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
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- A solid uniform 45-kg ball of diameter 32.0 cm is supported against a vertical, frictionless wall with a string of length 30.0 cm as shown below. Find the tension in the string.You can find the center of gravity of a long ruler by resting it horizontally on your two index fingers, and then slowly drawing your fingers together. First the ruler will slip on one finger, and then on the other, but eventually the fingers meet at the CG. Why does this workTwo children of mass 25 kg and 26 kg sit balanced on a seesaw with the pivot point located at the center of the seesaw. If the children are separated by a distance of 3.0 m, at what distance, in meters, from the pivot point is the smaller child sitting in order to maintain the balance?
- 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 cmA 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 NBart ( 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!
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