Many aspects of a gymnast's motion can be modeled by representing the gymnast by four segments consisting of arms, torso (including the head), thighs, and lower legs, as in the figure below. Thigh O Arm Leg 60° 60° Torso In the figure, (b) shows arrows of lengths r locating the center of gravity of each segment. Use the data below and the coordinate system shown in figure (b) to locate the center of gravity of the gymnast shown in figure (a). Masses for the arms, thighs, and legs include both appendages. (Enter your answers in m, to at least three significant figures.) Segment Mass (kg) Length (m) rcg (m) Arms 6.81 0.548 0.236 Torso 33.6 0.613 0.337 Thighs 14.1 0.368 0.149 Legs 7.50 0.350 0.227 HINT Xca = Yeg = m

Even when the head is held erect, as shown in the figure, its center of mass is not directly over the principal point of support (the atlanto-occipital joint, Point A). The muscles at the back of the neck should, therefore, exert a force to keep the head erect. That is why your head falls forward when you fall asleep in the class. If the head weighs 43 N, calculate the force exerted by the muscles FM using the information in the figure. Assume that x1 = 5.1 cm, x2 = 2.7 cm, and |Fw = 43 N. N What is the force Fj exerted by the pivot on the head? F; = N Question Credit: OpenStax College Physics

D3

The diagram shows a 7.0 meter log leaning on a rock. The wieght of the log is 780 Newton's. A 200 Newton boy walks up the log from the point where is touches the ground. He finds that he can only walk 5.0 meters up the log before it starts to tip over the rock WHrer is the center of gravity of the log located?

In the figure below, both the ceiling and the ruler accelerate together at 1.6 m/s2 in the +y direction, and the reading to the "new" length of the vertical wire is as indicated. Ignore the effect on the two diagonal wires. Other parameters are below: Weight of the pan = 5 N Weights (or loads) = 74 N Originally, the wire has a length 0.200 cm, and diameter of 2.7 cm. Calculate the Young's modulus of the wire in Pa. NOTES: Use pi = 3.14. Final answer in ZERO decimal place. 4.000 4.100 4.200 4.300 cm

The boom in the figure below (Figure 1) weighs 2600 N and is attached to a frictionless pivot at its lower end. It is not uniform; the distance of its center of gravity from the pivot is 37% of its length. A) Make a free-body diagram of the boom. The boom attaches to the building at dot A. The center of gravity of the boom is indicated by dot B. The guy wire attaches to the boom and holds the load at dot C. Draw the vectors starting at the black dots. The location and orientation of the vectors will be graded. The length of the vectors will not be graded. Positive torque is considered to be in the counterclockwise direction.   B) Find the tension in the guy wire. Express your answer in newtons.   C) Find the horizontal component of the force exerted on the boom at its lower end. Express your answer in newtons.   D) Find the vertical component of the force exerted on the boom at its lower end. Express your answer in newtons.

A large airplane typically has three sets of wheels: one at the front and two farther back, one on each side under the wings. Consider the Boeing 787 "Dreamliner", with a mass of 198000 kg. In this particular model, the distance from the front wheels to the rear set of wheels is 23.8 m. a) If the center of mass of the airplane is along a line through the center and 3.00 m in front of the rear wheels, how much force, in meganewtons, does the ground exert on each set of rear wheels when the plane is at rest on the runway?  b) How much force, in meganewtons, does the ground exert on the front set of wheels?

The two ends of the dumbbell shown below are made of the same material. Is the dumbbell’s center of gravity at point 1, 2, or 3? Explain.

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).

Suppose a horse leans against a wall as shown in the figure. The total of the horse and rider is 500 kg. Part a : calculate the magnitude of the force in newtons on each foot of the horse in the figure assuming the center of the mass of the horse between and the weight is equally divided between the two feet on the ground. Part b: what is the minimum coefficient of friction between the hooves and ground? Note that the force exerted by the wall is horizontal.