Question

1. The cantilever beam AB of length L shown in Fig.(a carries a uniformly distributed load of intensity wo, which includes the weight of the beam. Equation of the elastic curve is given by the following differential equation Af _irer where M is the bending moment of the beam. it is also given that of the beam and I modulus of Inertia. where E- Modulus of the elasticity v is the deflection of the beam. Compute the maximum displacement of the beam using L-2.5 m.w0 # 500 kg /m, and E-21 10 pa. 2. According to Newton's Law of Universal Gravitation, the gravitational force on an object of mass m that has been projected vertically upward from Earth's surface is F= where x =x(t) is the object's distance above the surface at time t Rís Earth's radius x+R) and g is the acceleration due to gravity. Also, by Newton's Second law, dv = n =- dt mgR2 (x+R)2 a. Suppose a rocket is fired vertically upward with an initial velocity vo Let h be the maximu height above the surfaced reached by the object. Show that 2gRh R + h dv dt du (hint: m-= mv -) b. Calculate ve = him vo . This limit is called escape velocity for Earth. c. Use R-64 x 106 m and g= 9.8 m/s2 to calculate ve in m/s.

Answer 1

Solution- W o 8 าเ en dota ulhete M-bunding moment of bom also e hat dtv dx2 E Modulus of theelostcty he beom

Modulue of the Inesia v = deflection oe -the beam 500 kg Inn ET dv グ、 noa2 沒ㄐ 3 At x1、v-o -from (2)

니 Equation becomes &у ETV g ET - 1162 XLD datement)