3. True or False? (a) The location of the center of mass coincides with that of the center of gravity. (b) The centroid of a body always coincides with the body's center of mass. (c) The centroid of a body is always located on the body in question. (d) The formula for the centroid for the surface area of a plate involves integrals over the same surface area
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- 1. Examine the diagram below and then sketch the extended free-body diagram for the plank. Assume that the plank has a uniform mass so that its center of mass is located at its center. SnA 1 555-kg automobile has a wheel base (the distance between the axles) of l = 2.85 m. The automobile's center of mass is on the centerline at a point 1.35 m behind the front axle. Find the force exerted by the ground on each wheel. Part 1 of 3 - Conceptualize Since the center of mass is located in the front half of the car, there should be more force on the front wheels than the rear ones. The sum of the wheel forces must equal the weight of the car. Part 2 of 3 - Categorize Use the figure as a force diagram. Apply Newton's second law and sum the torques to find the unknown forces. l Part 3 of 3 - Analyze The torque about the front axle is zero, so we have Στις = 0 = (d Fg) - l (2F₁). Thus the force at each rear wheel is given by d F F₁ = 2Ff g || d 21 2F, m)(1. X Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step da N. Since the sum of the wheel forces equals the weight of the car, we have 2F₁ + 2F₁ = Fg.…10-
- 2. Consider an isosceles triangle with base length b and height h. What is the vertical position of its center of mass? Your answer should only depend on h (for example, 0.1h). Ytop = h .... Ycm MJ ydm Уст Yam = ? ****** CM Ybottom = 0-+Determine location of the center of mass of steel sheet that is shaped as shown below. Give your answer in the form (xCM; YCM), where xCM and ycm are in cm, to one decimal place. у (ст) 3L 2L IL x (cm) IL 2L 3LOne study suggests that a brain concussion can occur if a person's head is subjected to an acceleration as small as 60g, where g is the acceleration of gravity. For the steps and strategies involved in solving a similar problem, you may view the following Example 9-5 video: Part A If the mass of the person's head is 4.7 kg, what is the magnitude of the force? Express your answer using appropriate units. Templates Symbols undo redo reset keyboard shortcuts help, Value Units Submit Part B Request Answer If the impulse delivered to the person's head is 17 kg. m/s, over what time interval is the force applied? Express your answer using appropriate units. Templates Symbols undo redo reset keyboard shortcuts help Value Units REASONING AND STRATEGY Two ways to think about net impulse L-FM - What we know already Applying a force for some time causes a change in momentum Ap -2.7 kg-m/s; 7,-26.2 kg-m/s A4,-0.30 M, -0.50s m-71 kg
- Three identical coins lie on three corners of a square a = 11.0 cm on a side, as shown in (Figure 1). Determine the x coordinate of the center of gravity of the three coins. Express your answer with the appropriate units. Determine the y coordinate of the center of gravity of the three coins. Express your answer with the appropriate units.3. The Earth has a mass of 5.97 X 10²4 kg, and the Moon has a mass of 7.36 × 102 kg. The Moon orbits the Earth at a distance of 384,000 km; that is, the center of the Moon is a distance of 384,000 km from the center of the Earth, as shown below. How far from the center of the Earth is the center of mass of the Earth-Moon system? Earth -5.97-104 kg 384,000 km -7.36 102 kg MoonYou have a summer internship at NASA and are working on plans for a new space station to be launched into orbit around the Earth. The design of the space station is shown. i It is to be constructed in the shape of a hollow ring of mass 52,000 kg. The structures other than the ring shown in the figure have negligible mass compared to the ring. Members of the crew will walk on a deck formed by the inner surface of the outer cylindrical wall of the ring, with radius r = 140 m. The thickness of the ring is very small compared to the radius, so we can model the ring as a hoop. At rest when constructed, the ring is to be set rotating about its axis so that the people standing inside on this deck experience an effective free-fall acceleration equal to g. The rotation is achieved by firing two small rockets attached tangentially to opposite points on the rim of the ring. Your supervisor asks you to determine the following: (a) the time interval during which the rockets must be fired if each…
- 1.Your car rolls slowly in a parking lot and bangs into the metal base of a light pole. In terms of safety, is it better for your collision with the light pole to be elastic, inelastic, or is the safety risk the same for either case? Explain and labled the problem.50 300g 10 10 25 cm 3) A kinetic sculpture consists of two rods of negligible mass, each suspended 10 cm from their ends. The longer rod has a length of 50 cm and the shorter has a length of 25 cm. If the square mass is 300 g, then what must the triangular mass and circular masses be to achieve equilibrium?A. Three identical coins, labeled A, B, and C in the figure, lie on three corners of a square 10.0 cm on a side. Determine the x coordinate of each coin, xA, xB, and xC B. Determine the y coordinate of each coin described in Part A: yA, yB, and yC. C. Determine the x and y coordinates xcg and ycg of the center of gravity of the three coins described in Part A.