The angle strut is welded to the end C of the I-beam and supports the 1.6-kN vertical force. Determine the bending moment at B and the distance x to the left of C at which the bending moment is zero. Also construct the moment diagram for the beam.

Assume that A and B are constants. $y=B+A \sin t$

The curved beam is subjected to a bending moment of $M=900 \mathrm{~N} \cdot \mathrm{m}$ as shown. Determine the stress at points $A$ and $B$, and show the stress on a volume element located at each of these points.

A vertical force $P=10 \mathrm{kips}$ acts downward at the apex $B$ of frame $A B C$, as shown in Fig. The frame is supported by a frictionless pin at $C$ and rests on a roller support at $A$. (a) Determine the reactions at $A$ and $C$, and (b) determine the internal resultants (axial force, shear force, and bending moment) at arbitrary cross sections of legs $A B$ and $B C$, using the respective notations shown in the two cutaways.

The steel beam has the cross-sectional area shown. If $w_0=2 \mathrm{kip} / \mathrm{ft}$, determine the maximum bending stress in the beam.

An L2 steel strap having a thickness of 0.125 in. and a width of 2 in. is bent into a circular arc of radius 600 in. Determine the maximum bending stress in the strap.

If X is x²(12). find constants a and b such that P(a < X < b) = 0.90 and P(X < a) = 0.05.

Assume that A and B are constants. $f(x)=2 x \sin (3 x)$

Show that $\| a|-| b|| \leq|a-b|$ for all constants a and b.

Why is it important to use constants in an experiment?

A carpenter’s trick to keep nails from bending when they are pounded into a hard material is to grip the center of the nail with pliers. Why does this help?

Demonstrate the impact toughness of a piece of round chalk by first using a triangular file to produce a V-notch on the cylindrical surface and then bending the chalk to break it.

In designing airplanes, an important feature is the so-called drag factor; that is, the retarding force exerted on the plane by the air. One model measures drag by a function of the form $F(v)=A v^{2}+\frac{B}{v^{2}}$ where v is the velocity of the plane and A and B are constants. Find the velocity (in terms of A and B) that minimizes F(v). Show that you have found the minimum rather than a maximum.

Assume $a, b, c,$ and $k$ are constants.

$$f(x) = x^e$$