A paper tube is formed by rolling a paper strip in a spiral and then gluing the edges together as shown. Determine the shear stress acting along the seam, which is at $30^{\circ}$ from the vertical, when the tube is subjected to an axial force of $10 \mathrm{~N}$. The paper is $1 \mathrm{~mm}$ thick and the tube has an outer diameter of $30 \mathrm{~mm}$.

The deflection curve for a cantilever beam AB is given by the following equation: $v=-\frac{q_{0} x^{2}}{360 L^{2} E I}\left(45 L^{4}-40 L^{3} x+15 L^{2} x^{2}-x^{4}\right)$ (a) Describe the load acting on the beam. (b) Determine the reactions $R_{A}$ and $M_{A}$ at the support.

In a common but dangerous prank, a chair is pulled away as a person is moving downward to sit on it, causing the victim to land hard on the floor. Suppose the victim falls by 0.50 meter, the mass that moves downward is 70 kilogram, and the collision on the floor lasts 0.082 second. What is the magnitudes of the impulse acting on the victim from the floor during the collision?

A simply supported steel beam of length $l$ with a concentrated load, $F$, acting at midspan has a rectangular cross-section of width, $b$, and depth, $h$. If the strain energy due to transverse shear loading is $U_s$ and that due to bending loading is $U_b$, derive an expression for the ratio $U_s / U_b$ and plot it as a function of $h / l$ over the range $0.0$ to $0.10$.

In this exercise, perform the indicated operations.

In designing a building, it was determined that the forces acting on an I beam would deflect the beam an amount (in cm), given by $\frac{x\left(1000-20 x^2+x^3\right)}{1850}$, where $x$ is the distance (in $\mathrm{m}$ ) from one end of the beam. Find the deflection for $x=6.85 \mathrm{~m}$. (The $1000$ and $20$ are exact.)

Two boxes, A and B, are at rest. Box A is on level ground, while box B rests on an inclined plane tilted at angle θ with the horizontal. (a) Write expressions for the normal force acting on each block. (b) Compare the two forces; that is, tell which one is larger or whether they are equal in magnitude. (c) If the angle of incline is 10°, which force is greater?

A 70-kg base runner begins his slide into second base when he is moving at a speed of 4.0 m/s. The coefficient of friction between his clothes and Earth is 0.70. He slides so that his speed is zero just as he reaches the base. How much mechanical energy is lost due to friction acting on the runner?

The equation of the deflection curve for a simply supported beam is

$$v(x)=\frac{q_0}{24 E I}\left(2 L x^3-x^4-L^3 x\right)$$

(a) Derive the slope equation of the beam. (b) Derive the bending-moment equation of the beam. (c) Derive the shear-force equation of the beam. (d) Describe the loading acting on the beam.

Consider a 6-m-diameter spherical gate holding a body of water whose height is equal to the diameter of the gate. Atmospheric pressure acts on both sides of the gate. The horizontal component of the hydrostatic force acting on this curved surface is (a) 709 kN(b) 832 kN(c) 848 kN(d) 972 kN(e) 1124 kN

The drag coefficient of a car at the design conditions of 1 atm, $25^{\circ} \mathrm{C}$, and 90 km/h is to be determined experimentally in a large wind tunnel in a full-scale test. The height and width of the car are 1.25 m and 1.65 m, respectively. If the horizontal force acting on the car is measured to be 220 N, determine the total drag coefficient of this car.

The p21 protein is strongly expressed in cells that have been irradiated. Researchers have thought that this strong expression is elicited by transcriptional activation of the p21 gene by the p53 protein acting as a transcription factor. Does this hypothesis fit with the observation that p$21$ expression is induced by radiation treatment in mice homozygous for a knockout mutation in the TP$53$ gene? Explain

A projectile is fired with initial speed $v_{0}$ feet per second from a height of h feet at an angle of $\theta$ above the horizontal. Assuming that the only force acting on the object is gravity, find the maximum altitude, horizontal range and speed at impact. $v_{0}=80, h=6, \theta=\frac{\pi}{4}$

When April provides an input force of 10 N, the drum key provides an output force of 15 N.

Is the output force acting in the same direction as the input force?

Calculate the mechanical advantage of the drum key.

Since the drum key increases April's input force, is her input distance greater or smaller than the key's output distance?

An air puck of mass $m_1$ is tied to a string and allowed to revolve in a circle of radius $R$ on a frictionless horizontal table. The other end of the string passes through a small hole in the center of the table, and a load of mass $m_2$ is tied to the string. The suspended load remains in equilibrium while the puck on the tabletop revolves. What are
(b) the radial force acting on the puck,