of the continental United States has...Ch. 8 - A spring with spring constant k = 200 N/m is...Ch. 8 - Fasten one end of a vertical spring to a ceiling,...Ch. 8 - The maximum force you can exert on an object with...Ch. 8 - Conservative force Fx acts on a particle that...Ch. 8 - Figure 8-73a shows a molecule consisting of two...Ch. 8 - Repeat Problem 83, but now with the block...Ch. 8 - A spring with spring constant k = 620 N/m is...

Knowledge Booster

a) Magnitude of force |F(x)| b) Directionof force |F(x)| c) Position of the particle to the left x(left) d) Position of the particle to the right, x(right) e) particles speed at x = 7.0 m, V(7)

To find: a) Magnitude of force |F(x)| b) Directionof force |F(x)| c) Position of the particle to the left x(left) d) Position of the particle to the right, x(right) e) particles speed at x = 7.0 m, V(7)

Want to see the full answer?

Chapter 8 Solutions

To find:

a) Magnitude of force |F(x)|

b) Directionof force |F(x)|

c) Position of the particle to the left x(left)

d) Position of the particle to the right, x(right)

e) particles speed at x = 7.0 m, V(7)