A force $P=300 ~\mathrm{kN}$ is needed to just open the gate of Fig. with $R=1.2 \mathrm{~m}$ and $H=4 \mathrm{~m}$. How wide is the gate? (A) $2.98 \mathrm{~m}$ (B) $3.67 \mathrm{~m}$ (C) $4.32 \mathrm{~m}$ (D) $5.16 \mathrm{~m}$

The rectangular gate shown in Fig. is $3 \mathrm{~m}$ wide. The force $P$ needed to hold the gate in the position shown is nearest: (A) $24.5 ~\mathrm{kN}$ (B) $32.7 ~\mathrm{kN}$ (C) $98 ~\mathrm{kN}$ (D) $147 ~\mathrm{kN}$

The pressure in the foothills of the Rockies near Boulder, Colorado is $84 ~\mathrm{kPa}$. The pressure, assuming a constant density of $1.00 ~\mathrm{~kg} / \mathrm{m}^3$, at the top of a nearby $4000$-$\mathrm{m}$-$\mathrm{high}$ mountain is closest to: (A) $60~ \mathrm{kPa}$ (B) $55 ~\mathrm{kPa}$ (C) $50 ~\mathrm{kPa}$ (D) $45 ~\mathrm{kPa}$

An iceberg can be idealized as a cube of side length $L$, as in Fig. P2.128. If seawater is denoted by $S=1.0$, then glacier ice (which forms icebergs) has $S=0.88$. Find if this "cubic" iceberg is stable for the position shown in Fig. P2.128.

Find the force $P$ needed to just open the gate shown in Fig. if: (a) $H=6 \mathrm{~m}, R=2 \mathrm{~m}$, and the gate is $4 \mathrm{~m}$ wide. (b) $H=20 ~\mathrm{ft}, R=6 ~\mathrm{ft}$, and the gate is $12 ~\mathrm{ft}$ wide.

Race car A follows path a-a while race car B follows path b-b on the unbanked track. If each car has a constant speed limited to that corresponding to a lateral (normal) acceleration of 0.8g, determine the times $t_{A}$ and $t_{B}$ for both cars to negotiate the turn as delimited by the line C-C.

Find the force $P$ needed to hold the $10 -\text{m}$-long cylindrical object in position as shown.

A football player releases a ball with the initial conditions shown in the figure. Determine the radius of curvature $\rho$ of the path and the time rate of change $\dot{v}$ of the speed at times $t=1 \mathrm{sec}$ and $t=2 \mathrm{sec}$, where $t=0$ is the time of release from the quarterback's hand.

The car is traveling at a speed of 60 mi/hr as it approaches point A. Beginning at A, the car decelerates at a constant 7$ft/sec^{2}$ until it gets to point B, after which its constant rate of decrease of speed is 3$ft/sec^{2}$ as it rounds the interchange ramp. Determine the magnitude of the total car acceleration (a) just before it gets to B, (b) just after it passes B, and (c) at point C.

The pin-connected structure shown in Figure P5.63 consists of a rigid bar $A B C D$ and two axial members. Bar (1) is steel $\left[E=200 \mathrm{GPa} ; \alpha=11.7 \times 10^{-6 /{ }^{\circ} \mathrm{C}}\right]$, with a cross-sectional area of $A_1=400 \mathrm{~mm}^2$. Bar (2) is an aluminum alloy $[E=70 \mathrm{GPa}$; $\left.\alpha=22.5 \times 10^{-6} /{ }^{\circ} \mathrm{C}\right]$, with a cross-sectional area of $A_2=400 \mathrm{~mm}^2$. The bars are unstressed when the structure is assembled. After a concentrated load of $P=36 \mathrm{kN}$ is applied and the temperature is increased by $25^{\circ} \mathrm{C}$, determine (a) the normal stresses in bars (1) and (2). (b) the deflection of point $D$ on the rigid bar.

A team of engineering students is designing a catapult to launch a small ball at A so that it lands in the box. If it is known that the initial velocity vector makes a 300 angle with the horizontal, determine the range of launch speeds $v_{0}$ for which the ball will land inside the box.

A projectile is launched with an initial speed of 200 m/s at an angle of 60$^{\circ}$ with respect to the horizontal. Compute the range R as measured up the incline.

A pin-connected structure is supported as shown in Figure P5.37/38. Bar (1) is made of brass $\left[\sigma_Y=330 \mathrm{MPa} ; E=\right.$ $105 \mathrm{GPa}$. Bar $(2)$ is made of an aluminum alloy $\left[\sigma_Y=275 \mathrm{MPa}\right.$; $E=70 \mathrm{GPa}$ ]. Bars (1) and (2) each have cross-sectional areas of $225 \mathrm{~mm}^2$. Member $A B C D$ is rigid. If the minimum factor of safety required for bars (1) and (2) is $2.50$, calculate the maximum load $P$ that can be applied to the rigid bar at $A$.

The two cars A and B enter an unbanked and level turn. They cross line C-C simultaneously, and each car has the speed corresponding to a maximum normal acceleration of 0.9g in the turn. Determine the elapsed time for each car between its two crossings of line C-C. What is the relative position of the two cars as the second car exits the turn? Assume no speed changes throughout.