Principles of Physics: A Calculus-Based Text
5th Edition
ISBN: 9781133104261
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 7, Problem 6P
A block of mass m = 5.00 kg is released from point Ⓐ and slides on the frictionless track shown in Figure P7.6. Determine (a) the block’s speed at points Ⓑ and © and (b) the net work done by the gravitational force on the block as it moves from point Ⓐ to point ©.
Figure P7.6
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Principles of Physics: A Calculus-Based Text
Ch. 7.1 - By what transfer mechanisms does energy enter and...Ch. 7.1 - Consider a block sliding over a horizontal surface...Ch. 7.2 - Prob. 7.3QQCh. 7.2 - Prob. 7.4QQCh. 7.4 - Prob. 7.5QQCh. 7 - You hold a slingshot at arms length, pull the...Ch. 7 - An athlete jumping vertically on a trampoline...Ch. 7 - Prob. 3OQCh. 7 - Two children stand on a platform at the top of a...Ch. 7 - Answer yes or no to each of the following...
Ch. 7 - A ball of clay falls freely to the hard floor. It...Ch. 7 - What average power is generated by a 70.0-kg...Ch. 7 - In a laboratory model of cars skidding to a stop,...Ch. 7 - At the bottom of an air track tilted at angle , a...Ch. 7 - One person drops a ball from the top of a building...Ch. 7 - Prob. 2CQCh. 7 - Does everything have energy? Give the reasoning...Ch. 7 - Prob. 4CQCh. 7 - Prob. 5CQCh. 7 - Prob. 6CQCh. 7 - A block is connected to a spring that is suspended...Ch. 7 - Consider the energy transfers and transformations...Ch. 7 - Prob. 9CQCh. 7 - Prob. 10CQCh. 7 - Prob. 1PCh. 7 - Prob. 2PCh. 7 - Review. A bead slides without friction around a...Ch. 7 - At 11:00 a.m, on September 7, 2001, more than one...Ch. 7 - A block of mass 0.250 kg is placed on top of a...Ch. 7 - A block of mass m = 5.00 kg is released from point...Ch. 7 - Two objects are connected by a light string...Ch. 7 - Prob. 8PCh. 7 - Prob. 9PCh. 7 - Prob. 10PCh. 7 - Prob. 11PCh. 7 - A crate of mass 10.0 kg is pulled up a rough...Ch. 7 - Prob. 13PCh. 7 - Prob. 14PCh. 7 - A block of mass m = 2.00 kg is attached to a...Ch. 7 - Prob. 16PCh. 7 - A smooth circular hoop with a radius of 0.500 m is...Ch. 7 - Prob. 18PCh. 7 - Prob. 19PCh. 7 - As shown in Figure P7.20, a green bead of mass 25...Ch. 7 - A 5.00-kg block is set into motion up an inclined...Ch. 7 - The coefficient of friction between the block of...Ch. 7 - Prob. 23PCh. 7 - Prob. 24PCh. 7 - Prob. 25PCh. 7 - Prob. 26PCh. 7 - A child of mass m starts from rest and slides...Ch. 7 - The electric motor of a model train accelerates...Ch. 7 - Prob. 29PCh. 7 - Prob. 30PCh. 7 - Prob. 31PCh. 7 - Sewage at a certain pumping station is raised...Ch. 7 - Prob. 33PCh. 7 - Prob. 34PCh. 7 - Prob. 35PCh. 7 - Prob. 36PCh. 7 - Prob. 37PCh. 7 - Prob. 38PCh. 7 - Prob. 39PCh. 7 - Prob. 40PCh. 7 - A loaded ore car has a mass of 950 kg and rolls on...Ch. 7 - Prob. 42PCh. 7 - A certain automobile engine delivers 2.24 104 W...Ch. 7 - Prob. 44PCh. 7 - A small block of mass m = 200 g is released from...Ch. 7 - Prob. 46PCh. 7 - Prob. 47PCh. 7 - Prob. 48PCh. 7 - Prob. 49PCh. 7 - Prob. 50PCh. 7 - Prob. 51PCh. 7 - Prob. 52PCh. 7 - Jonathan is riding a bicycle and encounters a hill...Ch. 7 - Prob. 54PCh. 7 - A horizontal spring attached to a wall has a force...Ch. 7 - Prob. 56PCh. 7 - Prob. 57PCh. 7 - Prob. 58PCh. 7 - Prob. 59PCh. 7 - Prob. 60PCh. 7 - Prob. 61PCh. 7 - Prob. 62PCh. 7 - Make an order-of-magnitude estimate of your power...Ch. 7 - Prob. 64PCh. 7 - Prob. 65PCh. 7 - Review. As a prank, someone has balanced a pumpkin...Ch. 7 - Review. The mass of a car is 1 500 kg. The shape...Ch. 7 - A 1.00-kg object slides to the right on a surface...Ch. 7 - A childs pogo stick (Fig. P7.69) stores energy in...Ch. 7 - Prob. 70PCh. 7 - Prob. 71PCh. 7 - Prob. 72PCh. 7 - A block of mass m1 = 20.0 kg is connected to a...Ch. 7 - Prob. 74PCh. 7 - Prob. 75PCh. 7 - Prob. 76PCh. 7 - Prob. 77PCh. 7 - Prob. 78PCh. 7 - A block of mass 0.500 kg is pushed against a...Ch. 7 - A pendulum, comprising a light string of length L...Ch. 7 - Jane, whose mass is 50.0 kg, needs to swing across...Ch. 7 - A roller-coaster car shown in Figure P7.82 is...Ch. 7 - Prob. 83P
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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 ail angle = 25 below the horizontal as shown in Figure P7.5. 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.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_forwardA 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 P5.8. Determine the work done by (a) the applied force, (b) the normal force exerted by the table, (c) the force of gravity, and (d) the net force on the block. Figure P5.8arrow_forward
- A 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_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_forwardA 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 P5.8. Determine the work done by (a) the applied force, (b) the normal force exerted by the table, (c) the force of gravity, and (d) the net force on the block. Figure P5.8arrow_forward
- As shown in Figure P7.20, a green bead of mass 25 g slides along a straight wire. The length of the wire from point to point is 0.600 m, and point is 0.200 in higher than point . A constant friction force of magnitude 0.025 0 N acts on the bead. (a) If the bead is released from rest at point , what is its speed at point ? (b) A red bead of mass 25 g slides along a curved wire, subject to a friction force with the same constant magnitude as that on the green bead. If the green and red beads are released simultaneously from rest at point , which bead reaches point first? Explain. Figure P7.20arrow_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_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_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_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 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_forward
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