A person is standing on a level floor. His head, upper torso, arms, and hands together weigh 435 N and have a center of gravity that is 1.33 m above the floor. His upper legs weigh 134 N and have a center of gravity that is 0.714 m above the floor. Finally, his lower legs and feet together weigh 83.1 N and have a center of gravity that is 0.201 m above the floor. Relative to the floor, find the location of the center of gravity for the entire body. Number i Units

You have been hired to design a family-friendly see-saw. Your design will feature a uniform board (mass M = 11 kg, length L = 11 m) that can be moved so that the pivot is a distance d from the center of the board. This will allow riders to achieve static equilibrium even if they are of different mass, as most people are. You have decided that each rider will be positioned so that his/her center of mass will be a distance xoffset = 29 cm from the end of the board when seated as shown.You have selected a child of mass m = 23 kg (shown on the right), and an adult of mass n =3 times the mass of the child (shown on the left) to test out your prototype. 1) Determine the distance d in m. d = 2) Determine the magnitude of the force exerted on the pivot point by the see-saw in N. Fb =

A man holds a 186-N ball in his hand, with the forearm horizontal (see the figure). He can support the ball in this position because of the flexor muscle force M, which is applied perpendicular to the forearm. The forearm weighs 21.6 N and has a center of gravity as indicated. Find (a) the magnitude of M and the (b) magnitude and (c) direction (as a positive angle counterclockwise from horizontal) of the force applied by the upper arm bone to the forearm at the elbow joint. (a) Number (b) Number i (c) Number i Upper arm bone- Elbow joint 0.0510 m+ Units Units Units Flexor muscle M -0.0890 m -0.330 m-

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).

A meter stick is hanging from the ceiling at the 50 cm marker, perfectly in balance.. A 10 kg mass is tied to the meter stick at the 70 cm marker. A 10 kg mass is tied to the meter stick at the 80 cm marker. Where should a 20 kg mass be placed to maintain equilibrium? 25 cm 10 cm 20 cm 35 cm

A uniform barbell has length 1.5 m and mass 60 kg. Your left hand is placed 25 cm to the left of the center, while your right hand is placed 35 cm to the right of the center. What is the magnitude of force exerted by your left hand? 420 N 823 N 343 N 294 N 245 N

Bart ( whose mass is 31.1 kg) and Milhouse (whose mass is 20.4 kg) sit balanced on a teeter -totter that has its pivot point at its exact center . If the two boys are separated by a distance of 2.52 m, at what distance (in m) from the pivot point must Milhouse be sitting at in order to maintain the balance? Explain how you solved the problem involving children balancing on a teeter-totter. Be sure to state what your known and unknown quantities are, what concepts were applied, and what equations were used!

The experiment you did in lab is repeated, using a uniform metal bar that is 80.0 cm long instead of the meterstick. Since the bar is uniform, its center of gravity is at its center. The new experiment uses different hooks for hanging the masses from the bar, with mhook 5.0 g. As in the experiment you did in lab, X1 = 5.00 cm, m1 300.0 g, and Xp = 25.0 cm. In the 1 new experiment, you make the same measurements as in your lab and plot x versus The line that is the best fit to your data has slope 3800 cm · g. What is the mass of m2 + mhook the bar?

A diver dives from a cliff when her center of gravity is 46 feet above the surface of the water. Her initial vertical velocity leaving the cliff is 9 feet per second. After how many seconds does her center of gravity enter the water?

In the figure, a lead brick rests horizontally on cylinders A and B. The areas of the top faces of the cylinders are related by Aa= 2.4 Ag: the Young's moduli of the cylinders are related by EA 1.6 Ea. The cylinders had identical lengths before the brick was placed on them. What fraction of the brick's mass is supported (a) by cylinder A and (b) by cylinder B? The horizontal distances between the center of mass of the brick and the centerlines of the cylinders are d,for cylinder A and dg for cylinder B. (c) What is the ratio d,/dg? com of brick