Essential University Physics, Volume 1 and Volume 2 - With Access
3rd Edition
ISBN: 9780134645490
Author: Wolfson
Publisher: PEARSON
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Chapter 7, Problem 50P
In ionic solids such as NaCl (salt), the potential energy of a pair of ions takes the form U = b/rn – a/r, where r is the separation of the ions. For NaCl, a and b have the SI values 4.04 × 10−28 and 5.52 × 10−98, respectively, and n = 8.22. Find the equilibrium separation in NaCl.
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Essential University Physics, Volume 1 and Volume 2 - With Access
Ch. 7.1 - Suppose it takes the same amount of work to push a...Ch. 7.2 - Gravitational force actually decreases with...Ch. 7.3 - A bowling ball is tied to the end of a long rope...Ch. 7.4 - For which of the following systems is (1)...Ch. 7.5 - A bowling ball is tied to the end of a long rope...Ch. 7.6 - The figure shows the potential energy associated...Ch. 7 - Figure 7.14 shows force vectors at different...Ch. 7 - Is the conservation-of-mechanical-energy principle...Ch. 7 - Why cant we define a potential energy associated...Ch. 7 - Can potential energy be negative? Can kinetic...
Ch. 7 - If the potential energy is zero at a given point,...Ch. 7 - If the difference in potential energy between two...Ch. 7 - If the difference in potential energy between two...Ch. 7 - A tightrope walker follows an essentially...Ch. 7 - If conservation of energy is a law of nature, why...Ch. 7 - Determine the work you would have to do to move a...Ch. 7 - Now lake Fig. 7.15 lo lie in a vertical plane, and...Ch. 7 - Rework Example 7.1, now taking the zero of...Ch. 7 - Find the potential energy associated with a 70-kg...Ch. 7 - You fly from Bostons Logan Airport, at sea level,...Ch. 7 - The potential energy associated with a 60-kg hiker...Ch. 7 - How much energy can be stored in a spring with k =...Ch. 7 - How far would you have to stretch a spring with k...Ch. 7 - A biophysicist grabs the ends of a DNA strand with...Ch. 7 - A skier starts down a frictionless 32 slope. After...Ch. 7 - A 10,000-kg Navy jet lands on an aircraft carrier...Ch. 7 - A 120-g arrow is shot vertically from a bow whose...Ch. 7 - In a railroad yard, a 35,000-kg boxcar moving at...Ch. 7 - You work for a toy company, and youre designing a...Ch. 7 - A 54-kg ice skater pushes off the wall of the...Ch. 7 - Prob. 25ECh. 7 - A particle slides along the frictionless track...Ch. 7 - A particle slides back and forth on a frictionless...Ch. 7 - A particle is trapped in a potential well...Ch. 7 - The reservoir at Northfield Mountain Pumped...Ch. 7 - The force in Fig. 7.14a is given by Fa=FoJ, where...Ch. 7 - A 1.50-kg brick measures 20.0 cm 8.00 cm 5.50...Ch. 7 - A carbon monoxide molecule can be modeled as a...Ch. 7 - A more accurate expression for the force law of...Ch. 7 - For small stretches, the Achilles tendon can be...Ch. 7 - The force exerted by an unusual spring when its...Ch. 7 - The force on a particle is given by F=Al/x2, where...Ch. 7 - A particle moves along the x-axis under the...Ch. 7 - As a highway engineer, youre asked to design a...Ch. 7 - A spring of constant k, compressed a distance x,...Ch. 7 - A child is on a swing whose 3.2-m-long chains make...Ch. 7 - With x x0 = h and a = g, Equation 2.11 gives the...Ch. 7 - The nuchal ligament is a cord-like structure that...Ch. 7 - A 200-g block slides back and forth on a...Ch. 7 - Automotive standards call for bumpers that sustain...Ch. 7 - A block slides on the frictionless loop-the-loop...Ch. 7 - The maximum speed of the pendulum bob in a...Ch. 7 - A mass m is dropped from height h above the top of...Ch. 7 - A particle with total energy 3.5 J is trapped in a...Ch. 7 - (a) Derive an expression for the potential energy...Ch. 7 - In ionic solids such as NaCl (salt), the potential...Ch. 7 - Repeat Exercise 19 for the case when the...Ch. 7 - As an energy-efficiency consultant, youre asked to...Ch. 7 - A spring of constant k = 340 N/m is used to launch...Ch. 7 - A bug slides back and forth in a bowl 15 cm deep,...Ch. 7 - A 190-g block is launched by compressing a spring...Ch. 7 - A block slides down a frictionless incline that...Ch. 7 - An 840-kg roller-coaster car is launched from a...Ch. 7 - A particle slides back and forth in a frictionless...Ch. 7 - A child sleds down a frictionless hill whose...Ch. 7 - A bug lands on top of the frictionless, spherical...Ch. 7 - A particle of mass m is subject to a force...Ch. 7 - A block of weight 4.5 N is launched up a 30...Ch. 7 - Your engineering department is asked to evaluate...Ch. 7 - Your roommate is writing a science fiction novel...Ch. 7 - You have a summer job at your universitys zoology...Ch. 7 - Biomechanical engineers developing artificial...Ch. 7 - Blocks with different masses are pushed against a...Ch. 7 - Nuclear fusion is the process that powers the Sun....Ch. 7 - Nuclear fusion is the process that powers the Sun....Ch. 7 - Nuclear fusion is the process that powers the Sun....Ch. 7 - Nuclear fusion is the process that powers the Sun....
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- If the net work done by external forces on a particle is zero, which of the following statements about the particle must be true? (a) Its velocity is zero. (b) Its velocity is decreased. (c) Its velocity is unchanged. (d) Its speed is unchanged. (e) More information is needed.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 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_forwardAs 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_forward
- Consider a particle on which a force acts that depends on the position of the particle. This force is given by . Find the work done by this force when the particle moves from the origin to a point 5 meters to the right on the x-axis.arrow_forward(a) Can the kinetic energy of a system be negative? (b) Can the gravitational potential energy of a system be negative? Explain.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
- Repeat the preceding problem, but this time, suppose that the work done by air resistance cannot be ignored. Let the work done by the air resistance when the skier goes from A to B along the given hilly path be —2000 J. The work done by air resistance is negative since the air resistance acts in the opposite direction to the displacement. Supposing the mass of the skier is 50 kg, what is the speed of the skier at point B ?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_forwardWhat average power is generated by a 70.0-kg mountain climber who climbs a summit of height 325 m in 95.0 min? (a) 39.1 W (b) 54.6 W (c) 25.5 W (d) 67.0 W (e) 88.4 Warrow_forward
- A 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 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_forwardAt the start of a basketball game, a referee tosses a basketball straight into the air by giving it some initial speed. After being given that speed, the ball reaches a maximum height of 4.25 m above where it started. Using conservation of energy, find a. the balls initial speed and b. the height of the ball when it has a speed of 2.5 m/s.arrow_forward
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