A $700 \mathrm{~kg}$ horse $A$ lifts a $50 \mathrm{~kg}$ hay bale $B$ as shown. At the instant when $r=8 \mathrm{~m}$ and $\theta=60^{\circ}$, the velocity and acceleration of the horse are $2 \mathrm{~m} / \mathrm{s}$ to the right and $0.5 \mathrm{~m} / \mathrm{s}^2$ to the left, respectively. Neglecting the mass of the pulley, determine at that instant $(a)$ the tension in the cable, $(b)$ the average horizontal force between the ground and the horse's feet.

A steel pipe of 400-mm outer diameter is fabricated from 10-mm-thick plate by welding along a helix that forms an angle of 20° with a plane perpendicular to the axis of the pipe. Knowing that a 300-kN axial force P is applied to the pipe, determine the normal and shearing stresses in directions respectively normal and tangential to the weld.

$1.4 \mathrm{~kg}$ model rocket is launched vertically from rest with a constant thrust of $25 \mathrm{~N}$ until the rocket reaches an altitude of $15 \mathrm{~m}$ and the thrust ends. Neglecting air resistance, determine $(a)$ the speed of the rocket when the thrust ends, $(b)$ the maximum height reached by the rocket, $(c)$ the speed of the rocket when it returns to the ground.

Knowing that at the instant shown the velocity of collar A is 900 $\mathrm{mm} / \mathrm{s}$ to the left, determine $(a)$ the angular velocity of $\operatorname{rod} A D B$, (b) the velocity of point $B$.

Knowing that the swings of an amusement park ride form an angle of $40^{\circ}$ with respect to the horizontal, determine $(a)$ the speed of rotation, $(b)$ the force in the cable for a swing and person weighing $250 \mathrm{~lb}$.

Spheres of 40-mm diameter heated to a uniform temperature of $400^{\circ} \mathrm{C}$ are suddenly removed from the oven and placed in a forced-air bath operating at $25^{\circ} \mathrm{C}$ with a convection coefficient of $300 \mathrm{W} / \mathrm{m}^{2} \cdot \mathrm{K}$ on the sphere surfaces. The thermophysical properties of the sphere material are $\rho=3000 \mathrm{kg} / \mathrm{m}^{3}, c=850 \mathrm{J} / \mathrm{kg} \cdot \mathrm{K}$, and $k=15 \mathrm{W} / \mathrm{m} \cdot \mathrm{K}$. (a) How long must the spheres remain in the air bath for 80% of the thermal energy to be removed? (b) The spheres are then placed in a packing carton that prevents further heat transfer to the environment. What uniform temperature will the spheres eventually reach?

Two $2.6 \mathrm{~lb}$ collars $A$ and $B$ can slide without friction on a frame, consisting of the horizontal rod $O E$ and the vertical rod $C D$, which is free to rotate about $C D$. The two collars are connected by a cord running over a pulley that is attached to the frame at $O$, and a stop prevents collar $B$ from moving. The frame is rotating at the rate $\dot{\theta}=12 \mathrm{rad} / \mathrm{s}$ and $r=0.6 \mathrm{ft}$ when the stop is removed, allowing collar $A$ to move out along rod $O E$. Neglecting friction and the mass of the frame, determine, for the position $r=1.2 \mathrm{ft},(a)$ the transverse component of the velocity of collar $A$, $(b)$ the tension in the cord and the acceleration of collar $A$ relative to the rod $O E$.

A pump operating at steady state receives liquid water at $20^{\circ} \mathrm{C}$, $100\ \mathrm{kPa}$ with a mass flow rate of $53 \mathrm{~kg} / \mathrm{min}$. The pressure of the water at the pump exit is $5\ \mathrm{MPa}$. The isentropic pump efficiency is $70 \%$. Stray heat transfer and changes in kinetic and potential energy are negligible. Determine the power required by the pump, in $\mathrm{kW}$.

Is it possible to produce a perfect crystalline solid that does not contain any vacancies.

The flat-bed trailer carries two 1500-kg beams with the upper beam secured by a cable. The coefficients of static friction between the two beams and between the lower beam and the bed of the trailer are 0.25 and 0.30, respectively. Knowing that the load does not shift, determine (a) the maximum acceleration of the trailer and the corresponding tension in the cable, (b) the maximum deceleration of the trailer.

A heat engine receives heat from a source at 1100 K at a rate of 400 kJ/s, and it rejects the waste heat to a medium at 320 K. The measured power output of the heat engine is 120 kW, and the environment temperature is $25^{\circ} \mathrm{C}$. Determine (a) the reversible power, (b) the rate of irreversibility, and (c) the second-law efficiency of this heat engine.

The W $10 \times 45$ is made of A-36 steel and is used as a column that has a length of 15ft. If its ends are assumed pin supported, and it is subjected to an axial load of $100 \mathrm{kip}$, determine the factor of safety with respect to buckling.

The roller-coaster track shown is contained in a vertical plane. The portion of track between $A$ and $B$ is straight and horizontal, while the portions to the left of $A$ and to the right of $B$ have radii of curvature as indicated. A car is traveling at a speed of $72 \mathrm{~km} / \mathrm{h}$ when the brakes are suddenly applied, causing the wheels of the car to slide on the track $\left(\mu_k=0.20\right)$. Determine the initial deceleration of the car if the brakes are applied as the car $(a)$ has almost reached $A$, $(b)$ is traveling between $A$ and $B,(c)$ has just passed $B$

Pin $B$ weighs $4 \mathrm{oz}$ and is free to slide in a horizontal plane along the rotating arm $O C$ and along the circular slot $D E$ of radius $\underline{b}=20 \mathrm{in}$. Neglecting friction and assuming that $\dot{\theta}=15 \mathrm{rad} / \mathrm{s}$ and $\ddot{\theta}=250 \mathrm{rad} / \mathrm{s}^2$ for the position $\theta=20^{\circ}$, determine for that position (a) the radial and transverse components of the resultant force exerted on pin $B,(b)$ the forces $\mathbf{P}$ and $\mathbf{Q}$ exerted on pin $B$, respectively, by rod $O C$ and the wall of slot $D E$.