Question

Phys 201 Name: Hwk 8 A shape in the graph is bounded by the functions shown and has a mass of 10.0 kg. Assume all distances are in meters. 5. a. Solve for the Area of the shape by integrating dA. (ans: 50m2 b. Solve for the Moment of Inertia of the shape around the point (0,0). (Ans: 611 kg m2) (5m, 4.5m). Ans: lem 159 kg m2 c. Use the Parallel Axis theorm to find the Moment of Interia around the center of mass 10 6 105 10-15 20 25 use Parrall axis theor e

Answer 1

y = 0 0 lessthanorequalto x < infinity y = 10.e^- x/5 0 lessthanorequalto x, infinity} area of strip da = y dx therefore da = 10 e^- x/5 dx hence area a = integral^infinity_0 da = integral^infinity_0 10 e^- x/5 dx = 10 [e^- x/5/(- 1/5]^infinity_0 = 10 (- 5) [e^- x/5]^infinity_0 = (- 50) [e^- infinity/5 - e^- 0] = (- 50) [- 1] a = 50 m^2 \r\n moment of inertia about origin perpendicular (and out off paper) is i_0 = i_x + i_y along y - axis along x - axis mu = total mass/total area = 10 kg/50 m^2 = 1/5 kg/m^2 dm = mu da mu = mass per unit area. da = x dy = -5 ln (y/10) dy at x = 0, y = 10 at x = infinity y = 10 e^- infinity = 0 hence limit is y = 0 to y = 10