A 40 kg, S.0-m-long beam is supported by, but not attachedto, the two posts in Figure

An object is acted upon by two (and only two) forces that are of equal magnitude and oppositely directed. Is the object necessari ly in static equil ibrium?

Sketch a force acting at point P in Figure Q8.2 that would make the rod be in static equilibrium. Is there only one such force?

Could a ladder on a level floor lean against a wall in static equilibrium if there were no friction forces? Explain.

If you are using a rope to raise a tall mast, attaching the rope to the middle of the mast as in Figure Q8.4a gives a very small torque about the base of the mast when the mast is at a shallow angle. You can get a larger torque by adding a pole with a pulley on top, as in Figure Q8.4b. Draw a diagram showing all of the forces acting on the mast and explain why, for the same tension in the rope, addi ng this pole increases the torque on the mast.

As divers stand on tiptoes on the edge of a divi ng platform, in preparation for a high dive, as shown in Figure Q8.5, they usually extend their arms in front of them. Why do they do this?

Where are the centers of gravity of the two people doing the c lassic yoga poses shown in (b) Figure Q8.6?

You must lean quite far forward as you rise from a chair (try it!). Explain why.

A spring exerts a 10 N force after being stretched by 1 cm from its equilibrium length. By how much will the spring force increase if the spri ng is stretched from 4 cm away from equilibrium to 5 cm from equil ibrium?

The left end of a spring is attached to a wall. When Bob pulls on the right end with a 200 N force, he stretches the spring by 20 cm. The same spring is then used for a tug-of-war between Bob and Carlos. Each pulls on his end of the spring with a 200 N force. a. How far does Bob's end of the spring move? Explain. b. How far does Carlos's end of the spring move? Explain.

A spring is attached to the floor and pulled straight up by a string. The string's tension is measured. The graph in Figure Q8. LO shows the tension in the spring as a fun ction of the spring's length L. a. Does this spring obey Hooke's law? Explain. b. If it does, what is the spring constant?

A typical mattress has a network of springs that provide support. If you sit on a mattress, the spri ngs compress. A heavier person compresses the springs more than a lighter person. Use the properties of springs and spring forces to explain why this is so.

Take a spring and c ut it in half to make two springs. ls the spring constant of these smaller springs larger than, smaller than, or the same as the spri ng constant of the original spring? Explain.

A wi re is stretched right to its breaking point by a 5000 N force. A longer wire made of the same material has the same diameter. ls the force that will stretch it right to its breaking point larger than, smaller than, or equal to 5000 N? Explain.

Steel nai ls are rigid and unbending. Steel wool is soft and squishy. How would you account for this difference?

The rod in Figure Q8. l 5 pivots around an axle at the left end. With forces appl ied as noted, the object A. Will rotate counterclockwise. B. ls in static equilibrium. C. Will rotate clockwise.

Two children hold opposite ends of a lightweight, I .S-m-long horizontal pole with a water bucket hanging from it. The older child suppons twice as much weight as the younger child. How far is the bucket from the older child? A. 0.3 m B. 0.6 m C. 0.9 m D. 1.2 m

The uniform rod in Figure QS. 17 has a weight of 14.0 N. What is the magn itude of the normal force exerted on the rod by the surface? A. 7N B. 14 N C. 20 N D. 2S N

A student I ies on a very light, rigid board with a scale under each end. Her feet are directly over one scale, and her body is positioned as shown in Figure QS. !S. The two scales read the values shown in the figure. What is the student' s weight? A. 65 lb B. 75 lb C. 100 lb D. 165 lb

For the student in Figure QS. IS, approximately how far from her feet is her center of gravity? A. 0.6 m B. O.S m C. 1.0 m D. 1.2 m

How much force must the tendon exert to keep the leg in this position? A. 40N B. 200 N C. 400N D. IOOO N

As you hold your leg in this position, the upper leg exerts a force on the lower leg at the knee joint. What is the d irection of this force? A. Up B. Down C. Right D. Left

What is the magnitude of the force of the upper leg on the BIO lower leg at the knee joint? A. 40N B. 160 N C. 200N D. 240N

You have a heavy piece of equipment hanging from a 1.0-mmdiameter wire. Your supervisor asks that the length of the wire be doubled without changing how far the wire stretches. What diameter must the new wire have? A. 1.0 mm B. 1.4 mm C. 2.0 mm D. 4.0 mm

A 30.0-cm-long board is placed on a table such that its right end hangs over the edge by S.O cm. A second identical board is stacked o n top of the fi rst, as shown in Figure QS.24. What is the largest that the distance x can be before both boards topple over? A. 4.0 cm B. S.O cm C. 14 cm D. 15cm

A 20 kg block resting on the floor is to be raised by a 5.0-mmdiameter rope with Young's modulus 1.5 x I09 N/m2 The rope goes up and over a pulley that is 2.5 m above the floor. You hold the rope at a point 1.5 m above the floor and pull hard enough to lift the block just off the floor. By how much does the rope stretc h? A. 3.0 mm B. 6.3 mm C. 9.3 mm D. 13 mm

A spring has an unstretched length of I 0 cm. It exerts a restoring force F when stretched to a length of 11 cm. a. For what total stretched length of the spring is its restoring force 3F? b. At what compressed length is the restoring force 2F?

One end of a JO-cm-long spring is attached to the ceiling. When a 2.0 kg mass is hung from the other end, the spring stretches to a length of 15 cm. a. What is the spring constant? b. How long is the spring when a 3.0 kg mass is suspended from it?

A spring stretches 5.0 cm when a 0.20 kg block is hung from it. If a 0. 70 kg block replaces the 0.20 kg block, how far does the spring stretch?

A 1.2 kg block is hung from a vertical spring, causing the spring to stretch by 2.4 cm. How much farther will the spring stretch if a 0.60 kg block is added to the 1.2 kg block?

You need to make a spring scale to measure the mass of objects hung from it. You want each 1.0 cm length along the scale to con-espond to a mass difference of 0.10 kg. What should be the value of the spring constant?

A force stretches a wire by 1.0 mm. a. A second wire of the same material has the same cross section and twice the length. How far wi ll it be stretched by the same force? b. A third wire of the same material has the same length and twice the diameter as the fi rst. How far will it be stretched by the same force?

What hanging mass wi ll stretch a 2.0-m-long, 0.50-mmdiameter steel wire by 1.0 mm?

How much force does it take to stretch a I 0-m-long, 1.0-cmdiameter steel cable by 5.0 mm?

An 80-cm-long, 1.0-mm-diameter steel guitar string must be tightened to a tension of 2.0 kN by turning the tuning screws. By how much is the string stretched?

A student is testing a 1.0 m length of 2.5-mm-diameter steel wire. a. How much force is required to stretch this wire by 1.0 mm? b. What length of 5.0-mm-diameter wire would be stretched by 1.0 mm by this force?

A 1. 2-m-long steel rod with a diameter of 0.50 cm hangs vertically from the ceiling. An auto engine weighing 4.7 kN is hung from the rod. By how much does the rod stretch?

A mineshaft has an ore elevator hung from a single braided cable of diameter 2.5 cm. Young's modulus of the cable is 10 x 1010 N/m2 When the cable is fully extended, the end of the cable is 800 m below the support. How much does the fully extended cable stretch when I 000 kg of ore is loaded into the elevator?

The normal force of the ground on the foot can reach three times a runner's body weight when the foot strikes the pavement. By what amount does the S2-cm-long femur of an 80 kg runner compress at this moment? The cross-section area of the bone of the femur can be taken as S.2 X 10-4 m2.

A three-legged wooden bar stool made out of solid Douglas fir has legs that are 2.0 cm in diameter. When a 7S kg man sits on the stool, by what percent does the length of the legs dec,rease? Assume, for simplicity, that the stool's legs are vettical and that each bears the same load.

A 3.0-m-tall, SO-cm-diameter concrete column supports a 200,000 kg load. By how much is the column compressed?

A glass optical fiber in a communications system has a diameter of 9.0 .m. a. What maximum force could this fiber support without breaking? b. Assume that the fiber stretches in a linear fashion until the instant it breaks. By how much will a JO-m-long fiber have stretched when it is at the breaking point?

The Achilles tendon connects the muscles in your calf to the BIO back of your foot. When you are sprinting, your Achilles tendon alternately stretches, as you bring your weight down onto your forward foot, and contracts to push you off the ground. A 70 kg runner has an Achilles tendon that is IS cm long and has a cross-section area of 110 mm2, typical values for a person of this size. a. By how much wi ll the runner's Achilles tendon stretch if the maximum force on it is 8.0 times his weight, a typical value whi le running? b. What fraction of the tendon's length does this correspond to?

A 3.0-m-long rigid beam with a mass of 100 kg is supported at each end, as shown in Figure P8.43. An 80 kg student stands 2.0 m from support I . How much upward force does each support exert on the beam?

An 80 kg construction worker sits down 2.0 m from the end of a I 4SO kg steel beam to eat his lunch, as shown in Figure P8.44. The cable supporting the beam is rated at IS,000 N. Should the worker be worried?

Using the information in Figure 8.2, calculate the tension in the biceps tendon if the hand is holding a I 0 kg ball while the forearm is held 4S0 below horizontal.

A woman weighing S80 N does a pushup from her knees, as shown in Figure P8.46. What are the normal forces of the floor on (a) each of her hands and (b) each of her knees?

When you bend over, a series of large muscles, the erector spinae, pull on your spine to hold you up. Figure P8.47 shows a simplified model of the spine as a rod of length L that pivots at its lower end. In this model, the center of gravity of the 320 N weight of the upper torso is at the center of the spine. The 160 N weight of the head and arms acts at the top of the spine. The erector spinae muscles are modeled as a single muscle that acts at an 12 angle to the spine. Suppose the person in Figure P8.47 bends over to an angle of 30 from the horizontal. a. What is the tension in the erector muscle? Hint: Align your x-axis with the axis of the spine. b. A force 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 force is the cause of many back inj uries).

A man is attempting to raise a 7.S-m-long, 28 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 P8.48. With what force does the man have to pull on the rope to hold the pole motionless in this position?

A 40 kg, S.0-m-long beam is supported by, but not attached to, the two posts in Figure P8.49. A 20 kg boy starts walking along the beam. How close can he get to the right end of the beam without it tipping?

The wheel of mass min Figure PS.SO is pulled on by a horizontal force applied at its center. The wheel is touching a curb whose height is half the wheel's radius. What is the minimum force required to just raise the wheel off the ground?

A S.O kg mass hanging from a spring scale is slowly lowered onto a vertical spring, as shown in Figure P8.S I. The scale reads in newtons. a. What does the spring scale read just before the mass touches the lower spring? b. The scale reads 20 N when the lower spring has been compressed by 2.0 cm. What is the value of the spring constant for the lower spring? c. At what compression distance will the scale read zero?

Two identical, side-by-side spri ngs with spring constant 240 Nim support a 2.00 kg ha nging box. Each spri ng supports the same weight. By how much is each spring stretched?

Two springs have the same equilibrium length but different spring constants. They are arranged as shown in Figure P8.53, then a block is pushed against them, compressing both by 1.00 CJJl. With what net force do they push back on the block?

Figure P8.54 shows two springs attached to a block that can slide on a frictionless smface. In the block's equilibrium position, the left spring is FIGURE PB.54 compressed by 2.0 cm. a. By how much is the right spring compressed? b. What is the net force on the block if it is moved 15 cm to the right of its equil ibrium position?

A 60 kg student is standing atop a spring in an elevator that is accelerating upward at 3.0 m/s2 The spring constant is 2.5 X I03 Nim. By how much is the spring compressed?

A 25 kg chi ld bounces on a pogo stick. The pogo stick has a spring with spring constant 2.0 X !04 N/m. When the child makes a nice big bounce, she finds that at the bottom of the bounce she is accelerating upward at 9.8 m/s2 . How much is the spring compressed?

Figure P8.57 shows a lightweight plank supported at its right end by a 7.0-mm-diameter rope with a tensi le strength of 6.0 x !07 N/m2 a. What is the maximum force that the rope can that the rope can support? b. What is the greatest distance, measured from the pivot, that the center of gravity of an 800 kg piece of heavy machinery can be placed without snapping the rope?

In the hammer throw, an INT athlete spins a heavy mass in a circle at the end of a cable before releasi ng it for distance. For male athletes, the "hammer" is a mass of 7.3 kg at the end of a 1.2 m cable, which is typically a 3.0-mm-diameter steel cable. A world-class thrower can get the hammer up to a speed of 29 m/s. Tf an athlete swings the mass in a horizontal circle centered on the handle he uses to hold the cable a. What is the tension in the cable? b. How much does the cable stretc h?

There is a disk of cartilage between each pair of vertebrae in your spine. Suppose a disk is 0.50 cm thick and 4.0 cm in diameter. If this disk supports half the we ight of a 65 kg person, by what fraction of its thickness does the disk compress?

In Example 8. 1, the tension in the biceps tendon for a person doing a strict curl of a 900 N barbell was found to be 3900 N. What frac tion does this represent of the maximum possible tension the biceps tendon can support? You can assume a typical cross-section area of 130 mm2.

Larger animals have sturdier bones than smaller animals. A mouse's skeleton is only a few percent of its body weight, compared to 16% for an e lephant. To see why this must be so, recall , from Example 8. 10, that the stress on the femur for a man standing on one leg is 1.4% of the bone's tensile strength. Suppose we scale this man up by a factor of 10 in all dimensions, keeping the same body proportions. Use the data for Example 8.10 to compute the fo llowing. a. Both the inside and outside diameter of the femur, the region of cortical bone, wi ll increase by a factor of I 0. What will be the new cross-section area? b. The man's body will increase by a factor of 10 in each dimension. What will be his new mass? c. If the scaled-up man now stands on one leg, what fraction of the tensi le stre ngth is the stress on the femur? 62. II Orb spiders make silk with a typic al diameter of 0.1 5 mm. BIO a. A typical large orb spider has a mass of 0.50 g. If this spider suspends itself from a single 12-cm-long strand of silk, by how much will the silk stretch? b. What is tbe maximum weight that a single thread of this silk could support?

Orb spiders make silk with a typic al diameter of 0.1 5 mm. BIO a. A typical large orb spider has a mass of 0.50 g. If this spider suspends itself from a single 12-cm-long strand of silk, by how much will the silk stretch? b. What is tbe maximum weight that a single thread of this silk could support?

What is the upward force of the floor on the toes of one foot? A. 140N B. 290 N C. 420 N D. 590 N

What upward force does the Achilles tendon exert on the heel of her foot? A. 290 N B. 420 N C. 590 N D. 880 N

The tension in the Achi lles tendon will cause it to stretch. If the Achilles tendon is 15 cm long and has a cross-section area of 110 mm2 , by how much will it stretch under this force? A. 0.2 mm B. 0.8 mm C. 2.3 mm D. 5.2 mm