A 16 inch thin-crust cheese pizza is cut equally into eight slices. Assuming a uniform distribution of sauce and toppings, determine the position vector r_cm of the center of mass for the slice highlighted. Use ijk vector notation, and enter a numerical value with two significant figures for each component.
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- A 3 kg plank is 0.6 m in length and has its center of mass at the geometrical center. Masses of 1 kg an 3 kg are attached at opposite ends of the plank. Find the center of mass of the whole system. 1 kg 3 kg Where is the COM? 3 kgA cubical box, open at the top, with edge length 36 cm, is constructed from metal plate of uniform density and negligible thickness (see the figure). Find the z-coordinate of the center of mass of the box ( cm).Problem 23: Three beads are placed on the vertices of an equilateral triangle of side d = 4.1 cm. The first bead of mass m1 = 135 g is placed on the top vertex. The second bead of mass m2= 55 g is placed on the left vertex. The third bead of mass m3 = 85 g is placed on the right vertex. Part (a) Write a symbolic equation for the horizontal component of the center of mass relative to the left vertex of the triangle. Part (c) Write a symbolic equation for the vertical component of the center of mass relative to the base of the triangle.
- Find the position of the center of mass of a thin rod that extends from 0 to 0.890 m along the x axis of a Cartesian coordinate system and has a linear density given by µ(x) = 0.3 kg/m? x2A 1200 kg car driving due north at 15 m/s collides with a 2300 kg truck traveling east at aspeed of 10 m/s. After the collision, they lock bumpers traveling together. What is the final velocityvector of the combined car/truck after the collision? Give in unit vector notation and compute amagnitude and direction.A uniform density sheet of metal is cut into the shape of an isosceles triangle, which is oriented with the base at the bottom and a corner at the top. It has a base B = 43 cm, height H = 25 cm, and area mass density σ. - The horizontal center of mass of the sheet will be located: On the center line. Not enough information to determine. To the left of the center line. To the right of the center line. - The vertical center of mass of the sheet will be located: Below the mid height. Not enough information to determine. Above the mid height. At the mid height. - Write a symbolic equation for the total mass of the triangle. -Consider a horizontal slice of the triangle that is a distance y from the top of the triangle and has a thickness dy. Write an equation for the area of this slice in terms of the distance y, and the base B and height H of the triangle. - Set up an integral to calculate the vertical center of…
- a shape is on an x-y axis, beginning at x = 0. The bottom of the shape is 25 cm long and it reaches a height of 20 cm. The shape weights 450 g. The shape has a triangular form, like a wedge. If shape has a uniform density and a uniform width in the z-direction, find the x-component of the center-of-mass.A rod of length 23.00 cm has linear density (mass per length) given by 1 = 50.0 + 17.5x where x is the distance from one end, and 2 is measured in grams/meter. (a) What is its mass? (b) How far from the x = 0 end is its center of mass? mThe three masses shown in (Figure 1) are connected by massless, rigid rods. Assume that m₁ = 180 g and m2 = 300 g. Figure A y 200 g 12 cm B m₂ 10 cm C m₁ -X 1 of 1 Part A What is the x-coordinate of the center of mass? Express your answer with the appropriate units. ► View Available Hint(s) x = Submit Part B Value y = μA What is the y-coordinate of the center of mass? Express your answer with the appropriate units. ► View Available Hint(s) Submit Value Provide Feedback μA Units ? Units ?
- A man with mass m1 = 51 kg stands at the left end of a uniform boat with mass m2 = 168 kg and a length L = 3.3 m. Let the origin of our coordinate system be the man’s original location as shown in the drawing. Assume there is no friction or drag between the boat and water. 1) If the man now walks to the right edge of the boat, what is the location of the center of mass of the system? 2) After walking to the right edge of the boat, how far has the man moved from his original location? (What is his new location?) 3) After the man walks to the right edge of the boat, what is the new location the center of the boat? 4) Now the man walks to the very center of the boat. At what location does the man end up?Objects with a uniform mass distribution and a symmetric shape have a center of mass at the center of the object. For non-uniform objects, the center of mass needs to be determined experimentally. To measure the center of mass of such an object, a pivot is placed in the middle of a board and the top of the non-uniform object is placed to the right of the pivot. When a uniform 10.0 kg mass has its center placed 60.0 cm to the left of the pivot the system balances perfectly (as shown below). The mass of the non-uniform object is measured with an electronic scale in the lab and found to beM = 39.8 kg . Top of non-uniform object 10.0 kg M 60.0 cm Part A Where is the center of mass of the non-uniform object? (report the location from the top of the object, and in cm) ΑΣΦ ? dCM = стMacmillan Learning A thin stick is placed along the x-axis so that one of its ends is at x₁ = 0.00 m and the other one at x₂ = 4.15 m. The stick has a non-uniform mass density λ(x) = ax + b, where a = 0.089 kg/m² and b = 1.077 kg/m. What is the x-coordinate of the center of mass of the stick? Xcm = m