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A thin plate has been bent so as to take the shape of the surface parameterized...
Question A thin plate has been bent so as to take the shape of the area...
Question A thin plate has been bent so as to take the shape of the area pasameleared by R (av) = (2-4 Joos fu? tujt (2-us en (v) & with - 1 4 UK 1 and OSVK 2T Si The density of the plate is proportional to Ho C distance to its left end ; that is, the plane ly= Determine the center of mass of the plate & the m= Sss 3 the da = dudu Follow the steps...
Question 2 A thin plate in the shape of the region in gray in the figure...
Question 2 A thin plate in the shape of the region in gray in the figure below! that is to say a half-desc from wich arecangle has been removed the density of the plate is inversely proportional to the distance from the ongin . Delemine the center of mass coordinates of this plate hist give an exact answer then goire an approximahe Tounded th to the nearest thousarth Figure: 2 4 4 Note: you must the data of the following...
Find the center of mass of the lamina (thin plate) corresponding to the region 0 lessthanorequalto...
Find the center of mass of the lamina (thin plate) corresponding to the region 0 lessthanorequalto y lessthanorequalto 4 - x^2 in the xy plane if the density of the plate is proportional to the distance from the r axis.
Question 1 1 pts Let F= (2,0, y) and let S be the oriented surface parameterized...
Question 1 1 pts Let F= (2,0, y) and let S be the oriented surface parameterized by G(u, v) = (u? – v, u, v2) for 0 <u < 12, -1 <u< 4. Calculate | [F. ds. (enter an integer) Question 2 1 pts Calculate (F.ds for the oriented surface F=(y,z,«), plane 6x – 7y+z=1,0 < x <1,0 Sysi, with an upward pointing normal. (enter an integer) Question 3 1 pts Calc F. ds for the oriented surface F =...
A frictionless wire is bent into the shape of a cycloid curve, with coordinates given by...
A frictionless wire is bent into the shape of a cycloid curve,
with coordinates given by the parametric equations
? = ?(? + sin ?), ? = ?(1 − cos ?), for −? < ? < ?. The x
axis is horizontal, and y is vertically upwards. A bead of
mass m slides freely on the wire. Show that the distance s,
measured along the wire from the origin, is given by
? = 4? sin. Write out the potential...
QUESTION 2 [25 marks] Figure 2 depicts a thin plate where its shape is the region,...
QUESTION 2 [25 marks] Figure 2 depicts a thin plate where its shape is the region, R bounded by the graphs y 3 and yx2. If the density distribution function of a thin plate is given by p(x, y) -1 2y 6x2, show the fastest way to find the centre of mass. Note: show your detailed calculation steps. a) (12 marks) -4 -2 Figure 2 b)x, y)represents a velocity field of a fluid over a surface S defined by z...
7.7 A thin plate is rigidly fixed at its edges (see Figure Ex7.7). The plate has...
7.7 A thin plate is rigidly fixed at its edges (see Figure Ex7.7). The plate has a height L and thickness t (normal to the plane of the figure). A crack moves from left to right through the plate. Every time the crack moves a distance Ax, two things happen: 1. Two new surfaces (with specific surface energy) are created. 2. The stress falls to zero behind the advancing crack front in a certain volume of the material. Obtain an...
Problem 3. Electrostatics An electron is a distance x from the surface of an infinitely large perfect conductor plate. The electron induces a distribution of charge in the conductor plate. Assume...
Problem 3. Electrostatics An electron is a distance x from the surface of an infinitely large perfect conductor plate. The electron induces a distribution of charge in the conductor plate. Assume free space (i.e. vacuum, with permittivity ε.-8.85x 10-12 F/m, or ε。~ ( i/36π)" 10-9 F/m as a useful approximation in some numerical calculations). The electron charge is -q1.6x 10-19 C. (1) Is the electron attracted or repelled by the conductor plate? Find an expression of the attraction or repelling...
QUESTION 1 A uniform bar of total mass m and total length L has been bent into an L-shape such th...
QUESTION 1 A uniform bar of total mass m and total length L has been bent into an L-shape such that the shorter segment is 1/4 of the total length. The free end of the longer segment is connected to a fixed frame with a frictionless revolute joint at A and the rod is initially held stationary with the longer segment horizontal and the shorter segment vertical as shown in the figure below. 3L 4 4 The horizontal distance from...
3. You're so thrilled by your geometric and designing capabilities (see problems 1 and 2) that you decide to design a thin dinner plate that on your blueprint covers the region between the r-...
3. You're so thrilled by your geometric and designing capabilities (see problems 1 and 2) that you decide to design a thin dinner plate that on your blueprint covers the region between the r-axis and the curve To impress the friends, you decide to make two versions of the plate and exhibit them by holding them up on a single finger. In order to do this, you need to calculate the center of mass of each. (a) (5 points) One...
Question A thin plate has been bent so as to take the shape of the area pasameleared by R (av) = (2-4 Joos fu? tujt (2-us en (v) & with - 1 4 UK 1 and OSVK 2T Si The density of the plate is proportional to Ho C distance to its left end ; that is, the plane ly= Determine the center of mass of the plate & the m= Sss 3 the da = dudu Follow the steps...
Question 2 A thin plate in the shape of the region in gray in the figure below! that is to say a half-desc from wich arecangle has been removed the density of the plate is inversely proportional to the distance from the ongin . Delemine the center of mass coordinates of this plate hist give an exact answer then goire an approximahe Tounded th to the nearest thousarth Figure: 2 4 4 Note: you must the data of the following...
Find the center of mass of the lamina (thin plate) corresponding to the region 0 lessthanorequalto y lessthanorequalto 4 - x^2 in the xy plane if the density of the plate is proportional to the distance from the r axis.
Question 1 1 pts Let F= (2,0, y) and let S be the oriented surface parameterized by G(u, v) = (u? – v, u, v2) for 0 <u < 12, -1 <u< 4. Calculate | [F. ds. (enter an integer) Question 2 1 pts Calculate (F.ds for the oriented surface F=(y,z,«), plane 6x – 7y+z=1,0 < x <1,0 Sysi, with an upward pointing normal. (enter an integer) Question 3 1 pts Calc F. ds for the oriented surface F =...
A frictionless wire is bent into the shape of a cycloid curve,
with coordinates given by the parametric equations
? = ?(? + sin ?), ? = ?(1 − cos ?), for −? < ? < ?. The x
axis is horizontal, and y is vertically upwards. A bead of
mass m slides freely on the wire. Show that the distance s,
measured along the wire from the origin, is given by
? = 4? sin. Write out the potential...
QUESTION 2 [25 marks] Figure 2 depicts a thin plate where its shape is the region, R bounded by the graphs y 3 and yx2. If the density distribution function of a thin plate is given by p(x, y) -1 2y 6x2, show the fastest way to find the centre of mass. Note: show your detailed calculation steps. a) (12 marks) -4 -2 Figure 2 b)x, y)represents a velocity field of a fluid over a surface S defined by z...
7.7 A thin plate is rigidly fixed at its edges (see Figure Ex7.7). The plate has a height L and thickness t (normal to the plane of the figure). A crack moves from left to right through the plate. Every time the crack moves a distance Ax, two things happen: 1. Two new surfaces (with specific surface energy) are created. 2. The stress falls to zero behind the advancing crack front in a certain volume of the material. Obtain an...
Problem 3. Electrostatics An electron is a distance x from the surface of an infinitely large perfect conductor plate. The electron induces a distribution of charge in the conductor plate. Assume free space (i.e. vacuum, with permittivity ε.-8.85x 10-12 F/m, or ε。~ ( i/36π)" 10-9 F/m as a useful approximation in some numerical calculations). The electron charge is -q1.6x 10-19 C. (1) Is the electron attracted or repelled by the conductor plate? Find an expression of the attraction or repelling...
QUESTION 1 A uniform bar of total mass m and total length L has been bent into an L-shape such that the shorter segment is 1/4 of the total length. The free end of the longer segment is connected to a fixed frame with a frictionless revolute joint at A and the rod is initially held stationary with the longer segment horizontal and the shorter segment vertical as shown in the figure below. 3L 4 4 The horizontal distance from...
3. You're so thrilled by your geometric and designing capabilities (see problems 1 and 2) that you decide to design a thin dinner plate that on your blueprint covers the region between the r-axis and the curve To impress the friends, you decide to make two versions of the plate and exhibit them by holding them up on a single finger. In order to do this, you need to calculate the center of mass of each. (a) (5 points) One...
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