Essential University Physics (3rd Edition)
3rd Edition
ISBN: 9780134202709
Author: Richard Wolfson
Publisher: PEARSON
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Chapter 6, Problem 28E
To determine
To find: How much work is done in accelerating a particle from rest to some final speed (W).
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Chapter 6 Solutions
Essential University Physics (3rd Edition)
Ch. 6.2 - Two objects are each displaced the same distance,...Ch. 6.3 - Three forces have magnitudes in newtons that are...Ch. 6.4 - For each situation, tell whether the net work done...Ch. 6.5 - Prob. 6.4GICh. 6 - Give two examples of situations in which you might...Ch. 6 - If the scalar product of two nonzero vectors is...Ch. 6 - Must you do work to whirl a ball around on the end...Ch. 6 - If you pick up a suitcase and put it down, how...Ch. 6 - You want to raise a piano a given height using a...Ch. 6 - Does the gravitational force of the Sun do work on...
Ch. 6 - A pendulum bob swings back and forth on the end of...Ch. 6 - Does your cars kinetic energy change if you drive...Ch. 6 - A watt-second is a unit of what quantity? Relate...Ch. 6 - A truck is moving northward at 55 mi/h. Later, its...Ch. 6 - Is it possible for you to do work on an object...Ch. 6 - How much work do you do as you exert a 75-N force...Ch. 6 - If the coefficient of kinetic friction is 0.21,...Ch. 6 - A crane lifts a 650-kg beam vertically upward 23 m...Ch. 6 - The worlds highest waterfall, the Cherun-Meru in...Ch. 6 - A meteorite plunges to Earth, embedding itself 75...Ch. 6 - An elevator of mass m rises a vertical distance h...Ch. 6 - Show that the scalar product obeys the...Ch. 6 - Find the work done by a force F = 1.8 + 2.2 N as...Ch. 6 - To push a stalled car, you apply a 470-N force at...Ch. 6 - Find the total work done by the force shown in...Ch. 6 - How much work does it take to stretch a spring...Ch. 6 - Uncompressed, the spring for an automobile...Ch. 6 - You do 8.5 J of work to stretch a spring with k =...Ch. 6 - Spider silk is a remarkable elastic material. A...Ch. 6 - Whats the kinetic energy of a 2.4105-kg airplane...Ch. 6 - Prob. 28ECh. 6 - At what speed must a 950-kg subcompact car be...Ch. 6 - A 60-kg skateboarder comes over the top of a hill...Ch. 6 - After a tornado, a 0.50-g drinking straw was found...Ch. 6 - From what height would you have to drop a car for...Ch. 6 - A typical human diet is 2000 calories per day,...Ch. 6 - A horse plows a 200-m-long furrow in 5.0 min,...Ch. 6 - A typical car battery stores about 1 kWh of...Ch. 6 - A sprinter completes a 100-m dash in 10.6 s. doing...Ch. 6 - How much work can a 3.5-hp lawnmower engine do in...Ch. 6 - A 75-kg long-jumper takes 3.1 s to reach a prejump...Ch. 6 - Estimate your power output as you do deep knee...Ch. 6 - In midday sunshine, solar energy strikes Earth at...Ch. 6 - It takes about 20 kJ to melt an ice cube. A...Ch. 6 - Prob. 42ECh. 6 - You slide a box of books at constant speed up a 30...Ch. 6 - Two people push a stalled car at its front doors,...Ch. 6 - Youre at the gym, doing arm raises. With each rep....Ch. 6 - A locomotive does 7.9 1011 J of work in pulling a...Ch. 6 - You pull a box 23 in horizontally, using the rope...Ch. 6 - Prob. 48PCh. 6 - (a) Find the scalar product of the vectors a + b...Ch. 6 - Looking to cut costs, the airline you work for...Ch. 6 - How much work does a force F = 67 + 23 + 55k N do...Ch. 6 - A force F Facts in the x-direction, its magnitude...Ch. 6 - A certain amount of work is required to stretch...Ch. 6 - A force with magnitude F = a x acts in the...Ch. 6 - The force exerted by a rubber band is given...Ch. 6 - You put your little sister (mass m) on a swing...Ch. 6 - Two unknown elementary particles pass through a...Ch. 6 - A tractor tows a plane from its airport gate,...Ch. 6 - E. coli bacteria swim by means of flagella that...Ch. 6 - On February 15, 2013, an asteroid moving at 19...Ch. 6 - An elevator ascends from the ground floor to the...Ch. 6 - Youre asked to assess the reliability of a nuclear...Ch. 6 - A force pointing in the x-direction is given by F...Ch. 6 - A force pointing in the x-direction is given by F...Ch. 6 - Two vectors have equal magnitude, and their scalar...Ch. 6 - At what rate can a half-horsepower well pump...Ch. 6 - The rate at which the United States imports oil,...Ch. 6 - By measuring oxygen uptake, sports physiologists...Ch. 6 - Youre writing performance specifications for a new...Ch. 6 - A 1400-kg car ascends a mountain road at a steady...Ch. 6 - You do 2.2 kJ of work pushing a 78-kg trunk at...Ch. 6 - (a) Find the work done in lifting 1 L of blood...Ch. 6 - (a) What power is needed to push a 95-kg crate at...Ch. 6 - You mix flour into bread dough, exerting a 45-N...Ch. 6 - A machine does work at a rate given by P = ct2,...Ch. 6 - A typical bumblebee has mass 0.25 mg. It beats its...Ch. 6 - Youre trying to decide whether to buy an...Ch. 6 - Your friend does five reps with a barbell, on each...Ch. 6 - A machine delivers power at a decreasing rate P =...Ch. 6 - A locomotive accelerates a freight train of total...Ch. 6 - A force given by F = b/x acts in the x-direction,...Ch. 6 - Youre assisting a cardiologist in planning a...Ch. 6 - Youre an engineer for a company that makes...Ch. 6 - You push an object of mass m slowly, partway up a...Ch. 6 - A particle moves from the origin to the point x =...Ch. 6 - Repeat Problem 85 for the following cases: (a) the...Ch. 6 - The worlds fastest elevator, in Taiwans Taipei 101...Ch. 6 - An experimental measurement of the force required...Ch. 6 - Youre an expert witness in a medical malpractice...Ch. 6 - The energy in a batted baseball comes from the...Ch. 6 - The energy in a batted baseball comes from the...Ch. 6 - The energy in a batted baseball comes from the...Ch. 6 - The energy in a batted baseball comes from the...
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- Explorers in the jungle find an ancient monument in the shape of a large isosceles triangle as shown in Figure P9.25. The monument is made from tens of thousands of small stone blocks of density 3 800 kg/m3. The monument is 15.7 m high and 64.8 m wide at its base and is everywhere 3.60 m thick from front to back. Before the monument was built many years ago, all the stone blocks lay on the ground. How much work did laborers do on the blocks to put them in position while building the entire monument? Note: The gravitational potential energy of an objectEarth system is given by Ug = MgyCM, where M is the total mass of the object and yCM is the elevation of its center of mass above the chosen reference level.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 mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance?arrow_forward
- . In the annual Empire State Building race, contestants run up 1,575 steps to a height of 1,050 ft. In 2003, Australian Paul Crake completed the race in a record time of 9 min and 33 S, Mr., Crake weighed 143 lb (65 kg) , (a) How much work did Mr., Crake do in reaching the top of the building? (b) What was his average power output (in ft-lb/s and in hp)?arrow_forward(a) Suppose a constant force acts on an object. The force does not vary with time or with the position or the velocity of the object. Start with the general definition for work done by a force W=ifFdr and show that the force is conservative, (b) As a special case, suppose the force F =(3i + 4j)N acts on a particle that moves from O to in Figure P7.43. Calculate the work done by F on the particle as it moves along each one of the three paths shown in the figure and show that the work done along the three paths identical.arrow_forwardA sled of mass 70 kg starts from rest and slides down a 10 incline 80 m long. It then travels for 20 m horizontally before starting back up an 8° incline. It travels 80 m along this incline before coming to rest. What is the magnitude of the net work done on the sled by friction?arrow_forward
- What 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_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_forwardIntegrated Concepts (a) What force must be supplied by an elevator cable to produce an acceleration of 0.800 m/s2 against a 200-N frictional force, if the mass of the loaded elevator is 1500 kg? (b) How much work is done by the cable in lifting the elevator 20.0 m? (c) What is the final speed of the elevator if it starts from rest? (d) How much work went into thermal energy?arrow_forward
- The 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_forwardWhich of the following is a unit of work? (4.1) (a) W (b) J s (c) N/s (d) N marrow_forward(a) A force F=(4xi+3yj), where F is in newtons and x and y are in meters, acts on an object as the object moves in the x direction from the origin to x = 5.00 m. Find the work W=Fdr done by the force on the object. (b) What If? Find the work W=Fdr done by the force on the object if it moves from the origin to (5.00 m, 5.00 m) along a straightline path making an angle of 45.0 with the positive x axis. Is the work done by this force dependent on the path taken between the initial and final points?arrow_forward
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