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Hookes law describes an ideal spring. Many real springs are better described by the restoring force (F Sp ) s = -ks - q(s) 3 , where q is a constant. Consider a spring with k = 250 N/m and q = 800... The force acting on a particle is F x = F 0 e-x/L . How much work does this force do as the particle moves along the x-axis from x = 0 to x = L? An electric dipole consists of two equal but opposite electric charges, +q and -q, separated by a small distance d. If another charge Q is distance x from the center of the dipole, in the plane... When a 65 kg cheerleader stands on a vertical spring, the spring compresses by 5.5 cm. When a second cheerleader stands on the shoulders of the first, the spring compresses an additional 4.5 cm. What... Two identical horizontal springs are attached to opposite sides of a box that sits on a frictionless table. The outer ends of the springs are clamped while the springs are at their equilibrium... Hydrogen embrittlement weakens the mechanical strength of cast iron. This phenomenon frequently occurs in cast-iron pressure vessels containing hydrogen (H 2 ) gas. The H 2 gas dissolves into the... A simple experiment is set up to measure the effective diffusion coefficient of blue dextran dye into a rigid agarose gel. An aqueous, well-mixed solution of liquid height 10 cm con taining 1.0 g/L... The contamination of water-saturated soils with toxic organic solvents is an important environmental problem. The organic solvents can dissolve into to the water and diffuse through the... A spring of equilibrium length L 1 and spring constant k 1 hangs from the ceiling. Mass m 1 is suspended from its lower end. Then a second spring, with equilibrium length L 2 and spring constant k 2... Consider the porous slab shown in the figure below. Very tiny pores of 20 A diameter run through the 2.0 cm slab in parallel array. This device will ultimately serve as a drug delivery vehicle for a... A horizontal spring with spring constant 250 N/m is compressed by 12 cm and then used to launch a 250 g box across the floor. The coefficient of kinetic friction between the box and the floor is... A 90 kg firefighter needs to climb the stairs of a 20-m-tall building while carrying a 40 kg backpack filled with gear. How much power does he need to reach the top in 55 s? A hydroelectric power plant uses spinning turbines to transform the kinetic energy of moving water into electric energy with 80% efficiency. That is, 80% of the kinetic energy becomes electric... The block of mass M in FIGURE P7.36 slides on a frictionless surface. Find an expression for the tension in the string. Massless string Massless, fric- tionless pulley FIGURE P7.36 A farmer uses a tractor to pull a 150 kg bale of hay up a 15 incline to the barn at a steady 5.0 km/h. The coefficient of kinetic friction between the bale and the ramp is 0.45. What is the tractors... A Porsche 944 Turbo has a rated engine power of 217 hp. 30% of the power is lost in the drive train, and 70% reaches the wheels. The total mass of the car and driver is 1480 kg, and two-thirds of the... One step in the processing of cucumbers to pickles is the pickling process itself. In one method of making pickles, young cucumbers with no waxy skins are soaked in a NaC1 solution overnight. To... A 5.0 kg mass hanging from a spring scale is slowly lowered onto a vertical spring, as shown in FIGURE EX9.29. The scale reads in newtons. a. What does the spring scale read just before the mass... The coefficient of static friction is 0.60 between the two blocks in FIGURE P7.35. The coefficient of kinetic friction between the lower block and the floor is 0.20. Force F causes both blocks to... Two 3.0-cm-diameter aluminum electrodes are spaced 0.50 mm apart. The electrodes are connected to a 100 V battery. a. What is the capacitance? b. What is the magnitude of the charge on each electrode? Light from the sun allows a solar cell to move electrons from the positive to the negative terminal, doing 2.4 10 -19 J of work per electron. What is the emf of this solar cell? Figure Q26.10 shows a 3 V battery with metal wires attached to each end. What are the potential differences ÎV 12 = V 2 - V 1 , ÎV 23 = V 3 - V 2 , ÎV 34 = V 4 - V 3 , and ÎV... Figure Q26.8 shows a negatively charged electroscope. The gold leaf stands away from the rigid metal post. Is the electric potential of the leaf higher than, lower than, or equal to the potential of... The electron drift speed in a wire is exceedingly slow typically only a fraction of a millimeter per second. Yet when you turn on a flashlight switch, the light comes on almost instantly. Resolve... Is Figure Q27.4 a possible surface charge distribution for a current-carrying wire? If so, in which direction is the current? If not, why not? FIGURE Q27.4 ++ ++ The electric field in a 2.0 mm 2.0 mm square aluminum wire is 0.012 V/m. What is the current in the wire? What electric field strength is needed to create a 5.0 A current in a 2.0-mm-diameter iron wire? A 0.0075 V/m electric field creates a 3.9 mA current in a 1.0-mm-diameter wire. What material is the wire made of? Upon what basic quantity does kinetic energy depend? Upon what basic quantity does potential energy depend? Object A is stationary while objects B and C are in motion. Forces from object A do 10 J of work on object B and 5 J of work on object C. Forces from the environment do 4 J of work on object B and 8... Can kinetic energy ever be negative? Can gravitational potential energy ever be negative? For each, give a plausible reason for your answer without making use of any equations. The lowest point in Death Valley is 85 m below sea level. The summit of nearby Mt. Whitney has an elevation of 4420 m. What is the change in potential energy when an energetic 65 kg hiker makes it... a. What is the kinetic energy of a 1500 kg car traveling at a speed of 30 m/s ( 65 mph)? b. From what height would the car have to be dropped to have this same amount of kinetic energy just before... Rank in order, from most to least, the elastic potential energy (U Sp ) a to (U Sp ) d stored in the springs of FIGURE Q10.5. Explain. a Compressed d Stretched d 2k Stretched 2d Stretched d FIGURE... a. With what minimum speed must you toss a 100 g ball straight up to just touch the 10-m-high roof of the gymnasium if you release the ball 1.5 m above the ground? Solve this problem using energy. b.... A spring gun shoots out a plastic ball at speed v 0 . The spring is then compressed twice the distance it was on the first shot. By what factor is the balls speed increased? Explain. A 55 kg skateboarder wants to just make it to the upper edge of a quarter pipe, a track that is one-quarter of a circle with a radius of 3.0 m. What speed does he need at the bottom? What minimum speed does a 100 g puck need to make it to the top of a 3.0-m-long, 20 frictionless ramp? A particle with the potential energy shown in FIGURE Q10.8 is moving to the right at x = 5 m with total energy E. a. At what value or values of x is this particles speed a maximum? b. Does this... A compressed spring launches a block up an incline. Which objects should be included within the system in order to make an energy analysis as easy as possible? A pendulum is made by tying a 500 g ball to a 75-cm-long string. The pendulum is pulled 30 to one side, then released. What is the balls speed at the lowest point of its trajectory? A process occurs in which a systems potential energy decreases while the system does work on the environment. Does the systems kinetic energy increase, decrease, or stay the same? Or is there not... A 20 kg child is on a swing that hangs from 3.0-m-long chains. What is her maximum speed if she swings out to a 45 angle? A process occurs in which a systems potential energy increases while the environment does work on the system. Does the systems kinetic energy increase, decrease, or stay the same? Or is there not... FIGURE Q10.12 is the energy bar chart for a firefighter sliding down a fire pole from the second floor to the ground. Let the system consist of the firefighter, the pole, and the earth. What are the... The maximum energy a bone can absorb without breaking is surprisingly small. Experimental data show that the leg bones of a healthy, 60 kg human can absorb about 200 J. From what maximum height could... a. If the force on a particle at some point in space is zero, must its potential energy also be zero at that point? Explain. b. If the potential energy of a particle at some point in space is zero,... A cannon tilted up at a 30 angle fires a cannon ball at 80 m/s from atop a 10-m-high fortress wall. What is the balls impact speed on the ground below? In a hydroelectric dam, water falls 25 m and then spins a turbine to generate electricity. a. What is U G of 1.0 kg of water? b. Suppose the dam is 80% efficient at converting the waters potential... How far must you stretch a spring with k = 1000 N/m to store 200 J of energy? A stretched spring stores 2.0 J of energy. How much energy will be stored if the spring is stretched three times as far? A student places her 500 g physics book on a frictionless table. She pushes the book against a spring, compressing the spring by 4.0 cm, then releases the book. What is the books speed as it slides... A block sliding along a horizontal frictionless surface with speed v collides with a spring and compresses it by 2.0 cm. What will be the compression if the same block collides with the spring at a... A 10 kg runaway grocery cart runs into a spring with spring constant 250 N/m and compresses it by 60 cm. What was the speed of the cart just before it hit the spring? As a 15,000 kg jet plane lands on an aircraft carrier, its tail hook snags a cable to slow it down. The cable is attached to a spring with spring constant 60,000 N/m. If the spring stretches 30 m to... The elastic energy stored in your tendons can contribute up to 35%, of your energy needs when running. Sports scientists find that (on average) the knee extensor tendons in sprinters stretch 41 mm... The spring in FIGURE EX10.22a is compressed by Îx. It launches the block across a frictionless surface with speed v 0 . The two springs in FIGURE EX10.22b are identical to the spring of Figure... The spring in FIGURE EX10.23a is compressed by Îx. It launches the block across a frictionless surface with speed v 0 . The two springs in FIGURE EX10.23b are identical to the spring of Figure... FIGURE EX10.25 is the potential-energy diagram for a 500 g particle that is released from rest at A. What are the particles speeds at B, C, and D? U (J) 5- 4 3 2- 0+ B D FIGURE EX10.25 In FIGURE EX10.28, what is the maximum speed a 200 g particle could have at x = 2.0 m and never reach x = 6.0 m? U (J) 16- 12 - 8- 4. 0+ x (m) FIGURE EX10.28 4 2. 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? U (J) 10- 0+ -x (cm) 40 T... FIGURE EX10.28 shows the potential energy of a 500 g particle as it moves along the x-axis. Suppose the particle??s mechanical energy is 12 J. a. Where are the particle??s turning points?b. What is... A system in which only one particle can move has the potential energy shown in FIGURE EX10.31. What is the y component of the force on the particle at y = 0.5 m and 4 m? U (J) 60 ry (m) 5 0- 2 FIGURE... FIGURE EX10.34 shows the potential energy of a system in which a particle moves along the x-axis. Draw a graph of the force F x as a function of position x. U (J) 2- 04 FIGURE EX10.34 A particle moves from A to D in FIGURE EX10.35 while experiencing force F = (6iÌ + 8jÌ) N. How much work does the force do if the particle follows path (a) ABD, (b) ACD, (c) AD? Is this... A force does work on a 50 g particle as the particle moves along the following straight paths in the xy-plane: 25 J from (0 m, 0 m) to (5 m, 0 m); 35 J from (0 m, 0 m) to (0 m, 5 m); 5 J from (5 m, 0... A system loses 400 J of potential energy. In the process, it does 400 J of work on the environment and the thermal energy increases by 100 J. Show this process on an energy bar chart. How much work is done by the environment in the process shown in FIGURE EX10.39? Is energy transferred from the environment to the system or from the system to the environment? E (J) 1,2.1 01 K; + U... A very slippery ice cube slides in a vertical plane around the inside of a smooth, 20-cm-diameter horizontal pipe. The ice cubes speed at the bottom of the circle is 3.0 m/s. What is the ice cubes... A 50 g ice cube can slide up and down a frictionless 30 slope. At the bottom, a spring with spring constant 25 N/m is compressed 10 cm and used to launch the ice cube up the slope. How high does it... You have been hired to design a spring-launched roller coaster that will carry two passengers per car. The car goes up a 10-m-high hill, then descends 15 m to the tracks lowest point. Youve... Its been a great day of new, frictionless snow. Julie starts at the top of the 60° slope shown in FIGURE P10.44. At the bottom, a circular arc carries her through a 90 turn, and she then launches... A block of mass m slides down a frictionless track, then around the inside of a circular loop-the-loop of radius R. From what minimum height h must the block start to make it around without falling... You have a ball of unknown mass, a spring with spring constant 950 N/m, and a meter stick. You use various compressions of the spring to launch the ball vertically, then use the meter stick to... Truck brakes can fail if they get too hot. In some mountainous areas, ramps of loose gravel are constructed to stop runaway trucks that have lost their brakes. The combination of a slight upward... Use work and energy to find an expression for the speed of the block in FIGURE P10.52 just before it hits the floor if (a) The coefficient of kinetic friction for the block on the table is k (b) The... A system has potential energy U(x) = x + sin((2 rad/m)x) as a particle moves over the range 0 m x m. a. Where are the equilibrium positions in this range? b. For each, is it a point of stable or... An object moving in the xy-plane is subjected to the force F = (2xy i + x 2 j) N, where x and y are in m. a. The particle moves from the origin to the point with coordinates (a, b) by moving first... An object moving in the xy-plane is subjected to the force Fu = (2xy i + 3y j) N, where x and y are in m. a. The particle moves from the origin to the point with coordinates (a, b) by moving first... Rank in order, from largest to smallest, the momenta (p x ) a to (p x ) e of the objects in FIGURE Q11.1. 20 g 20 g 200 g b 2 m/s 1 m/s 0.1 m/s 10 g 10 g 1 m/s 2 m/s FIGURE Q11.1 A 2 kg object is moving to the right with a speed of 1 m/s when it experiences an impulse of 4 N s. What are the objects speed and direction after the impulse? What is the magnitude of the momentum of a. A 3000 kg truck traveling at 15 m/s? b. A 200 g baseball thrown at 40 m/s? In FIGURE EX11.5, what value of F max gives an impulse of 6.0 N s? F, max 0+ 2 t (ms) 10 4 8. FIGURE EX11.5 FIGURE EX11.7 is an incomplete momentum bar chart for a 50 g particle that experiences an impulse lasting 10 ms. What were the speed and direction of the particle before the impulse? kg m/s -2 -4- J.... A sled slides along a horizontal surface on which the coefficient of kinetic friction is 0.25. Its velocity at point A is 8.0 m/s and at point B is 5.0 m/s. Use the momentum principle to find how... Far in space, where gravity is negligible, a 425 kg rocket traveling at 75 m/s fires its engines. FIGURE EX11.11 shows the thrust force as a function of time. The mass lost by the rocket during these... A 600 g air-track glider collides with a spring at one end of the track. FIGURE EX11.12 shows the gliders velocity and the force exerted on the glider by the spring. How long is the glider in contact... A 5000 kg open train car is rolling on frictionless rails at 22 m/s when it starts pouring rain. A few minutes later, the cars speed is 20 m/s. What mass of water has collected in the car? A 10,000 kg railroad car is rolling at 2.0 m/s when a 4000 kg load of gravel is suddenly dropped in. What is the cars speed just after the gravel is loaded? A 10-m-long glider with a mass of 680 kg (including the passengers) is gliding horizontally through the air at 30 m/s when a 60 kg skydiver drops out by releasing his grip on the glider. What is the... A 300 g bird flying along at 6.0 m/s sees a 10 g insect heading straight toward it at a speed of 30 m/s. The bird opens its mouth wide and enjoys a nice lunch. What is the birds speed immediately... The parking brake on a 2000 kg Cadillac has failed, and it is rolling slowly, at 1.0 mph, toward a group of small children. Seeing the situation, you realize you have just enough time to drive your... Fred (mass 60 kg) is running with the football at a speed of 6.0 m/s when he is met head-on by Brutus (mass 120 kg), who is moving at 4.0 m/s. Brutus grabs Fred in a tight grip, and they fall to the... A 50 g ball of clay traveling at speed v 0 hits and sticks to a 1.0 kg brick sitting at rest on a frictionless surface. a. What is the speed of the brick after the collision? b. What percentage of... package of mass m is released from rest at a warehouse loading dock and slides down the 3.0-m-high, frictionless chute of FIGURE EX11.25 to a waiting truck. Unfortunately, the truck driver went on a... A 50 kg archer, standing on frictionless ice, shoots a 100 g arrow at a speed of 100 m/s. What is the recoil speed of the archer? A 70.0 kg football player is gliding across very smooth ice at 2.00 m/s. He throws a 0.450 kg football straight forward. What is the players speed afterward if the ball is thrown at a. 15.0 m/s... Dan is gliding on his skateboard at 4.0 m/s. He suddenly jumps backward off the skateboard, kicking the skateboard forward at 8.0 m/s. How fast is Dan going as his feet hit the ground? Dans mass is... Two ice skaters, with masses of 50 kg and 75 kg, are at the center of a 60-m-diameter circular rink. The skaters push off against each other and glide to opposite edges of the rink. If the heavier... A ball of mass m and another ball of mass 3m are placed inside a smooth metal tube with a massless spring compressed between them. When the spring is released, the heavier ball flies out of one end...
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