Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)
4th Edition
ISBN: 9780133942651
Author: Randall D. Knight (Professor Emeritus)
Publisher: PEARSON
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Chapter 10, Problem 30EAP
A system in which only one particle can move has the potential energy shown in FIGURE EX10.30. What is the x-component of the force on the particle at x = 5, 15, and 25 cm?
FIGURE EX10.30
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Chapter 10 Solutions
Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)
Ch. 10 - Prob. 1CQCh. 10 - Can kinetic energy ever be negative? Can...Ch. 10 - Prob. 3CQCh. 10 - 4. The three balls in FIGURE Q1O.4, which have...Ch. 10 - Rank in order, from most to least, the elastic...Ch. 10 - 6. A spring is compressed 1.0 cm. How far must you...Ch. 10 - Prob. 7CQCh. 10 - A particle with the potential energy shown in...Ch. 10 - A compressed spring launches a block up an...Ch. 10 - 10. A process occurs in which a system’s potential...
Ch. 10 - A process occurs in which a system’s potential...Ch. 10 - FIGURE Q10.12 is the energy bar chart for a...Ch. 10 - Prob. 13CQCh. 10 - Object A is stationary while objects B and C are...Ch. 10 - Prob. 2EAPCh. 10 - 3. The lowest point in Death Valley is 85 m below...Ch. 10 - Prob. 4EAPCh. 10 - Prob. 5EAPCh. 10 - 6. What height does a frictionless playground...Ch. 10 - 7. A 55 kg skateboarder wants to just make it to...Ch. 10 - Prob. 8EAPCh. 10 - A pendulum is made by tying a 500 g ball to a...Ch. 10 - A 20 kg child is on a swing that hangs from...Ch. 10 - A 1500 kg car traveling at 10 m/s suddenly runs...Ch. 10 - Prob. 12EAPCh. 10 - A cannon tilted up at a 30° angle fires a cannon...Ch. 10 - In a hydroelectric dam, water falls 25 m and then...Ch. 10 - How far must you stretch a spring with k = 000 N/m...Ch. 10 - A stretched spring stores 2.0 J of energy. How...Ch. 10 - A student places her 500 g physics book on a...Ch. 10 - A block sliding along a horizontal frictionless...Ch. 10 - A 10 kg runaway grocery cart runs into a spring...Ch. 10 - As a 15,000 kg jet plane lands on an aircraft...Ch. 10 - The elastic energy stored in your tendons can...Ch. 10 - The spring in FIGURE EX10.22a is compressed by ?x....Ch. 10 - The spring in FIGURE EXIO.23a is compressed by ?x....Ch. 10 - FIGURE EX10.24 is the potential-energy diagram for...Ch. 10 - Prob. 25EAPCh. 10 - In FIGURE EX10.26, what is the maximum speed of a...Ch. 10 - Prob. 27EAPCh. 10 - FIGURE EX10.28 shows the potential energy of a 500...Ch. 10 - In FIGURE EX10.28, what is the maximum speed a 200...Ch. 10 - A system in which only one particle can move has...Ch. 10 - A system in which only one particle can move has...Ch. 10 - A particle moving along the y-axis is in a system...Ch. 10 - A particle moving along the x-axis is in a system...Ch. 10 - FIGURE EX10.34 shows the potential energy of a...Ch. 10 - A particle moves from A to D in FIGURE EX10.35...Ch. 10 - A force does work on a 50 g particle as the...Ch. 10 - A system loses 400 J of potential energy. In the...Ch. 10 - What is the final kinetic energy of the system for...Ch. 10 - How much work is done by the environment in the...Ch. 10 - A cable with 20.0 N tension pulls straight up on a...Ch. 10 - A very slippery ice cube slides in a vertical...Ch. 10 - A 50 g ice cube can slide up and down a...Ch. 10 - You have been hired to design a spring-launched...Ch. 10 - It’s been a great day of new, frictionless snow....Ch. 10 - Prob. 45EAPCh. 10 - A 1000 kg safe is 2.0 m above a heavy-duty spring...Ch. 10 - You have a ball of unknown mass, a spring with...Ch. 10 - Sam, whose mass is 75 kg, straps on his skis and...Ch. 10 - A horizontal spring with spring constant 100 N/m...Ch. 10 - Truck brakes can fail if they get too hot. In some...Ch. 10 - Prob. 51EAPCh. 10 - Use work and energy to find an expression for the...Ch. 10 - Prob. 53EAPCh. 10 - The spring shown in FIGURE 10.54 is compressed 50...Ch. 10 - Prob. 55EAPCh. 10 - Prob. 56EAPCh. 10 - A system has potential energy U(x) = x + sin ((2...Ch. 10 - Prob. 58EAPCh. 10 - Prob. 59EAPCh. 10 - Prob. 60EAPCh. 10 - The potential energy for a particle that can move...Ch. 10 - A particle that can move along the x-axis...Ch. 10 - An object moving in the xy-plane is subjected to...Ch. 10 - An object moving in the xy-plane is subjected to...Ch. 10 - Prob. 65EAPCh. 10 - In Problems 66 through 68 you are given the...Ch. 10 - Prob. 67EAPCh. 10 - Prob. 68EAPCh. 10 - A pendulum is formed from a small ball of mass m...Ch. 10 - Prob. 70EAPCh. 10 - Prob. 71EAPCh. 10 - Prob. 72EAPCh. 10 - The spring in FIGURE CP10.73 has a spring constant...Ch. 10 - A sled starts from rest at the top of the...
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- A 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_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_forwardThe force acting on a particle varies as shown in Figure P6.14. Find the work done by the force on the particle as it moves (a) from x = 0 to x = 8.00 m, (b) from x = 8.00 m to x= 10.0 m, and (c) from x = 0 to x = 10.0 m.arrow_forward
- The force acting on a particle is Fx = (8x 16), where F is in newtons anti x is in meters. (a) Make a plot of this force versus x from x = 0 to x = 3.00 m. (b) From your graph, find the net work done by this force on the particle as it moves from x = 0 to x = 3.00 m.arrow_forwardSuppose the ski patrol lowers a rescue sled and victim, having a total mass of 90.0 kg, down a 60.0° slope at constant speed, as shown in Figure 7.37. The coefficient of friction between the sled and the snow is 0.100. (a) How much work is done by friction as the sled moves 30.0 m along the hill? (b) How much work is done by the rope on the sled in this distance? (c) What is the work done by the gravitational force on the sled? (d) What is the total work done?arrow_forwardA 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_forward
- A boy starts at rest and slides down a frictionless slide as in Figure P5.64. The bottom of the track is a height h above the ground. The boy then leaves the track horizontally, striking the ground a distance d as shown. Using energy methods, determine the initial height H of the boy in terms of h and d. Figure P5.64arrow_forward(a) Sketch a graph of the potential energy function U(x)=kx2/2+Aex2 where k , A, and are constants. (b) What is the force corresponding to this potential energy? (c) Suppose a particle of mass in moving with this potential energy has a velocity v when its position is x = . Show that the particle does not pass 2+2 through the origin unless Amv2=k22(1e a 2 ) .arrow_forwardA large cruise ship of mass 6.50 107 kg has a speed of 12.0 m/s at some instant. (a) What is the ships kinetic energy at this time? (b) How much work is required to stop it? (c) What is the magnitude of the constant force required to stop it as it undergoes a displacement of 2.50 km?arrow_forward
- A 4.00-kg particle moves from the origin to position , having coordinates x = 5.00 m and y = 5.00 m (Fig. P7.31). One force on the particle is the gravitational force acting in the negative y direction. Using Equation 7.3, calculate the work done by the gravitational force on the particle as it goes from O to along (a) the purple path, (b) the red path, and (c) the blue path, (d) Your results should all be identical. Why? Figure P7.31arrow_forwardReview. A bead slides without friction around a loop-the-loop (Fig. P7.3). The bead is released from rest at a height h = 3.50R. (a) What is its speed at point ? (b) How large is the normal force on the bead at point if its mass is 5.00 g? Figure P7.3arrow_forwardA 4.00-kg particle moves from the origin to position ©, having coordinates x = 5.00 m and y = 5.00 m (Fig. P6.42). One force on the particle is the gravitational force acting in the negative y direction. Using Equation 6.3, calculate the work done by the gravitational force on the particle as it goes from O to © along (a) the purple path, (b) the red path, and (c) the blue path. (d) Your results should all be identical. Why? Figure P6.42 Problems 42 through 45.arrow_forward
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Kinetic Energy and Potential Energy; Author: Professor Dave explains;https://www.youtube.com/watch?v=g7u6pIfUVy4;License: Standard YouTube License, CC-BY