please help with all parts ) Problem 3: A rectangular plate of length B=15cm and height A=38cm has a rectangular corner
cut out of it of length D=10cm and height C=7cm. The plate is made of a material of uniform mass
density sigma . For this problem we set the origin at the lower left corner of the plate with the x-axis horizontal
and the y-axis vertical.
6% Part (a) The vertical center of mass of the plate will be located:
A,B,CDA,B,CD6%A,B,C,Dsigma 6%A,B,CD6%A,B,CD/_(/)6%A,B,C,Dsigma 6%A imes Bsigma C imes D-sigma A imes B6%A imes B6%A imes BA,B,C,Dsigma 6%C imes DA,B,CD6%C imes DA,B,CD6%C imes DA,B,C,Dsigma 6%cm6%xcmx_(cm) Correct!
6% Part (c) Write an equation for the total mass of the plate.
6% Part (d) Treat the plate as two small rectangles cut at the dotted line in the figure. What is the x-coordinate of the location of the center of mass of the upper
rectangle in terms of A,B,C, and D ?
6% Part (e) Treat the plate as two small rectangles cut at the dotted line in the figure. What is the y-coordinate of the location of the center of mass of the upper
rectangle in terms of A,B,C, and D ?
A 6% Part (f) What is the mass of the upper rectangle in terms of A,B,C,D, and sigma ?
A 6% Part (g) What is the x-coordinate of the center of mass of the lower rectangle in terms of A,B,C, and D ?
A 6% Part (h) What is the y-coordinate of the center of mass of the lower rectangle in terms of A,B,C, and D ?()/(_(/))
6% Part (i) What is the mass of this lower rectangle in terms of A,B,C,D, and sigma ?
A 6% Part (j) Alternatively, we can treat the plate as the full rectangle A imes B of density sigma , superimposed with the smaller rectangle C imes D of density -sigma . What is
the location of the y-coordinate of the center of mass of the full rectangle A imes B ?
6% Part (k) What is the location of the x-coordinate of the center of mass of the full rectangle A imes B ?
6% Part (l) What is the mass of the plate A imes B in term of A,B,C,D, and sigma .
6% Part (m) What is the location of the y-coordinate of the center of mass of the rectangle C imes D in terms of A,B,C, and D ?
A 6% Part (n) What is the location of the x-coordinate of the center of mass of the rectangle C imes D in terms of A,B,C, and D ?
A 6% Part (o) What is the effective mass of the rectangle C imes D in terms of A,B,C,D, and sigma ? Recall what we said about the density of this rectangle.
4 6% Part (p) Use either method to find the numeric value of the y-coordinate for the center of mass of the plate in cm.
A 6% Part (q) Use either method to find the numeric value of the x-coordinate for the center of mass of the plate in cm.Y_(cm) Correct!
6% Part (b) The horizontal center of mass of the plate will be located:
x_(cm) Correct!
6% Part (c) Write an equation for the total mass of the plate.
6% Part (d) Treat the plate as two small rectangles cut at the dotted line in the figure. What is the x-coordinate of the location of the center of mass of the upper
rectangle in terms of A,B,C, and D ?
6% Part (e) Treat the plate as two small rectangles cut at the dotted line in the figure. What is the y-coordinate of the location of the center of mass of the upper
rectangle in terms of A,B,C, and D ?
A 6% Part (f) What is the mass of the upper rectangle in terms of A,B,C,D, and sigma ?
A 6% Part (g) What is the x-coordinate of the center of mass of the lower rectangle in terms of A,B,C, and D ?
A 6% Part (h) What is the y-coordinate of the center of mass of the lower rectangle in terms of A,B,C, and D ?()/(_(/))
6% Part (i) What is the mass of this lower rectangle in terms of A,B,C,D, and sigma ?
A 6% Part (j) Alternatively, we can treat the plate as the full rectangle A imes B of density sigma , superimposed with the smaller rectangle C imes D of density -sigma . What is
the location of the y-coordinate of the center of mass of the full rectangle A imes B ?
6% Part (k) What is the location of the x-coordinate of the center of mass of the full rectangle A imes B ?
6% Part (l) What is the mass of the plate A imes B in term of A,B,C,D, and sigma .
6% Part (m) What is the location of the y-coordinate of the center of mass of the rectangle C imes D in terms of A,B,C, and D ?
A 6% Part (n) What is the location of the x-coordinate of the center of mass of the rectangle C imes D in terms of A,B,C, and D ?
A 6% Part (o) What is the effective mass of the rectangle C imes D in terms of A,B,C,D, and sigma ? Recall what we said about the density of this rectangle.
4 6% Part (p) Use either method to find the numeric value of the y-coordinate for the center of mass of the plate in cm.
A 6% Part (q) Use either method to find the numeric value of the x-coordinate for the center of mass of the plate in cm.
6%) Problem 3:A rectangular plate of length B=15 cm and height A =38 cm has a rectangular corner cut out of it of length D = 10 cm and height C = 7 cm. The plate is made of a material of uniform mass density . For this problem we set the origin at the lower left corner of the plate with the x-axis horizontal and the y-axis vertical.
c
D
A
B
6% PartaThe vertical center of mass of the plate will be located: Yem < A/2 V Correct!
6% Part (b)The horizontal center of mass of the plate will be located: Xcm B/2V Correct!
6% Part c Write an equation for the total mass of the plate. 6% Part (d) Treat the plate as two small rectangles cut at the dotted line in the figure. What is the x-coordinate of the location of the center of mass of the upper rectangle in terms of A, B, C, and D? 6% Part (e) Treat the plate as two small rectangles cut at the dotted line in the figure. What is the y-coordinate of the location of the center of mass of the upper rectangle in terms of A, B, C, and D? 6% Part (fWhat is the mass of the upper rectangle in terms of A, B, C, D, and ? 6% Part (g) What is the x-coordinate of the center of mass of the lower rectangle in terms of A, B, C, and D? 6% Part (h) What is the y-coordinate of the center of mass of the lower rectangle in terms of A, B, C, and D? 6% Part (i) What is the mass of this lower rectangle in terms of A, B, C, D, and ? 6% Part (j) Alternatively, we can treat the plate as the full rectangle A x B of density , superimposed with the smaller rectangle C x D of density -. What is the location of the y-coordinate of the center of mass of the full rectangle A x B? 6% Part (k) What is the location of the x-coordinate of the center of mass of the full rectangle A x B? 6% Part (I)What is the mass of the plate A x B in term of A, B, C, D, and . 6% Part (m) What is the location of the y-coordinate of the center of mass of the rectangle C x D in terms of A, B, C, and D? 6% Part (n) What is the location of the x-coordinate of the center of mass of the rectangle C x D in terms of A, B, C, and D? 6% Parto What is the effective mass of the rectangle C x D in terms of AB.C,D.and ? Recall what we said about the density of this rectangle 6% Part (p) Use either method to find the numeric value of the y-coordinate for the center of mass of the plate in cm. 6% Part (q Use either method to find the numeric value of the x-coordinate for the center of mass of the plate in cm. Grade Summary