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 = 49 cm, height H = 23 cm, and area mass density σ. Part (a) The horizontal center of mass of the sheet will be located: Not enough information to determine. To the left of the center line. To the right of the center line. On the center line. Part (b) The vertical center of mass of the sheet will be located: Part (c) Write a symbolic equation for the total mass of the triangle. Part (d) 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. Part (e) Set up an integral to calculate the vertical center of mass of the triangle, assuming it will have the form C ∫ f(y) where C has all the constants in it and f(y) is a function of y. What is f(y)? Part (f) Integrate to find an equation for the location of the center of mass in the vertical direction. Use the coordinate system specified in the previous parts, with the origin at the top and positive downward. Part (g) Find the numeric value for the distance between the top of the triangle and the center of mass in cm.
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 = 49 cm, height H = 23 cm, and area mass density σ.
Part (a) The horizontal center of mass of the sheet will be located:
| Not enough information to determine. | To the left of the center line. |
| To the right of the center line. | On the center line. |
Part (b) The vertical center of mass of the sheet will be located:
Part (c) Write a symbolic equation for the total mass of the triangle.
Part (d) 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.
Part (e) Set up an integral to calculate the vertical center of mass of the triangle, assuming it will have the form C ∫ f(y) where C has all the constants in it and f(y) is a function of y. What is f(y)?
Part (f) Integrate to find an equation for the location of the center of mass in the vertical direction. Use the coordinate system specified in the previous parts, with the origin at the top and positive downward.
Part (g) Find the numeric value for the distance between the top of the triangle and the center of mass in cm.
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