University Physics Volume 1
18th Edition
ISBN: 9781938168277
Author: William Moebs, Samuel J. Ling, Jeff Sanny
Publisher: OpenStax - Rice University
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Chapter 7, Problem 88AP
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.
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Chapter 7 Solutions
University Physics Volume 1
Ch. 7 - Check Your Understanding Can kinetic friction ever...Ch. 7 - Check Your Understanding Can Earth’s gravity ever...Ch. 7 - Check Your Understanding Find the work done by the...Ch. 7 - Check Your Understanding The spring Example 7.5 is...Ch. 7 - Check Your Understanding (a) A car and a truck...Ch. 7 - Check Your Understanding You are rowing a boat...Ch. 7 - Check Your Understanding suppose the radius of the...Ch. 7 - Check Your Understanding Estimate the power...Ch. 7 - Give an example of something we think of as work...Ch. 7 - Give an example of a situation in which there is a...
Ch. 7 - Describe a situation in 4iich a force is exerted...Ch. 7 - A body moves in a circle at constant speed. Does...Ch. 7 - Suppose you throw a ball upward and catch it when...Ch. 7 - Why is it more difficult to do sit-ups while on a...Ch. 7 - As a young man, Tarzan climbed up a vine to reach...Ch. 7 - A particle of m has a velocity of . Is its kinetic...Ch. 7 - One particle has mass mand a second particle has...Ch. 7 - A person drops a pebble of mass m1from a height h,...Ch. 7 - The person shown below does work on the lawn...Ch. 7 - Work done on a system puts energy into it. Work...Ch. 7 - Two marbles of masses mand 2mare dropped from a...Ch. 7 - Compare the work required to accelerate a car of...Ch. 7 - Suppose you are jogging at constant velocity. Are...Ch. 7 - Two forces act to double the speed of a particle,...Ch. 7 - Most electrical appliances are rated in watts....Ch. 7 - Explain, in terms of the definition of power, why...Ch. 7 - A spark of static electricity, such as that you...Ch. 7 - Does the work done in lifting an object depend on...Ch. 7 - Can the power expended by a force be negative?Ch. 7 - How can a 50-W light bulb use more energy than a...Ch. 7 - Work How much work does a supermarket checkout...Ch. 7 - A 75.0-kg person climbs stairs, gaining 2.50 m in...Ch. 7 - (a) Calculate the work done on a 1500-kg elevator...Ch. 7 - Suppose a car travels 108 km at a speed of 30.0...Ch. 7 - Calculate the work done by an 85.0-kg man who...Ch. 7 - How much work is done by the boy pulling his...Ch. 7 - A shopper pushes a grocery cart 20.0 m at constant...Ch. 7 - Suppose the ski patrol lowers a rescue sled and...Ch. 7 - A constant 20-N force pushes a small ball in the...Ch. 7 - A toy cart is pulled a distance of 6.0 m in a...Ch. 7 - A 5.0-kg box rests on a horizontal surface. The...Ch. 7 - A sled plus passenger with total mass 50 kg is...Ch. 7 - Suppose that the sled plus passenger of the...Ch. 7 - How much work does the force do on a particle as...Ch. 7 - How much work is done against the gravitationaI...Ch. 7 - It takes 500 J of work to compress a spring 10 cm....Ch. 7 - A bungee cord is essentially a very long rubber...Ch. 7 - A bungee cord exerts a nonlinear elastic force of...Ch. 7 - Engineers desire to model the magnitude of the...Ch. 7 - A particle moving in the xy -plane is subject to a...Ch. 7 - A particle moves along a curved path...Ch. 7 - Kinetic Energy Compare the kinetic energy of a...Ch. 7 - (a) How fast must a 3000-kg elephant move to have...Ch. 7 - Estimate the kinetic energy of a 90,000-ton...Ch. 7 - Calculate the kinetic energies of (a) a 2000.0-kg...Ch. 7 - A 5.0-kg body has three times the kinetic energy...Ch. 7 - An 8.0-g bullet has a speed of 800 m/s. (a) What...Ch. 7 - (a) Calculate the force needed to bring a 950-kg...Ch. 7 - A car’s bumper is designed to withstand a 4.0-km/...Ch. 7 - Boxing gloves are padded to lessen the force of a...Ch. 7 - Using energy considerations, calculate the average...Ch. 7 - A 5.0-kg box has an acceleration of 2.0m/s2 when...Ch. 7 - A constant 10-N horizontal force is applied to a...Ch. 7 - In the preceding problem, the 10-N force is...Ch. 7 - Compare the work required to stop a 100-kg crate...Ch. 7 - A wagon with its passenger sits at the top of a...Ch. 7 - An 8.0-g bullet with a speed of 800 m/s is shot in...Ch. 7 - A 2.0-kg block starts with a speed of 10 m/s at...Ch. 7 - When a 3.0-kg block is pushed against a massless...Ch. 7 - A small block of mass 200 g starts at rest at A,...Ch. 7 - A small object is placed at the top of an incline...Ch. 7 - When released, a 100-g block slides down the path...Ch. 7 - A 0.22LR-caliber bullet like that mentioned in...Ch. 7 - A sled stalls from rest at the top of a...Ch. 7 - A person in good physical condition can put out...Ch. 7 - What is the cost of operating a 3.00-W electric...Ch. 7 - A large household air conditioner may consume 15.0...Ch. 7 - (a) What is the average power consumption in watts...Ch. 7 - (a) What is the average useful power output of a...Ch. 7 - A 500-kg dragster accelerates from rest to a final...Ch. 7 - (a) How long will it take an 850-kg car with a...Ch. 7 - (a) Fir the useful power output of an elevator...Ch. 7 - (a) How long would it take a 1.50105kg airplane...Ch. 7 - Calculate the power output needed for a 950-kg car...Ch. 7 - A man of mass 80 kg runs up a flight of stairs 20...Ch. 7 - The man of the preceding problem consumes...Ch. 7 - An electron in a television tube is accelerated...Ch. 7 - Coal is lifted out of a mine a vertical distance...Ch. 7 - A girl pulls her 15-kg wagon along a flat sidewalk...Ch. 7 - A typical automobile engine has an efficiency of...Ch. 7 - When jogging at 13 km/h on a level surface, a...Ch. 7 - A cart is pulled a distance D on a flat,...Ch. 7 - Consider a particle on which several forces act,...Ch. 7 - Consider a particle on which several forces act,...Ch. 7 - Consider a particle on which several forces act,...Ch. 7 - Consider a particle on which a force acts that...Ch. 7 - A boy pulls a 5-kg cart with a 20-N force at an...Ch. 7 - A crate of mass 200 kg is to be bright from a site...Ch. 7 - At hokey puck of mass 0.17 kg is shot across a...Ch. 7 - A horizontal force of 20 N is required to keep a...Ch. 7 - A 7.0-kg box slides along a horizontal...Ch. 7 - You are driving your car on a straight road with a...Ch. 7 - A crate is being pushed across a rough floor...Ch. 7 - Suppose a horizontal force of 20 N is required to...Ch. 7 - Grains from a hopper falls at a rate of 10 kg/s...Ch. 7 - A cyclist in a race must climb a 5 hill at a speed...Ch. 7 - Shown below is a 40-kg crate that is pushed at...Ch. 7 - The surface of the preceding problem is modified...Ch. 7 - The force F(x) varies with position, as shown...Ch. 7 - Find the work done by the same force in Example...Ch. 7 - Answer the preceding problem using polar...Ch. 7 - Find the work done by the same force in Example...Ch. 7 - Answer the preceding problem using polar...Ch. 7 - Constant power P is delivered to a car of mass m...Ch. 7 - Suppose that the air resistance a car encounters...Ch. 7 - Consider a linear spring, as in Figure 7.7(a),...
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- As a young man, Tarzan climbed up a vine to reach his tree house. As he got older, he decided to build and use a staircase instead. Since the work of the gravitational force mg is path Independent, what did the King of the Apes gain in using stairs?arrow_forwardIf 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_forwardRepeat 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_forward
- Consider a particle on which several forces act, one of which is known to be constant in time: . As a result, the particle moves along the x-axis from x=0 to x=5 m in some time interval. What is the work done by ?arrow_forwardA mysterious force acts on all particles along a particular line and always points towards a particular point P on the line. The magnitude of the force on a particle increases as the cube of the distance from that point; that is Fr3 , if the distance from P to the position of the particle is r. Let b be the proportionality constant, and write the magnitude of the force as F=br3. Find the potential energy of a particle subjected to this force when the particle is at a distance D from P, assuming the potential energy to be zero when the particle is at P.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_forward
- Consider a particle on which several forces act, one of which is known to be constant in time: . As a result, the particle moves along the x-axis from x=0 to x=5 m and then parallel to the y-axis from y=0 to y=6 m. What is the work done by ?arrow_forwardThe surface of the preceding problem is modified so that the coefficient of kinetic friction is decreased. The same horizontal force is applied to the crate, and after being pushed 8.0 m, its speed is 5.0 m/s. How much work is now done by the force of friction? Assume that the crate starts at rest.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_forward
- Consider a particle on which several forces act, one of which is known to be constant in time: . As a result, the particle moves along a straight path from a Cartesian coordinate of (0m,0m) to (5m,6m) . What is the work done by ?arrow_forwardCite two examples in which a force is exerted on an object without doing any work on the object.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_forward
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