EBK PHYSICS
5th Edition
ISBN: 8220103026918
Author: Walker
Publisher: PEARSON
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Chapter 8, Problem 48PCE
The potential energy of a particle moving along the x axis is shown in Figure 8-34. When the particle is at x = 1.0 m it has 3.6 J of kinetic energy. Give approximate answers to the following questions. (a) What is the total mechanical energy of the system? (b) What is the smallest value of x the particle can reach? (c) What is the largest value of x the particle can reach?
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Chapter 8 Solutions
EBK PHYSICS
Ch. 8.1 - 1. In Figure 8-8, the work done by a conservative...Ch. 8.2 - 1. The work done by a conservative force on a...Ch. 8.3 - A system with only conservative forces acting on...Ch. 8.4 - 4. A system is acted on by more than one force,...Ch. 8.5 - A system consists of an object moving along the x...Ch. 8 - Is it possible for the kinetic energy of an object...Ch. 8 - If the stretch of a spring is doubled, the force...Ch. 8 - When a mass is placed on top of a vertical spring,...Ch. 8 - If a spring is stretched so far that it is...Ch. 8 - An object is thrown upward to a person on a roof....
Ch. 8 - It is a law of nature that the total energy of the...Ch. 8 - Discuss the venous energy conversions that occur...Ch. 8 - Discuss the nature of the work done by the...Ch. 8 - It the force on an object is zero, does that mean...Ch. 8 - When a ball is thrown upward, its mechanical...Ch. 8 - When a ball is thrown upward, it spends the same...Ch. 8 - The work done by a conservative force is indicated...Ch. 8 - 2. Calculate the work done by gravity as a 3.2-kg...Ch. 8 - Calculate the work done by friction as a 37-kg box...Ch. 8 - Predict/Calculate A 2.8-kg block is attached to a...Ch. 8 - Predict/Calculate (a) Calculate the work done by...Ch. 8 - In the system shown in Figure 8-26, suppose the...Ch. 8 - Predict/Explain Ball 1 is thrown to the ground...Ch. 8 - A mass is attached to the bottom of a vertical...Ch. 8 - Find the gravitational potential energy of an...Ch. 8 - A student lifts a 1.42-kg book from her desk to a...Ch. 8 - At the local ski slope, an 82.0-kg skier rides a...Ch. 8 - BIO The Wing of the Hawkmoth Experiments performed...Ch. 8 - Predict/Calculate A vertical spring stores 0.962 J...Ch. 8 - Pushing on the pump of a soap dispenser compresses...Ch. 8 - BIO Mantis Shrimp Smasher A peacock mantis shrimp...Ch. 8 - Predict/Calculate The work required to stretch a...Ch. 8 - A 0.33-kg pendulum bob is attached to a string 1.2...Ch. 8 - Prob. 18PCECh. 8 - Prob. 19PCECh. 8 - For an object moving along the x axis, the...Ch. 8 - At an amusement park, a swimmer uses a water side...Ch. 8 - Prob. 22PCECh. 8 - A skateboarder at a skate park rides along the...Ch. 8 - Three balls are thrown upward with the same...Ch. 8 - A 0.21-kg apple falls from a tree to the ground,...Ch. 8 - Predict/Calculate A 2.9-kg block slides with a...Ch. 8 - A 0.26-kg rock is thrown vertically upward from...Ch. 8 - A 1 40-kg block sides with a speed of 0.950 m/s on...Ch. 8 - A 5.76-kg rock is dropped and allowed to fall...Ch. 8 - Predict/Calculate Suppose the pendulum bob m...Ch. 8 - The two masses in the Atwoods machine shown in...Ch. 8 - In the previous problem, suppose the masses have...Ch. 8 - Prob. 33PCECh. 8 - Catching a wave, a 77-kg surfer starts with a...Ch. 8 - At a playground, a 19-kg child plays on a slide...Ch. 8 - Starting at rest at the edge of a swimming pool, a...Ch. 8 - A 22,000-kg airplane lands with a speed of 64 m/s...Ch. 8 - A78-kg skateboarder grinds down a hubba ledge that...Ch. 8 - You ride your bicycle down a hill, maintaining a...Ch. 8 - A 111-kg seal at an amusement park slides from...Ch. 8 - A 1.9-kg rock is released from rest at the surface...Ch. 8 - A 1250-kg car drives up a hill that is 16.2 m...Ch. 8 - The Outlaw Run roller coaster in Branson,...Ch. 8 - A 1.80-kg block slides on a rough horizontal...Ch. 8 - Figure 8-34 shows a potential energy curve as a...Ch. 8 - An object moves along the x axis, subject to the...Ch. 8 - A 1.34-kg object moves along the x axis, subject...Ch. 8 - The potential energy of a particle moving along...Ch. 8 - A block of mass m = 0.88 kg is connected to a...Ch. 8 - A ball of mass m = 0.75 kg is thrown straight...Ch. 8 - Figure 8-35 depicts the potential energy of a...Ch. 8 - Figure 8-35 depicts the potential energy of a...Ch. 8 - CE You and a friend both solve a problem involving...Ch. 8 - CE A particle moves under the influence of a...Ch. 8 - A sled slides without friction down a small,...Ch. 8 - A 74 Kg skier encounters a dip in the snows...Ch. 8 - Running Shoes The soles of a popular make of...Ch. 8 - Nasal Strips The force required to flex a nasal...Ch. 8 - The water slide shown in Figure 8-37 ends at a...Ch. 8 - A skateboarder starts at point A in Figure 8-38...Ch. 8 - The Crash of Skylab NASAs Skylab, the largest...Ch. 8 - BIO Bird Tendons Several studies indicate that the...Ch. 8 - In the Atwoods machine of Problem 31, the mass m2...Ch. 8 - A 6.60-kg block slides with an initial speed of...Ch. 8 - Jeff of the Jungle swings on a 7.6-m vine that...Ch. 8 - A 1.9-kg block slides down a frictionless ramp, as...Ch. 8 - Suppose the ramp in Figure 8-40 is not motionless....Ch. 8 - BIO Compressing the Ground A running track at...Ch. 8 - BIO A Fleas Jump The resilin in the body of a flea...Ch. 8 - Predict/Calculate Tension at the Bottom A ball of...Ch. 8 - An ice cube is placed on top of an overturned...Ch. 8 - Predict/Calculate The two blocks shown in Figure...Ch. 8 - Predict/Calculate Loop-the-Loop (a) A block of...Ch. 8 - Figure 8-45 shows a 1.75-kg block at rest on a...Ch. 8 - In Figure 8-45 a 1.2-kg block is held at rest...Ch. 8 - BIO The Flight of the Dragonflies Of all the...Ch. 8 - BIO The Flight of the Dragonflies Of all the...Ch. 8 - BIO The Flight of the Dragonflies Of all the...Ch. 8 - BIO The Flight of the Dragonflies Of all the...Ch. 8 - Predict/Calculate Referring to Example 8-12...Ch. 8 - Referring to Example 8-12 Suppose the block is...Ch. 8 - Referring to Example 8-17 suppose we would like...
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- A block of mass m = 2.50 kg is pushed a distance d = 2.20 m along a frictionless, horizontal table by a constant applied force of magnitude F = 16.0 N directed at an angle = 25.0 below the horizontal as shown in Figure P6.3. Determine the work done on the block by (a) the applied force, (b) the normal force exerted by the table, (c) the gravitational force, and (d) the net force on the block. Figure P6.3arrow_forwardAnswer yes or no to each of the following questions. (a) Can an objectEarth system have kinetic energy and not gravitational potential energy? (b) Can it have gravitational potential energy and not kinetic energy? (c) Can it have both types of energy at the same moment? (d) Can it have neither?arrow_forwardA 5.00-kg block is set into motion up an inclined plane with an initial speed of i = 8.00 m/s (Fig. P7.21). The block comes to rest after traveling d = 3.00 m along the plane, which is inclined at an angle of = 30.0 to the horizontal. For this motion, determine (a) the change in the blocks kinetic energy, (b) the change in the potential energy of the block-Earth system, and (c) the friction force exerted on the block (assumed to be constant), (d) What is the coefficient of kinetic friction? Figure P7.21arrow_forward
- A particle moves in one dimension under the action of a conservative force. The potential energy of the system is given by the graph in Figure P8.55. Suppose the particle is given a total energy E, which is shown as a horizontal line on the graph. a. Sketch bar charts of the kinetic and potential energies at points x = 0, x = x1, and x = x2. b. At which location is the particle moving the fastest? c. What can be said about the speed of the particle at x = x3? FIGURE P8.55arrow_forwardA block of mass 0.500 kg is pushed against a horizontal spring of negligible mass until the spring is compressed a distance x (Fig. P7.79). The force constant of the spring is 450 N/m. When it is released, the block travels along a frictionless, horizontal surface to point , the bottom of a vertical circular track of radius R = 1.00 m, and continues to move up the track. The blocks speed at the bottom of the track is = 12.0 m/s, and the block experiences an average friction force of 7.00 N while sliding up the track. (a) What is x? (b) If the block were to reach the top of the track, what would be its speed at that point? (c) Does the block actually reach the top of the track, or does it fall off before reaching the top?arrow_forwardA jack-in-the-box is actually a system that consists of an object attached to the top of a vertical spring (Fig. P8.50). a. Sketch the energy graph for the potential energy and the total energy of the springobject system as a function of compression distance x from x = xmax to x = 0, where xmax is the maximum amount of compression of the spring. Ignore the change in gravitational potential energy. b. Sketch the kinetic energy of the system between these points the two distances in part (a)on the same graph (using a different color). FIGURE P8.50 Problems 50 and 79arrow_forward
- A small block of mass m = 200 g is released from rest at point along the horizontal diameter on the inside of a frictionless, hemispherical bowl of radius R = 30.0 cm (Fig. P7.45). Calculate (a) the gravitational potential energy of the block-Earth system when the block is at point relative to point . (b) the kinetic energy of the block at point , (c) its speed at point , and (d) its kinetic energy and the potential energy when the block is at point . Figure P7.45 Problems 45 and 46.arrow_forwardA nonconstant force is exerted on a particle as it moves in the positive direction along the x axis. Figure P9.26 shows a graph of this force Fx versus the particles position x. Find the work done by this force on the particle as the particle moves as follows. a. From xi = 0 to xf = 10.0 m b. From xi = 10.0 to xf = 20.0 m c. From xi = 0 to xf = 20.0 m FIGURE P9.26 Problems 26 and 27.arrow_forwardA block is placed on top of a vertical spring, and the spring compresses. Figure P8.24 depicts a moment in time when the spring is compressed by an amount h. a. To calculate the change in the gravitational and elastic potential energies, what must be included in the system? b. Find an expression for the change in the systems potential energy in terms of the parameters shown in Figure P8.24. c. If m = 0.865 kg and k = 125 N/m, find the change in the systems potential energy when the blocks displacement is h = 0.0650 m, relative to its initial position. FIGURE P8.24arrow_forward
- The force on a particle of mass 2.0 kg varies with position according to F(x)=3.0x2 (x in meters, F(x) in newtons). The particle’s velocity at x=2.0m is 5.0 m/s. Calculate the mechanical energy of the particle using (a) the origin as the reference point and (b) x = 4.0 m as the reference point. (c) Find the particle’s velocity at x=1.0m . Do this part of the problem for each reference point.arrow_forwardA particle moves in the xy plane (Fig. P9.30) from the origin to a point having coordinates x = 7.00 m and y = 4.00 m under the influence of a force given by F=3y2+x. a. What is the work done on the particle by the force F if it moves along path 1 (shown in red)? b. What is the work done on the particle by the force F if it moves along path 2 (shown in blue)? c. What is the work done on the particle by the force F if it moves along path 3 (shown in green)? d. Is the force F conservative or nonconservative? Explain. FIGURE P9.30 In each case, the work is found using the integral of Fdr along the path (Equation 9.21). W=rtrfFdr=rtrf(Fxdx+Fydy+Fzdz) (a) The work done along path 1, we first need to integrate along dr=dxi from (0,0) to (7,0) and then along dr=dyj from (7,0) to (7,4): W1=x=0;y=0x=7;y=0(3y2i+xj)(dxi)+x=7;y=0x=7;y=4(3y2i+xj)(dyj) Performing the dot products, we get W1=x=0;y=0x=7;y=03y2dx+x=7;y=0x=7;y=4xdy Along the first part of this path, y = 0 therefore the first integral equals zero. For the second integral, x is constant and can be pulled out of the integral, and we can evaluate dy. W1=0+x=7;y=0x=7;y=4xdy=xy|x=7;y=0x=7;y=4=28J (b) The work done along path 2 is along dr=dyj from (0,0) to (0,4) and then along dr=dxi from (0,4) to (7,4): W2=x=0;y=0x=0;y=4(3y2i+xj)(dyj)+x=0;y=4x=7;y=4(3y2i+xj)(dyi) Performing the dot product, we get: W2=x=0;y=0x=0;y=4xdy+x=0;y=4x=7;y=43y2dx Along the first part of this path, x = 0. Therefore, the first integral equals zero. For the second integral, y is constant and can be pulled out of the integral, and we can evaluate dx. W2=0+3y2x|x=0;y=4x=7;y=4=336J (c) To find the work along the third path, we first write the expression for the work integral. W=rtrfFdr=rtrf(Fxdx+Fydy+Fzdz)W=rtrf(3y2dx+xdy)(1) At first glance, this appears quite simple, but we cant integrate xdy=xy like we might have above because the value of x changes as we vary y (i.e., x is a function of y.) [In parts (a) and (b), on a straight horizontal or vertical line, only x or y changes]. One approach is to parameterize both x and y as a function of another variable, say t, and write each integral in terms of only x or y. Constraining dr to be along the desired line, we can relate dx and dy: tan=dydxdy=tandxanddx=dytan(2) Now, use equation (2) in (1) to express each integral in terms of only one variable. W=x=0;y=0x=7;y=43y2dx+x=0;y=0x=7;y=4xdyW=y=0y=43y2dytan+x=0x=7xtandx We can determine the tangent of the angle, which is constant (the angle is the angle of the line with respect to the horizontal). tan=4.007.00=0.570 Insert the value of the tangent and solve the integrals. W=30.570y33|y=0y=4+0.570x22|x=0x=7W=112+14=126J (d) Since the work done is not path-independent, this is non-conservative force. Figure P9.30ANSarrow_forwardA particle is subject to a force Fx that varies with position as shown in Figure P7.9. Find the work done by the force on the particle as it moves (a) from x = 0 to x = 5.00 m, (b) from x = 5.00 m to x = 10.0 m, and (c) from x = 10.0 m to x = 15.0 m. (d) What is the total work done by the force over the distance x = 0 to x = 15.0 m?arrow_forward
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