IND 604 Lecture 11: Police Car, Friday Tellers Examples

A simply supported beam having a span l =3.6m is to carry a uniformly distributed load of
intensity w = 1600kg/m. The cross-section is to be rectangular with depth h and width b = h/2. If
the allowable bending stress in tension or compression is σ w = 84 kg/cm 2 . What is the required
depth h for the cross-section?

A truck going 15 km/h has a head-on collision with a small car going 30 km/h, then discuss the change in kinetic energy and momentum using impulse equation and Newton’s law.

Let
H = {f : R → R | f(x) = ax + b; a, b ∈ R; a > 0}.
H1 = {f : R → R | f(x) = ax; a ∈ R; a > 0}.
H2 = {f : R → R | f(x) = x + b; b ∈ R}.
(a) Prove that H1 and H2 are subgroups of H.
(b) Determine whether each is a normal subgroup of H.