Physics for Scientists and Engineers with Modern Physics
10th Edition
ISBN: 9781337553292
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 12, Problem 3P
To determine
The center of gravity of the carpenters square.
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When you bend over, a series of large muscles, the erector spinae, pull on your spine to hold you up. The following figure 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 270 N270 N weight of the upper torso is at the center of the spine. The 140 N140 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 a 1212-degree angle to the spine. Suppose the person in the figure bends over to an angle of 3030 degrees from horizontal.
The center of gravity is half the length, and the center of gravity for the upper torso is 2/32/3 of the length
A. What is the tension in the erector muscle?
B. A force from the pelvic girdle acts on the base of the spine. What is the component of this force in the direction parallel to the spine? This large force is the cause of many back injuries.
The aluminum cylinder is attached to the steel hemisphere. Find the height h of the cylinder for which the center
of gravity of the assembly is at G. Use y=0.283 lb/in³ for steel and y=0.096 Ib/in³ for aluminum. Answers: 3.39 in.
9 in.
Aluminum
Steel -
Fig. P8.94
Chapter 12 Solutions
Physics for Scientists and Engineers with Modern Physics
Ch. 12.1 - Consider the object subject to the two forces of...Ch. 12.1 - Consider the object subject to the three forces in...Ch. 12.2 - A meterstick of uniform density is hung from a...Ch. 12.4 - For the three parts of this Quick Quiz, choose...Ch. 12 - You are building additional storage space in your...Ch. 12 - Why is the following situation impossible? A...Ch. 12 - Prob. 3PCh. 12 - A circular pizza of radius R has a circular piece...Ch. 12 - Your brother is opening a skateboard shop. He has...Ch. 12 - A uniform beam of length 7.60 m and weight 4.50 ...
Ch. 12 - Prob. 7PCh. 12 - A uniform beam of length L and mass m shown in...Ch. 12 - A flexible chain weighing 40.0 N hangs between two...Ch. 12 - A 20.0-kg floodlight in a park is supported at the...Ch. 12 - Prob. 11PCh. 12 - Review. While Lost-a-Lot ponders his next move in...Ch. 12 - Figure P12.13 shows a claw hammer being used to...Ch. 12 - A 10.0-kg monkey climbs a uniform ladder with...Ch. 12 - John is pushing his daughter Rachel in a...Ch. 12 - Prob. 16PCh. 12 - The deepest point in the ocean is in the Mariana...Ch. 12 - A steel wire of diameter 1 mm can support a...Ch. 12 - A child slides across a floor in a pair of...Ch. 12 - Evaluate Youngs modulus for the material whose...Ch. 12 - Prob. 21PCh. 12 - When water freezes, it expands by about 9.00%....Ch. 12 - Review. A 30.0-kg hammer, moving with speed 20.0...Ch. 12 - A uniform beam resting on two pivots has a length...Ch. 12 - A bridge of length 50.0 m and mass 8.00 104 kg is...Ch. 12 - Prob. 26APCh. 12 - The lintel of prestressed reinforced concrete in...Ch. 12 - Prob. 28APCh. 12 - A hungry bear weighing 700 N walks out on a beam...Ch. 12 - Prob. 30APCh. 12 - A uniform sign of weight Fg and width 2L hangs...Ch. 12 - When a person stands on tiptoe on one foot (a...Ch. 12 - A 10 000-N shark is supported by a rope attached...Ch. 12 - Assume a person bends forward to lift a load with...Ch. 12 - A uniform beam of mass m is inclined at an angle ...Ch. 12 - Prob. 36APCh. 12 - When a circus performer performing on the rings...Ch. 12 - Figure P12.38 shows a light truss formed from...Ch. 12 - Prob. 39APCh. 12 - A stepladder of negligible weight is constructed...Ch. 12 - A stepladder of negligible weight is constructed...Ch. 12 - Review. A wire of length L, Youngs modulus Y, and...Ch. 12 - Two racquetballs, each having a mass of 170 g, are...Ch. 12 - Prob. 44APCh. 12 - Review. An aluminum wire is 0.850 m long and has a...Ch. 12 - You have been hired as an expert witness in a case...Ch. 12 - A 500-N uniform rectangular sign 4.00 m wide and...Ch. 12 - A steel cable 3.00 cm2 in cross-sectional area has...Ch. 12 - A uniform rod of weight Fg and length L is...Ch. 12 - In the What If? section of Example 12.2, let d...
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- A uniform beam of length 7.60 m and weight 4.50 102 N is carried by two workers, Sam and Joe, as shown in Figure P12.6. Determine the force that each person exerts on the beam. Figure P12.6arrow_forwardRuby, with mass 55.0 kg, is trying to reach a box on a high shelf by standing on her tiptoes. In this position, half her weight is supported by the normal force exerted by the floor on the toes of each foot as shown in Figure P14.75A. This situation can be modeled mechanically by representing the force on Rubys Achilles tendon with FA and the force on her tibia as FT as shown in Figure P14.75B. What is the value of the angle and the magnitudes of the forces FA and FT? FIGURE P14.75arrow_forwardWhy is the following situation impossible? A uniform beam of mass mk = 3.00 kg and length = 1.00 m supports blocks with masses m1 = 5.00 kg and m2 = 15.0 kg at two positions as shown in Figure P12.2. The beam rests on two triangular blocks, with point P a distance d = 0.300 m to the right of the center of gravity of the beam. The position of the object of mass m2 is adjusted along the length of the beam until the normal force on the beam at O is zero. Figure P12.2arrow_forward
- A stepladder of negligible weight is constructed as shown in Figure P12.40, with AC = BC = . A painter of mass m stands on the ladder a distance d from the bottom. Assuming the floor is frictionless, find (a) the tension in the horizontal bar DE connecting the two halves of the ladder, (b) the normal forces at A and B, and (c) the components of the reaction force at the single hinge C that the left half of the ladder exerts on the right half. Suggestion: Treat the ladder as a single object, but also treat each half of the ladder separately. Figure P12.40 Problems 40 and 41.arrow_forwardThree forces are exerted on the disk shown in Figure P12.71,and their magnitudes are F3 = 2F2 = 2F1. The disks outer rimhas radius R, and the inner rim has radius R/2. As shown in thefigure, F1 and F3 are tangent to the outer rim of the disk, and F2 is tangent to the inner rim. F3 is parallel to the x axis, F2 is parallel to the y axis, and F1 makes a 45 angle with the negative x axis. Find expressions for the magnitude of each torque exertedaround the center of the disk in terms of R and F1. FIGURE P12.71 Problems 71-75arrow_forwardA 20.0-kg floodlight in a park is supported at the end of a horizontal beam of negligible mass that is hinged to a pole as shown in Figure P12.10. A cable at an angle of = 30.0 with the beam helps support the light. (a) Draw a force diagram for the beam. By computing torques about an axis at the hinge at the left-hand end of the beam, find (b) the tension in the cable, (c) the horizontal component of the force exerted by the pole on the beam, and (d) the vertical component of this force. Now solve the same problem from the force diagram from part (a) by computing torques around the junction between the cable and the beam at the right-hand end of the beam. Find (e) the vertical component of the force exerted by the pole on the beam, (f) the tension in the cable, and (g) the horizontal component of the force exerted by the pole on the beam. (h) Compare the solution to parts (b) through (d) with the solution to parts (c) through (g). Is either solution more accurate? Figure P12.10arrow_forward
- When a circus performer performing on the rings executes the iron cross, he maintains the position at rest shown in Figure P12.37a. In this maneuver, the gymnasts feet (not shown) are off the floor. The primary muscles involved in supporting this position are the latissimus dorsi (lats) and the pectoralis major (pecs). One of the rings exerts an upward force Fk on a hand as show n in Figure P12.37b. The force Fs, is exerted by the shoulder joint on the arm. The latissimus dorsi and pectoralis major muscles exert a total force Fm on the arm. (a) Using the information in the figure, find the magnitude of the force Fm for an athlete of weight 750 N. (b) Suppose a performer in training cannot perform the iron cross but can hold a position similar to the figure in which the arms make a 45 angle with the horizontal rather than being horizontal. Why is this position easier for the performer? Figure P12.37arrow_forwardA solid cylinder sits on top of a solid cube as shown in the figure. How far above the table's surface is the center of gravity of the combined object? 5.0 cm 400 g 5.0 cm 800 garrow_forwardA hippo’s body is 4.0 m long with front and rear feet located as shown. The hippo carries 60% of its weight on its front feet. How far from its tail is the hippo’s center of gravity?arrow_forward
- When you bend over, a series of large muscles, the erector spinae, pull on your spine to hold you up. Figure 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 shown 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 injuries).arrow_forwardIf the new center of gravity of a 14 m uniform steel rod with a mass m = 75 kg is situated to the left of its geometric center after a 50 kg object is attached to it, determine the point where the object is attached. 4.5 m O 8.5 m 9.5 m 7.0 marrow_forwardDo Chapter 12, Problem 6, with these numbers which I've decided to express in pounds and feet, English units. Sam and Joe carry a beam, walking to the right. Calculate the force that Sam exerts, in pounds. • The beam's weight is 92 lb. • The beam's length is 23 ft. • Sam is 5 ft from the back. • Joe is 4 ft from the front.arrow_forward
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