it takes 500 j of work to compress a spring 10 cm. what is the force constant of the spring?

7.1 Piece of work

23 .

How much work does a supermarket checkout attendant do on a tin can of soup he pushes 0.600 m horizontally with a force of v.00 N?

24 .

A 75.0-kg person climbs stairs, gaining ii.fifty m in summit. Find the work done to accomplish this chore.

25 .

(a) Calculate the work done on a 1500-kg elevator car by its cable to lift information technology twoscore.0 m at constant speed, assuming friction averages 100 N. (b) What is the work done on the lift past the gravitational force in this process? (c) What is the total work done on the lift?

26 .

Suppose a auto travels 108 km at a speed of thirty.0 k/due south, and uses ii.0 gal of gasoline. Only 30% of the gasoline goes into useful work by the strength that keeps the car moving at constant speed despite friction. (The energy content of gasoline is about 140 MJ/gal.) (a) What is the magnitude of the force exerted to go along the car moving at constant speed? (b) If the required force is directly proportional to speed, how many gallons will be used to drive 108 km at a speed of 28.0 m/s?

27 .

Calculate the work done by an 85.0-kg man who pushes a crate 4.00 m up along a ramp that makes an angle of $20.0\text{°}$ with the horizontal (meet below). He exerts a strength of 500 N on the crate parallel to the ramp and moves at a constant speed. Be certain to include the piece of work he does on the crate and on his body to get up the ramp.

28 .

How much work is done by the boy pulling his sis thirty.0 m in a carriage as shown below? Assume no friction acts on the railroad vehicle.

29 .

A shopper pushes a grocery cart xx.0 grand at constant speed on level basis, against a 35.0 N frictional force. He pushes in a direction $25.0\text{°}$ beneath the horizontal. (a) What is the work washed on the cart past friction? (b) What is the work done on the cart past the gravitational forcefulness? (c) What is the work done on the cart by the shopper? (d) Observe the force the shopper exerts, using energy considerations. (e) What is the total work washed on the cart?

thirty .

Suppose the ski patrol lowers a rescue sled and victim, having a full mass of 90.0 kg, downwards a $\mathrm{sixty.0}\text{°}$ gradient at abiding speed, as shown beneath. The coefficient of friction betwixt the sled and the snow is 0.100. (a) How much work is done past friction as the sled moves 30.0 yard along the hill? (b) How much piece of work is done past the rope on the sled in this distance? (c) What is the work washed by the gravitational force on the sled? (d) What is the total work done?

31 .

A constant xx-N strength pushes a small ball in the direction of the force over a altitude of v.0 thousand. What is the work done by the force?

32 .

A toy cart is pulled a altitude of 6.0 m in a straight line beyond the floor. The force pulling the cart has a magnitude of 20 N and is directed at $37\text{°}$ above the horizontal. What is the piece of work done by this strength?

33 .

A 5.0-kg box rests on a horizontal surface. The coefficient of kinetic friction betwixt the box and surface is ${\mu }_{\mathrm{Thou}}=0.50.$ A horizontal strength pulls the box at abiding velocity for 10 cm. Discover the work done by (a) the applied horizontal force, (b) the frictional force, and (c) the net force.

34 .

A sled plus passenger with total mass 50 kg is pulled twenty thousand beyond the snowfall $({\mu }_k=0.20)$ at constant velocity by a forcefulness directed $25\text{°}$ in a higher place the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.

35 .

Suppose that the sled plus passenger of the preceding problem is pushed 20 m across the snow at constant velocity by a force directed $\mathrm{xxx}\text{°}$ below the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.

36 .

How much work does the force $F(\mathrm{ten})=(\mathrm{-2.0}\text{/}x)\text{N}$ do on a particle as information technology moves from $x=\mathrm{ii.0}\text{thousand}$ to $x=5.0\text{1000?}$

37 .

How much work is done against the gravitational strength on a five.0-kg briefcase when it is carried from the basis floor to the roof of the Empire Land Building, a vertical climb of 380 grand?

38 .

It takes 500 J of work to compress a spring 10 cm. What is the force constant of the leap?

39 .

A bungee cord is essentially a very long safe ring that tin stretch up to four times its unstretched length. However, its spring constant varies over its stretch [see Menz, P.G. "The Physics of Bungee Jumping." The Physics Teacher (November 1993) 31: 483-487]. Accept the length of the cord to be along the x-management and define the stretch 10 as the length of the cord l minus its united nations-stretched length $l_0;$ that is, $x=l-l_0$ (see beneath). Suppose a particular bungee cord has a bound constant, for $0\le x\le \mathrm{four.88}\text{g}$ , of $k_1=204\text{North/m}$ and for $x\ge 4.88\text{m}$ , of ${\mathrm{yard}}_{\mathrm{ii}}=111\text{Due north/m}\text{.}$ (Recall that the spring abiding is the gradient of the force F(ten) versus its stretch x.) (a) What is the tension in the string when the stretch is 16.7 one thousand (the maximum desired for a given jump)? (b) How much work must exist washed against the elastic force of the bungee cord to stretch it sixteen.7 m?

Figure vii.16 (credit: modification of work by Graeme Churchard)

40 .

A bungee cord exerts a nonlinear rubberband strength of magnitude $F(x)={\mathrm{chiliad}}_{1}x+k_2{x}^3,$ where x is the distance the cord is stretched, ${\mathrm{one\; thousand}}_1=204\text{N/m}$ and ${\mathrm{1000}}_2=\mathrm{-0.233}{\text{North/m}}^3.$ How much work must exist washed on the cord to stretch it 16.7 m?

41 .

Engineers desire to model the magnitude of the elastic force of a bungee cord using the equation
$F(x)=a\left[\frac{\mathrm{10}+9\text{m}}{\mathrm{ix}\text{1000}}-{\left(\frac{9\text{m}}{x+9\text{m}}\right)}^2\right]$ ,
where x is the stretch of the cord along its length and a is a abiding. If it takes 22.0 kJ of piece of work to stretch the cord by 16.7 yard, determine the value of the constant a.

42 .

A particle moving in the xy-plane is subject to a strength
$\overrightarrow{F}(x,y)=(\mathrm{l}\text{N}/\text{m})(x\widehat{i}+\frac{y^2}{3\text{m}}\widehat{j})$
where x and y are in meters. Calculate the piece of work done on the particle by this forcefulness, as it moves in a straight line from the point (3 m, 4 thou) to the indicate (6 grand, eight m).

43 .

A particle moves along a curved path $y(x)=(10\text{m})\{1+\text{cos}[(0.1{\text{m}}^{\mathrm{-one}})x]\},$ from $x=0$ to $x=\mathrm{ten}\pi \text{grand,}$ subject to a tangential force of variable magnitude $F(x)=(\mathrm{ten}\text{N})\text{sin}[(0.1{\text{one thousand}}^{\mathrm{-ane}})\mathrm{ten}].$ How much work does the force practice? (Hint: Consult a tabular array of integrals or use a numerical integration programme.)

7.two Kinetic Energy

44 .

Compare the kinetic energy of a 20,000-kg truck moving at 110 km/h with that of an eighty.0-kg astronaut in orbit moving at 27,500 km/h.

45 .

(a) How fast must a 3000-kg elephant move to have the same kinetic energy as a 65.0-kg sprinter running at 10.0 m/s? (b) Discuss how the larger energies needed for the movement of larger animals would chronicle to metabolic rates.

46 .

Guess the kinetic free energy of a 90,000-ton shipping carrier moving at a speed of at 30 knots. You will need to look upward the definition of a nautical mile to utilise in converting the unit of measurement for speed, where one knot equals 1 nautical mile per hour. Furthermore for this trouble, 1 ton is equivalent to 2,000 pounds.

47 .

Calculate the kinetic energies of (a) a 2000.0-kg automobile moving at 100.0 km/h; (b) an 80.-kg runner sprinting at x. m/s; and (c) a $\mathrm{nine.ane}\times {10}^{\mathrm{-31}}\text{-kg}$ electron moving at $2.0\times {\mathrm{ten}}^7\text{m/south}\text{.}$

48 .

A 5.0-kg body has three times the kinetic free energy of an viii.0-kg body. Calculate the ratio of the speeds of these bodies.

49 .

An 8.0-yard bullet has a speed of 800 chiliad/s. (a) What is its kinetic energy? (b) What is its kinetic free energy if the speed is halved?

seven.three Piece of work-Free energy Theorem

50 .

(a) Calculate the force needed to bring a 950-kg car to rest from a speed of 90.0 km/h in a distance of 120 m (a fairly typical distance for a non-panic cease). (b) Suppose instead the car hits a concrete abutment at total speed and is brought to a stop in 2.00 m. Calculate the force exerted on the motorcar and compare it with the forcefulness found in part (a).

51 .

A car's bumper is designed to withstand a 4.0-km/h (one.1-m/s) standoff with an immovable object without impairment to the body of the car. The bumper cushions the stupor past absorbing the force over a distance. Calculate the magnitude of the average force on a bumper that collapses 0.200 m while bringing a 900-kg car to rest from an initial speed of 1.i m/s.

52 .

Battle gloves are padded to lessen the force of a blow. (a) Calculate the force exerted by a boxing glove on an opponent'southward face up, if the glove and face compress 7.l cm during a blow in which the 7.00-kg arm and glove are brought to residual from an initial speed of ten.0 m/south. (b) Calculate the force exerted by an identical blow in the days when no gloves were used, and the duke and face would compress simply 2.00 cm. Presume the change in mass by removing the glove is negligible. (c) Discuss the magnitude of the force with glove on. Does it seem high enough to crusade harm even though information technology is lower than the force with no glove?

53 .

Using energy considerations, calculate the average strength a 60.0-kg sprinter exerts astern on the track to accelerate from 2.00 to 8.00 m/s in a distance of 25.0 yard, if he encounters a headwind that exerts an boilerplate force of 30.0 N against him.

54 .

A five.0-kg box has an acceleration of $\mathrm{two.0}{\text{grand/s}}^2$ when it is pulled past a horizontal force across a surface with ${\mu }_{\mathrm{Thou}}=\mathrm{0.l}.$ Notice the work done over a distance of 10 cm past (a) the horizontal forcefulness, (b) the frictional force, and (c) the net force. (d) What is the change in kinetic free energy of the box?

55 .

A constant 10-N horizontal force is applied to a 20-kg cart at rest on a level flooring. If friction is negligible, what is the speed of the cart when it has been pushed 8.0 m?

56 .

In the preceding problem, the 10-Due north force is applied at an angle of $45\text{°}$ below the horizontal. What is the speed of the cart when information technology has been pushed 8.0 m?

57 .

Compare the piece of work required to stop a 100-kg crate sliding at i.0 one thousand/s and an eight.0-g bullet traveling at 500 1000/s.

58 .

A wagon with its passenger sits at the top of a hill. The wagon is given a slight push and rolls 100 chiliad down a $10\text{°}$ incline to the bottom of the colina. What is the wagon's speed when information technology reaches the end of the incline. Assume that the retarding strength of friction is negligible.

59 .

An viii.0-g bullet with a speed of 800 m/s is shot into a wooden block and penetrates 20 cm before stopping. What is the average forcefulness of the forest on the bullet? Assume the block does not movement.

sixty .

A two.0-kg block starts with a speed of 10 m/southward at the bottom of a plane inclined at $37\text{°}$ to the horizontal. The coefficient of sliding friction between the cake and plane is ${\mu }_g=0.30.$ (a) Apply the piece of work-free energy principle to determine how far the block slides along the airplane before momentarily coming to rest. (b) After stopping, the block slides dorsum down the aeroplane. What is its speed when it reaches the bottom? (Hint: For the round trip, only the strength of friction does piece of work on the block.)

61 .

When a 3.0-kg cake is pushed confronting a massless bound of forcefulness constant $\mathrm{4.five}\times {\mathrm{x}}^3\text{N/one thousand,}$ the spring is compressed eight.0 cm. The block is released, and information technology slides 2.0 m (from the point at which it is released) across a horizontal surface earlier friction stops it. What is the coefficient of kinetic friction between the block and the surface?

62 .

A small block of mass 200 grand starts at rest at A, slides to B where its speed is $v_B=8.0\text{k/s,}$ and then slides along the horizontal surface a altitude ten m before coming to rest at C. (See below.) (a) What is the work of friction along the curved surface? (b) What is the coefficient of kinetic friction along the horizontal surface?

63 .

A modest object is placed at the summit of an incline that is essentially frictionless. The object slides downwards the incline onto a crude horizontal surface, where information technology stops in 5.0 s after traveling threescore one thousand. (a) What is the speed of the object at the lesser of the incline and its acceleration along the horizontal surface? (b) What is the height of the incline?

64 .

When released, a 100-thou block slides downward the path shown below, reaching the bottom with a speed of four.0 m/s. How much work does the strength of friction do?

65 .

A 0.22LR-caliber bullet similar that mentioned in Instance vii.x is fired into a door made of a unmarried thickness of i-inch pino boards. How fast would the bullet be traveling later on information technology penetrated through the door?

66 .

A sled starts from residual at the top of a snowfall-covered incline that makes a $22\text{°}$ angle with the horizontal. Afterward sliding 75 k downward the slope, its speed is 14 1000/s. Use the work-energy theorem to calculate the coefficient of kinetic friction between the runners of the sled and the snowy surface.

7.four Power

67 .

A person in good physical condition can put out 100 Due west of useful power for several hours at a stretch, possibly past pedaling a mechanism that drives an electric generator. Neglecting whatsoever bug of generator efficiency and practical considerations such every bit resting time: (a) How many people would it take to run a 4.00-kW electric clothes dryer? (b) How many people would information technology take to replace a large electric ability constitute that generates 800 MW?

68 .

What is the price of operating a 3.00-W electrical clock for a yr if the cost of electricity is $0.0900 per $\text{kW}·\text{h}$ ?

69 .

A big household air conditioner may consume 15.0 kW of power. What is the cost of operating this air conditioner three.00 h per day for 30.0 d if the price of electricity is $0.110 per $\text{kW}·\text{h}$ ?

70 .

(a) What is the boilerplate power consumption in watts of an appliance that uses 5.00 $\text{kW}·\text{h}$ of energy per 24-hour interval? (b) How many joules of free energy does this appliance swallow in a year?

71 .

(a) What is the average useful power output of a person who does $\mathrm{half-dozen.00}\times {10}^{\mathrm{half\; dozen}}\text{J}$ of useful work in eight.00 h? (b) Working at this rate, how long volition it have this person to lift 2000 kg of bricks 1.fifty m to a platform? (Work washed to lift his torso can be omitted because it is not considered useful output here.)

72 .

A 500-kg dragster accelerates from rest to a terminal speed of 110 grand/s in 400 m (about a quarter of a mile) and encounters an average frictional force of 1200 N. What is its average power output in watts and horsepower if this takes 7.30 s?

73 .

(a) How long volition information technology have an 850-kg car with a useful power output of xl.0 hp (1 hp equals 746 W) to reach a speed of fifteen.0 m/s, neglecting friction? (b) How long will this acceleration take if the automobile also climbs a 3.00-thou high hill in the process?

74 .

(a) Find the useful ability output of an elevator motor that lifts a 2500-kg load a height of 35.0 m in 12.0 south, if information technology likewise increases the speed from rest to 4.00 grand/s. Note that the total mass of the counterbalanced system is ten,000 kg—and so that only 2500 kg is raised in acme, but the full ten,000 kg is accelerated. (b) What does it cost, if electricity is $0.0900 per $\text{kW}·\text{h}$ ?

75 .

(a) How long would it take a $\mathrm{ane.50}\times {10}^5\text{-kg}$ airplane with engines that produce 100 MW of ability to reach a speed of 250 m/s and an distance of 12.0 km if air resistance were negligible? (b) If it really takes 900 s, what is the power? (c) Given this power, what is the average force of air resistance if the aeroplane takes 1200 due south? (Hint: You must find the distance the plane travels in 1200 s assuming constant acceleration.)

76 .

Calculate the power output needed for a 950-kg car to climb a $\mathrm{ii.00}\text{°}$ slope at a constant 30.0 m/s while encountering wind resistance and friction totaling 600 Northward.

77 .

A man of mass 80 kg runs up a flight of stairs 20 thou high in ten due south. (a) how much power is used to lift the human being? (b) If the man'southward torso is 25% efficient, how much ability does he expend?

78 .

The man of the preceding problem consumes approximately $\mathrm{i.05}\times {10}^7\text{J}$ (2500 food calories) of energy per day in maintaining a abiding weight. What is the average power he produces over a day? Compare this with his power product when he runs up the stairs.

79 .

An electron in a television tube is accelerated uniformly from residual to a speed of $8.4\times {10}^7\text{m/s}$ over a distance of 2.v cm. What is the power delivered to the electron at the instant that its displacement is 1.0 cm?

eighty .

Coal is lifted out of a mine a vertical distance of 50 m by an engine that supplies 500 Due west to a conveyor belt. How much coal per infinitesimal can be brought to the surface? Ignore the furnishings of friction.

81 .

A girl pulls her 15-kg wagon along a apartment sidewalk by applying a 10-N strength at $37\text{°}$ to the horizontal. Presume that friction is negligible and that the wagon starts from rest. (a) How much work does the girl do on the railroad vehicle in the first 2.0 due south. (b) How much instantaneous ability does she exert at $t=2.0\text{s}$ ?

82 .

A typical auto engine has an efficiency of 25%. Suppose that the engine of a 1000-kg automobile has a maximum ability output of 140 hp. What is the maximum grade that the automobile tin can climb at 50 km/h if the frictional retarding forcefulness on it is 300 N?

83 .

When jogging at 13 km/h on a level surface, a 70-kg human being uses free energy at a rate of approximately 850 W. Using the facts that the "human engine" is approximately 25% efficient, determine the rate at which this man uses free energy when jogging up a $5.0\text{°}$ slope at this same speed. Assume that the frictional retarding forcefulness is the same in both cases.

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Source: https://openstax.org/books/university-physics-volume-1/pages/7-problems