to what angle can he tilt the cabinet before it tips over?
Problem 1
A 64 kg student stands on a very low-cal, rigid board that rests on a bathroom scale at each end, equally shown in Figure P8.one. What is the reading on each of the scales?
Narayan H.
Numerade Educator
Problem 2
Suppose the student in Figure $\mathrm{P} 8.ane$ is $54 \mathrm{kg}$, and the board existence stood on has a $ten \mathrm{kg}$ mass. What is the reading on each of the scales?
Narayan H.
Numerade Educator
Problem 3
Il How shut to the right edge of the 56 kg picnic table shown in Figure $\mathrm{P} 8.3$ can a $70 \mathrm{kg}$ man stand without the tabular array tipping over? Hint: When the tabular array is just almost to tip, what is the force of the ground on the table'south left leg?
Narayan H.
Numerade Educator
Trouble iv
In Effigy $\mathrm{P} viii.4,$ a $70 \mathrm{kg}$ man walks out on a $10 \mathrm{kg}$ beam that rests on, but is non attached to, two supports. When the beam just starts to tip, what is the force exerted on the axle by the correct support?
Narayan H.
Numerade Educator
Problem 5
You're carrying a $3.6-\mathrm{m}$ -long, $25 \mathrm{kg}$ pole to a construction site when you lot decide to stop for a residue. Yous place ane end of the pole on a fence postal service and hold the other end of the pole $35 \mathrm{cm}$ from its tip. How much force must y'all exert to go along the pole motionless in a horizontal position?
Narayan H.
Numerade Educator
Trouble half-dozen
A typical horse weighs $5000 \mathrm{N}$. The distance between the front end and rear hooves and the distance from the rear hooves to the centre of mass for a typical horse are shown in Figure P8.6. What fraction of the horse's weight is borne by the front hooves?
Narayan H.
Numerade Educator
Problem 7
A vendor hangs an $8.0 \mathrm{kg}$ sign in front of his shop with a cablevision held away from the building by a lightweight pole. The pole is free to pivot nigh the cease where information technology touches the wall, equally shown in Figure P8.7. What is the tension in the cable?
Narayan H.
Numerade Educator
Trouble 8
in Figure P8.viii. The hippo carries $60 \%$ of its weight on its front feet. How far from its tail is the hippo's middle of gravity?
Narayan H.
Numerade Educator
Problem 9
The two objects in Figure $\mathrm{P} viii.ix$ are balanced on the pivot. What is distance $d ?$
Narayan H.
Numerade Educator
Problem x
A bike mechanic is checking a road bike's chain. He applies a $45 \mathrm{N}$ force to a pedal at the bending shown in Figure P8.10 while keeping the cycle from rotating. The pedal is $17 \mathrm{cm}$ from the center of the crank; the gear has a diameter of $16 \mathrm{cm} .$ What is the tension in the chain?
Narayan H.
Numerade Educator
Trouble 11
A $60 \mathrm{kg}$ diver stands at the terminate of a $thirty \mathrm{kg}$ springboard, equally shown in Effigy $\mathrm{P} 8.11 .$ The board is attached to a swivel at the left end just simply rests on the correct support. What is the magnitude of the vertical force exerted by the hinge on the board?
Narayan H.
Numerade Educator
Problem 12
A wheel chain can support a tension of no more $9800 \mathrm{N}$. The pedal connects to a crank $17 \mathrm{cm}$ from the axle, and the gear pulling the chain has a $9.ane \mathrm{cm}$ radius. When riding at a constant speed, with the creepo and pedal horizontal, every bit in Figure P8.12, what is the maximum strength that tin can exist applied to the pedal before the concatenation breaks?
Narayan H.
Numerade Educator
Problem 13
A uniform axle of length $one.0 \mathrm{m}$ and mass $ten \mathrm{kg}$ is fastened to a wall by a cable, as shown in Effigy $\mathrm{P} eight.13 .$ The beam is costless to pin at the bespeak where it attaches to the wall. What is the tension in the cable?
Narayan H.
Numerade Educator
Problem 14
The towers holding small wind turbines are often raised and lowered for easy servicing of the turbine. Figure P8.14 shows a $m \mathrm{kg}$ wind turbine mounted on the terminate of a 24-m-long, 700 kg tower that connects to a support column at a pivot. A piston continued 3.0 $\mathrm{m}$ from the pivot applies the force needed to heighten or lower the belfry. At the instant shown, the current of air turbine is being raised at a very slow, abiding speed. What magnitude force is the piston applying?
Narayan H.
Numerade Educator
Problem 15
A standard four-drawer filing cabinet is 52 inches loftier and 15 inches wide. If it is evenly loaded, the center of gravity is at the center of the chiffonier. A worker is tilting a filing chiffonier to the side to clean nether it. To what angle can he tilt the cabinet before information technology tips over?
Narayan H.
Numerade Educator
Problem 16
A double-decker London bus might exist in danger of rolling over in a highway accident, but at the low speeds of its urban environment, information technology's plenty stable. The track width is $2.05 \mathrm{m}$. With no passengers, the summit of the middle of gravity is $1.45 \mathrm{m},$ ascension to $ane.73 \mathrm{thousand}$ when the omnibus is loaded to chapters. What are the disquisitional angles for both the unloaded and loaded bus?
Narayan H.
Numerade Educator
Trouble 17
The stability of a vehicle is oft rated by the static stability factor, which is half the rails width divided by the height of the center of gravity above the route. A typical SUV has a static stability factor of $1.2 .$ What is the critical bending?
Narayan H.
Numerade Educator
Problem 18
A magazine rack has a center of gravity 16 $\mathrm{cm}$ above the floor, every bit shown in Figure P8.eighteen. Through what maximum bending, in degrees, can the rack exist tilted without falling over?
Narayan H.
Numerade Educator
Problem 19
A machine manufacturer claims that you can drive its new vehicle across a hill with a $47^{\circ}$ slope earlier the vehicle starts to tip. If the vehicle is $2.0 \mathrm{m}$ wide, how loftier is its center of gravity?
Narayan H.
Numerade Educator
Trouble twenty
A sparse $2.00 \mathrm{kg}$ box rests on a $6.00 \mathrm{kg}$ board that hangs over the finish of a tabular array, equally shown in Figure $\mathrm{P} 8.xx .$ How far can the center of the box be from the stop of the tabular array earlier the lath begins to tilt?
Narayan H.
Numerade Educator
Trouble 21
An orthodontic spring, continued betwixt the upper and lower jaws, is adapted to provide no force with the oral cavity open. When the patient closes her oral fissure, however, the bound compresses by $6.0 \mathrm{mm} .$ What force is exerted if the jump abiding is $160 \mathrm{N} / \mathrm{m} ?$
Narayan H.
Numerade Educator
Trouble 22
The iv wheels of a car are continued to the car'south body past bound assemblies that let the wheels move up and down over bumps and dips in the road. When a $68 \mathrm{kg}$ (about $150 \mathrm{lb}$ ) person sits on the left front fender of a pocket-sized machine, this corner of the car dips by nigh $ane.two \mathrm{cm}$ (about $1 / 2$ in). If nosotros treat the spring associates equally a unmarried jump, what is the approximate spring constant?
Narayan H.
Numerade Educator
Problem 23
Experiments using "optical tweezers" measure the elasticity of individual DNA molecules. For small enough changes in length, the elasticity has the aforementioned form as that of a jump. A DNA molecule is anchored at one finish, and then a forcefulness of $1.v \mathrm{nN}$ $\left(ane.5 \times 10^{-9} \mathrm{North}\right)$ pulls on the other stop, causing the molecule to stretch by $five.0 \mathrm{nm}\left(5.0 \times 10^{-9} \mathrm{m}\right) .$ What is the spring constant of that Dna molecule?
Narayan H.
Numerade Educator
Problem 24
A passenger railroad car has a total of 8 wheels. Springs on each bicycle shrink - slightly -when the car is loaded. Ratings for the motorcar give the stiffness per wheel (the spring constant, treating the entire bound assembly as a single spring every bit $two.8 \times 10^{seven} \mathrm{N} / \mathrm{m} .$ When 30 passengers, each with average mass $80 \mathrm{kg},$ board the motorcar, how much does the car movement down on its leap break? Presume that each wheel supports $1 / eight$ the weight of the car.
Narayan H.
Numerade Educator
Problem 25
1 terminate of a 10-cm-long leap is attached to the ceiling. When a $2.0 \mathrm{kg}$ mass is hung from the other terminate, the leap stretches to a length of $15 \mathrm{cm}$.
a. What is the spring abiding?
b. How long is the spring when a $3.0 \mathrm{kg}$ mass is suspended from it?
Narayan H.
Numerade Educator
Problem 26
A scale used to weigh fish consists of a bound hung from a back up. The spring's equilibrium length is $x.0 \mathrm{cm} .$ When a $4.0 \mathrm{kg}$ fish is suspended from the end of the spring, information technology stretches to a length of $12.iv \mathrm{cm}$.
a. What is the spring constant $k$ for this spring?
b. If an $eight.0 \mathrm{kg}$ fish is suspended from the spring, what volition be the length of the leap?
Narayan H.
Numerade Educator
Problem 27
A spring has an unstretched length of $x \mathrm{cm}$. It exerts a restoring strength $F$ when stretched to a length of $11 \mathrm{cm} .$
a. For what total stretched length of the bound is its restoring force $3 F ?$
b. At what compressed length is the restoring force $two F ?$
Nafis F.
Numerade Educator
Problem 28
A spring stretches $5.0 \mathrm{cm}$ when a $0.20 \mathrm{kg}$ block is hung from it. If a $0.70 \mathrm{kg}$ block replaces the $0.20 \mathrm{kg}$ cake, how far does the leap stretch?
Narayan H.
Numerade Educator
Trouble 29
You need to make a spring scale to measure the mass of objects hung from it. Y'all desire each $1.0 \mathrm{cm}$ length along the calibration to correspond to a mass difference of 0.10 kg. What should exist the value of the bound constant?
Narayan H.
Numerade Educator
Trouble 30
Dynamic climbing ropes are designed to be quite pliant, assuasive a falling climber to slow downwardly over a long distance. The graph in Figure $\mathrm{P} eight.30$ shows force-versus-strain information for an 11-mm-diameter climbing rope. What is the Young's modulus for this rope?
Narayan H.
Numerade Educator
Problem 31
A force stretches a wire past $1.0 \mathrm{mm}$.
a. A second wire of the same fabric has the same cross section and twice the length. How far volition it be stretched by the same force?
b. A 3rd wire of the aforementioned material has the same length and twice the bore as the outset. How far will information technology be stretched by the aforementioned force?
Narayan H.
Numerade Educator
Problem 32
Static climbing ropes are designed to be relatively stiff so that they stretch less than dynamic ropes. To meet a certain specification, an 11 -mm-bore rope must experience a maximum elongation of $five.0 \%$ when supporting a $150 \mathrm{kg}$ load. What is the minimum Young's modulus?
Narayan H.
Numerade Educator
Problem 33
What hanging mass will stretch a 2.0-1000-long, $0.l-\mathrm{mm}$ diameter steel wire by $1.0 \mathrm{mm} ?$
Averell H.
Carnegie Mellon University
Trouble 34
An 80-cm-long, 1.0-mm-diameter steel guitar cord must be tightened to a tension of $2.0 \mathrm{kN}$ past turning the tuning screws. By how much is the cord stretched?
Narayan H.
Numerade Educator
Problem 35
A mineshaft has an ore elevator hung from a single braided cable of bore $ii.5 \mathrm{cm} .$ Young's modulus of the cable is $10 \times 10^{10} \mathrm{North} / \mathrm{chiliad}^{2} .$ When the cable is fully extended, the end of the cable is $800 \mathrm{m}$ below the support. How much does the fully extended cable stretch when $m \mathrm{kg}$ of ore is loaded?
Narayan H.
Numerade Educator
Problem 36
The normal strength of the ground on the foot can reach three times a runner's body weight when the foot strikes the pavement. Past what amount does the 52 -cm-long femur of an $80 \mathrm{kg}$ runner compress at this moment? The cantankerous-section area of the bone of the femur tin can be taken as $5.2 \times 10^{-4} \mathrm{m}^{2}$.
Narayan H.
Numerade Educator
Trouble 37
A iii-legged wooden bar stool fabricated out of solid Douglas fir has legs that are $two.0 \mathrm{cm}$ in diameter. When a $75 \mathrm{kg}$ human sits on the stool, by what percent does the length of the legs subtract? Assume, for simplicity, that the stool's legs are vertical and that each bears the aforementioned load.
Narayan H.
Numerade Educator
Problem 38
To penetrate armor, a projectile's point concentrates strength in a small surface area, creating a stress large plenty that the armor fails. A species of jellyfish launches a pointed needle that can penetrate the hard crush of a crustacean. The rapid deceleration on impact creates a $32 \mu \mathrm{N}$ force on the tip, which has a very small $15 \mathrm{nm}$ radius. What is the resulting stress? How does this compare to the ultimate stress of steel?
Narayan H.
Numerade Educator
Trouble 39
A 3.0-m-tall, l-cm-diameter physical column supports a $200,000 \mathrm{kg}$ load. Past how much is the column compressed?
Narayan H.
Numerade Educator
Problem forty
You've just put a new wood floor in your house. An object will paring the floor if the stress $-$ the strength divided past the area -exerted by the object is groovy plenty. Who is more than probable to paring your floor: a 50 kg adult female in high-heeled shoes (assume a round heel pad $0.50 \mathrm{cm}$ in diameter $)$ with all of her weight on 1 heel or a $5000 \mathrm{kg}$ African elephant (presume a circular contact area of $40 \mathrm{cm}$ in diameter for one foot) standing on all four feet?
Narayan H.
Numerade Educator
Problem 41
A glass optical fiber in a communications organisation has a diameter of $9.0 \mu \mathrm{thou}$
a. What maximum tension could this fiber support without breaking?
b. Assume that the fiber stretches in a linear style until the instant it breaks. By how much will a 10-m-long fiber accept stretched when it is at the breaking indicate?
Narayan H.
Numerade Educator
Problem 42
If you tethered a space station to the earth by a long cable, you could go to space in an lift that rides upward the cable—much simpler and cheaper than riding to space on a rocket. At that place's one big problem, however: In that location is no way to create a cable that is long enough. The cable would need to reach 36,000 km upward, to the height where a satellite orbits at the aforementioned speed as the world rotates; a cable this long made of ordinary materials couldn't even support its own weight. Consider a steel cablevision suspended from a point high above the earth. The stress in the cable is highest at the top; it must support the weight of cablevision below it. What is the greatest length the cable could accept without failing? For the purposes of this problem, you tin can ignore the variation in gravity near the surface of the world. Hint: The mass of the cable is the volume of the cable multiplied by the density. The density of steel is $7900 \mathrm{kg} / \mathrm{m}^{3}$.
Narayan H.
Numerade Educator
Trouble 43
The Achilles tendon connects the muscles in your calf to the back of your pes. When yous are sprinting, your Achilles tendon alternately stretches, as yous bring your weight down onto your frontwards foot, and contracts to push you off the ground. A $70 \mathrm{kg}$ runner has an Achilles tendon that is $15 \mathrm{cm}$ long with a typical $1.ane \times ten^{-four} \mathrm{m}^{2}$ area.
a. Past how much will the runner's Achilles tendon stretch if the maximum strength on it is eight.0 times his weight, a typical value while running?
b. What fraction of the tendon'south length does this represent to?
Narayan H.
Numerade Educator
Problem 44
A woman is pushing a load in a wheelbarrow, as in Figure P8.44. The combined mass of the wheel-barrow and the load is $110 \mathrm{kg}$, with a center of gravity $0.25 \mathrm{m}$ behind the axle. The woman supports the wheelbarrow at the handles, $1.1 \mathrm{k}$ behind the beam.
a. What is the force required to back up the wheelbarrow?
b. What fraction of the weight of the wheelbarrow and the load does this force represent?
Narayan H.
Numerade Educator
Trouble 45
Effigy $\mathrm{P} 8.45$ shows the operation of a garlic press. The lower part of the press is held steady, and the upper handle is pushed down, thereby crushing a garlic clove through a screen. Approximate distances are shown in the figure. If the user exerts a $12 \mathrm{Due north}$ force on the upper handle, approximate the force on the clove.
Problem 46
Consider a rower in a scull as in Figure $\mathrm{P} eight.46 .$ The oars aren't accelerating, and they are rotating at a constant speed, and so the net force and net torque on the oars are zero. An oar is $two.eight \mathrm{m}$ long, and the rower pulls with a $250 \mathrm{N}$ force on the handle, which is $0.92 \mathrm{1000}$ from the pivot.
a. Assume that the oar touches the water at its very end. What is the drag forcefulness from the water on the oar? Assume that the oar is perpendicular to the boat, and that the force of the rower and the drag force are both perpendicular to the oar.
b. Given that both oars are the same, what is the total strength propelling the boat forward?
Narayan H.
Numerade Educator
Problem 47
Hold your upper arm vertical and your lower arm horizontal with your hand palm-down on a table, as shown in Figure P8.47. If you now push down on the tabular array, you lot'll feel that your triceps muscle has contracted and is trying to pin your lower arm well-nigh the elbow joint. If a person with the arm dimensions shown pushes down hard with a $xc \mathrm{Due north}$ force (about $20 \mathrm{lb}),$ what forcefulness must the triceps musculus provide? You can ignore the mass of the arm and manus in your calculation.
Narayan H.
Numerade Educator
Trouble 48
If you stand on i foot while holding your other leg up behind you, your muscles employ a force to concord your leg in this raised position. We tin model this situation as in Figure $\mathrm{P} viii.48$. The leg pivots at the human knee articulation, and the strength that holds the leg upwards is provided by a tendon fastened to the lower leg as shown. Presume that the lower leg and the foot have a combined mass of $4.0 \mathrm{kg},$ and that their combined center of gravity is at the center of the lower leg.
a. How much strength must the tendon exert to keep the leg in this position?
b. As you concord your leg in this position, the upper leg exerts a force on the lower leg at the articulatio genus joint. What are the magnitude and management of this force?
Narayan H.
Numerade Educator
Problem 49
If yous concord your arm outstretched with palm upward, as in Figure $\mathrm{P} 8.49,$ the force to keep your arm from falling comes from your deltoid muscle. The arm of a typical person has mass $4.0 \mathrm{kg}$ and the distances and angles shown in the figure.
a. What strength must the deltoid muscle provide to proceed the arm in this position?
b. By what factor does this force exceed the weight of the arm?
Narayan H.
Numerade Educator
Problem 50
Dogs -similar many animals - stand and walk on their toes. A photo of the rear foot of a dog is shown in Figure $\mathrm{P} 8.50 \mathrm{a} ;$ Figure $\mathrm{P} 8.fifty \mathrm{b}$ shows the basic of the leg and foot along with relevant distances. The colored chemical element corresponds to your foot, and the connection with the leg corresponds to your ankle. The Achilles tendon pulls on the end of the human foot, along a line $4.0 \mathrm{cm}$ from the ankle. What is the tension in the tendon if a $twenty \mathrm{kg}$ dog is supporting $1 / 4$ of its weight on one rear human foot?
Narayan H.
Numerade Educator
Problem 51
A 3.0-m-long rigid axle with a mass of $100 \mathrm{kg}$ is supported at each terminate, as shown in Effigy $\mathrm{P} eight.51$. An $80 \mathrm{kg}$ student stands $2.0 \mathrm{m}$ from support ane How much upward force does each support exert on the axle?
Narayan H.
Numerade Educator
Trouble 52
An $80 \mathrm{kg}$ structure worker sits downward $ii.0 \mathrm{m}$ from the end of a $1450 \mathrm{kg}$ steel beam to eat his lunch, as shown in Effigy P8.52. The cable supporting the beam is rated at $15,000 \mathrm{N}$. Should the worker be worried?
Narayan H.
Numerade Educator
Problem 53
A man is attempting to raise a 7.v -m-long, $28 \mathrm{kg}$ flagpole that has a hinge at the base by pulling on a rope attached to the top of the pole, as shown in Figure P8.53. With what force does the man have to pull on the rope to hold the pole motionless in this position?
Narayan H.
Numerade Educator
Problem 54
An 85 kg human being stands in a very strong wind moving at $14 \mathrm{m} / \mathrm{southward}$ at torso height. Equally you lot know, he will need to lean in to the wind, and we tin model the situation to see why. Assume that the human has a mass of $85 \mathrm{kg},$ with a centre of gravity $1.0 \mathrm{m}$ above the ground. The action of the wind on his torso, which we approximate every bit a cylinder $50 \mathrm{cm}$ wide and $ninety \mathrm{cm}$ long centered $one.2 \mathrm{grand}$ above the ground, produces a force that tries to tip him over backward. To keep from falling over, he must lean forward.
a. What is the magnitude of the torque provided past the wind strength? Have the pin point at his feet. Assume that he is standing vertically.
b. At what angle to the vertical must the man lean to provide a gravitational torque that is equal to this torque due to the wind strength?
Problem 55
A 40 kg, 5.0-grand-long beam is supported by, but not attached to, the two posts in Figure P8.55. A 20 kg boy starts walking along the beam. How close can he get to the correct finish of the axle without it tipping?
Rashmi S.
Numerade Educator
Problem 56
2 identical, side-by-side springs with leap constant $240 \mathrm{N} / \mathrm{grand}$ support a $ii.00 \mathrm{kg}$ hanging box. Each bound supports the same weight. By how much is each spring stretched?
Narayan H.
Numerade Educator
Problem 57
A 5.0 kg mass hanging from a bound scale is slowly lowered onto a vertical bound, as shown in Figure P8.57. The calibration reads in newtons.
a. What does the spring scale read merely before the mass touches the lower leap?
b. The scale reads $20 \mathrm{N}$ when the lower leap has been compressed past $2.0 \mathrm{cm}$ What is the value of the leap constant for the lower jump?
c. At what compression distance volition the scale read naught?
Nafis F.
Numerade Educator
Trouble 58
Dna molecules are typically folded tightly. Stretching a strand of Deoxyribonucleic acid means straightening it, and the molecules resist this straightening. Investigators tin attach chaplet to the ends of a strand of DNA and, using "optical tweezers," mensurate the force required to produce a sure extension. Data for the stretch of a 3500 base pair strand of Dna approximately follow the line in the graph in Effigy $\mathrm{P} eight.58$. What is the bound constant for this strand of Deoxyribonucleic acid?
Problem 59
Effigy P8.59 shows 2 springs attached to a block that can slide on a frictionless surface. In the block's equilibrium position, the left bound is compressed by $ii.0 \mathrm{cm}$.
a. By how much is the right spring compressed?
b. What is the net forcefulness on the cake if it is moved $15 \mathrm{cm}$ to the right of its equilibrium position?
Narayan H.
Numerade Educator
Trouble 60
A $25 \mathrm{kg}$ child bounces on a pogo stick. The pogo stick has a spring with spring constant $2.0 \times 10^{4} \mathrm{North} / \mathrm{m}$. When the child makes a squeamish big bounce, she finds that at the bottom of the bounce she is accelerating upwardly at $9.8 \mathrm{grand} / \mathrm{south}^{2} .$ How much is the spring compressed?
Narayan H.
Numerade Educator
Problem 61
Effigy $\mathrm{P} 8.61$ shows a lightweight plank supported at its right end past a 7.0 -mm-bore rope with a tensile force of $6.0 \times 10^{7} \mathrm{N} / \mathrm{thou}^{2}.$
a. What is the maximum strength that the rope can support?
b. What is the greatest distance, measured from the pivot, that the center of gravity of an $800 \mathrm{kg}$ piece of heavy machinery can exist placed without snapping the rope?
Narayan H.
Numerade Educator
Problem 62
In the hammer throw, an athlete spins a heavy mass in a circle at the end of a cable before releasing information technology for distance. For male athletes, the "hammer" is a mass of $7.3 \mathrm{kg}$ at the end of a $1.ii \mathrm{m}$ cable, which is typically a $iii.0-\mathrm{mm}-$ diameter steel cable. A world-class thrower can get the hammer up to a speed of $29 \mathrm{one thousand} / \mathrm{s}$. If an athlete swings the mass in a horizontal circle centered on the handle he uses to concur the cable
a. What is the tension in the cable?
b. How much does the cable stretch?
Narayan H.
Numerade Educator
Problem 63
There is a disk of cartilage betwixt each pair of vertebrae in your spine. Suppose a disk is $0.50 \mathrm{cm}$ thick and $4.0 \mathrm{cm}$ in diameter. If this deejay supports half the weight of a $65 \mathrm{kg}$ person, past what fraction of its thickness does the disk compress?
Narayan H.
Numerade Educator
Problem 64
Orb spiders make silk with a typical bore of $0.15 \mathrm{mm}$.
a. A typical large orb spider has a mass of 0.50 grand. If this spider suspends itself from a single 12-cm long strand of silk, by how much will the silk stretch?
b. What is the maximum weight that a unmarried thread of this silk could support?
Narayan H.
Numerade Educator
Trouble 65
Larger animals have sturdier bones than smaller animals. A mouse'south skeleton is just a few pct of its body weight, compared to $sixteen \%$ for an elephant. To come across why this must be and then, remember, from Example $8.10,$ that the stress on the femur for a man standing on ane leg is $1.4 \%$ of the bone's tensile strength. Suppose we scale this man upwards by a gene of 10 in all dimensions, keeping the aforementioned torso proportions. Utilise the data for Example 8.10 to compute the following.
a. Both the inside and exterior diameter of the femur, the region of compact bone, will increase by a factor of $10 .$ What will be the new cantankerous-department expanse?
b. The man'southward torso volition increase past a gene of 10 in each dimension. What volition be his new mass?
c. If the scaled-up man now stands on one leg, what fraction of the tensile force is the stress on the femur?
Problem 66
The main muscles that hold your head upright attach to your spine in dorsum of the bespeak where your head pivots on your neck. Effigy $\mathrm{P} 8.66$ shows typical numbers for the distance from the pivot to the muscle zipper bespeak and the distance from the pivot to the center of gravity of the head. The muscles pull down to go on your head upright. If the muscle relaxes $-$ if, for instance, yous doze in one of your classes besides Physics - your head tips forward. In the questions that follow, assume that your head has a mass of $four.eight \mathrm{kg}$, and that you maintain the relative angle between your head and your spine.
a. With the head held level, as in Figure $\mathrm{P} 8.66,$ what muscle force is needed to keep a $4.8 \mathrm{kg}$ caput upright?
b. If y'all tip your torso forward so that your spine is level with the ground, what muscle forcefulness is needed to keep your head in the same orientation relative to the spine?
c. If you tip your body backward, you will attain a point where no muscle force is needed to proceed your head upright. For the distances given in Figure $\mathrm{P} 8.66,$ at what bending does this balance occur?
Narayan H.
Numerade Educator
Trouble 67
A woman weighing $580 \mathrm{N}$ does a pushup from her knees, every bit shown in Figure $\mathrm{P} 8.67 .$ What are the normal forces of the floor on (a) each of her hands and (b) each of her knees?
Narayan H.
Numerade Educator
Problem 68
When you bend over, a serial of big muscles, the erector spinae, pull on your spine to concur y'all up. Figure $\mathrm{P} viii.68$ shows a simplified model of the spine as a rod of length $L$ that pivots at its lower end. In this model, the centre of gravity of the $320 \mathrm{N}$ weight of the upper torso is at the center of the spine. The $160 \mathrm{North}$ weight of the head and artillery acts at the peak of the spine. The erector spinae muscles are modeled as a single muscle that acts at an $12^{\circ}$ angle to the spine. Suppose the person in Figure $\mathrm{P} viii.68$ bends over to an angle of $30^{\circ}$ from the horizontal.
a. What is the tension in the erector muscle?
Hint: Align your $ten$ -axis with the axis of the spine.
b. A strength from the pelvic girdle acts on the base of the spine. What is the component of this force in the direction of the spine? (This large forcefulness is the cause of many back injuries).
Khoobchandra A.
Numerade Educator
Problem 69
What is the approximate Immature's modulus for the ligament?
A. $4 \times 10^{5} \mathrm{N} / \mathrm{m}^{ii}$
B. $8 \times 10^{5} \mathrm{N} / \mathrm{chiliad}^{2}$
C. $three \times ten^{6} \mathrm{N} / \mathrm{m}^{2}$
D. $6 \times 10^{vi} \mathrm{N} / \mathrm{1000}^{2}$
Narayan H.
Numerade Educator
Problem 70
The segment of ligament tested has a resting length of $40 \mathrm{mm} .$ How long is the ligament at a strain of $0.60 ?$
A. $46 \mathrm{mm}$
B. $52 \mathrm{mm}$
C. 58 mm
D. $64 \mathrm{mm}$
Narayan H.
Numerade Educator
Trouble 71
Suppose the ligament has a circular cross section. For a certain ligament, an investigator measures the restoring force at a strain of $0.40 .$ If the ligament is replaced with ane that has twice the diameter, by what factor does the restoring force increase?
A. ane.4
B. 2
C. 4
D. 8
Narayan H.
Numerade Educator
Problem 72
The book of the ligament stays the same equally it stretches, and then the cross-department area decreases as the length increases. Given this, how would a strength $F$ versus modify in length $\Delta L$ bend announced?
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Source: https://www.numerade.com/books/chapter/equilibrium-and-elasticity-6/
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