This is the next homogeneous figure where each square measures 10 cm by 10 cm. Find the horizontal position of the center of mass in relation to the coordinate system. Give the answer in cm. y
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- What statements are true about the center of mass? Write the letters of all that apply in the box below. Use all capital letters, with no punctuation. For example, if A and B are correct, write "AB". If only A is correct, write "A". с A) The center of mass is always located inside the human body. B) The center of mass is the mean position of the mass of the human body. C) The center of mass can lie outside the body. D) The location of the center of mass is unchanged during body movements. ! No, that's not the correct answer.A child in a boat throws a 5.50-kg package out horizontally with a speed of 10.0 m/s. The mass of the child is 26.6 kg and the mass of the boat is 36.4 kg. Calculate the velocity of the boat immediately after, assuming it was initially at rest.Express your answer to three significant figures and include the appropriate units. Enter positive value if the direction of the velocity is in the direction of the velocity of the box and negative value if the direction of the velocity is in the direction opposite to the velocity of the box.A rod of length 3 meters with density 8(x) = 1.1 + 1.1x4grams/meter is positioned along the positive x-axis, with its left end at the origin. Find the total mass and the center of mass of the rod. Round your answers to four decimal places. The total mass of the rod is i The center of mass of the rod is i grams. meters.
- a. Assuming the given coordinate system below and the location and mass of the following four objects, calculate the center of mass of the system (answer in both Cartesian, and polar coordinates). b. If Mass D is moving at a constant velocity of 13.0m/s towards -y, with all other masses remaining stationary, what is the velocity of the center of mass of the system?Three particles are located as in the figure below. Find the center of mass of the system. Express you answer as a position vector in component form with the origin located at the 100g mass. Assume the positive x-axis is to the right and the positive y-axis is up. __cm i+ __ cm jYou are handed a bat that is 6 times as dense on one side as it is on the other side, and 3 times as dense in the middle as it is on the least dense side. Density varies quadratically. The mass of the bat is M and the length is L. Write your answers only in terms of these constants. Calculate center of mass using integral
- Question 2: A thin rod of length l has a non-uniform mass distribution as shown in Figure 2. The linear mass density d is given by A = Aæ² where A is a positive constant. a) Find the total mass of the rod. b) Find xem (the x coordinate of the center of mass of the rod) in terms of l. Figure 2A semicircular plate of radius R has the following surface mass density o = 0or where oo is a positive constant and r is the radial distance as shown in the Figure. Find the y coordinate of the position vector of the center of mass of the plate in terms of R. r.a) A metal sign has a shape of a right triangle whose dimensions are shown in figure. Determine the y coordinate of the centre of mass, assuming that the triangular sign has a uniform density and total mass M. b. b) Two friends of masses 40 kg and 60 kg are standing at the two extremes of a 6 m long boat of mass 100 kg. Sistem is at rest. Neglect the friction between water and boat. Find the displacement of the boat when both men move and interchange their positions. 40 kg 60 kg B 100 kg 6m
- Use vectors to solve the following problems. Both cars weigh 1500 kg. Use the scale 1 cm = 1,000 kg x m/s. Assume all collisions to be elastic and sticking. Draw a picture represents the problem too. The first car is travelling at 20 m/s east. The second car is travelling at 30m/s north. Using vectors draw to scale the component vectors and the resultant from their collision. Then solve using your trigonometric functions. Also: use Pythagorean TheoremВ. Solve the following problems below. You are required to show complete solution. Put your final answer inside a box with the final unit of measurement. 1. Four squares, with equal side length 1 m, are arranged based on a rectangular coordinate as shown in the figure. The masses of A, B, C, and D are 1 kg, 2kg, 3 kg and 4kg respectively. Find the center of mass of the system of four squares with respect to thex and y axis. DIA uniform piece of sheet metal is shaped as shown in the figure below. Compute the x and y coordinates of the center of mass of the plece. cm cm