A hockey player hits a puck so that it comes to rest in $10 \mathrm{~s}$ after sliding $100 \mathrm{ft}$ on the ice. Determine $(a)$ the initial velocity of the puck, (b) the coefficient of friction between the puck and the ice.

Determine the internal torque at each section and show the torsional stress on differential volume elements located at A, B, C, and D.

Astronauts who landed on the moon during the Apollo 15, 16, and 17 missions brought back a large collection of rocks to the earth. Knowing the rocks weighed 139 lb when they were on the moon, determine (a) the weight of the rocks on the earth, (b) the mass of the rocks in slugs. The acceleration due to gravity on the moon is 5.30 $ft/s^2$.

A spring scale $A$ and a lever scale $B$ having equal lever arms are fastened to the roof of an elevator, and identical packages are attached to the scales as shown. Knowing that when the elevator moves downward with an acceleration of $1 \mathrm{~m} / \mathrm{s}^2$ the spring scale indicates a load of $60 \mathrm{~N}$, determine $(a)$ the weight of the packages, $(b)$ the load indicated by the spring scale and the mass needed to balance the lever scale when the elevator moves upward with an acceleration of $1 \mathrm{~m} / \mathrm{s}^2$.

A system consisting of 1 kg of $H_{2}O$ undergoes a power cycle composed of the following processes: Process 1–2: Constant-volume heating from $p_{1}=5$ bar, $T_{1}=160^{\circ} \mathrm{C}$ to $p_{2}=10$ bar. Process 2–3: Constant-pressure cooling to saturated vapor. Process 3–4: Constant-volume cooling to $T_{4}=160^{\circ} \mathrm{C}$. Process 4–1: Isothermal expansion with $Q_{41}=815.8\: \mathrm{kJ}$. Sketch the cycle on $T–v$ and $p–v$ diagrams. Neglecting kinetic and potential energy effects, determine the thermal efficiency.

The turnbuckle is tightened until the tension in the cable AB equals 2.4 kN. Determine the vector expression for the tension T as a force acting on member AD. Also find the magnitude of the projection of T along the line AC.

The conveyor belt is moving at 4 m/s. If the coefficient of static friction between the conveyor and the 10-kg package B is $\mu_s = 0.2$ , determine the shortest time the belt can stop so that the package does not slide on the belt.

The 125-kg homogeneous rectangular solid is held in the arbitrary position shown by the tension T in the cable. Determine and plot the following quantities as functions of $\theta$ over the range $0 \leq \theta \leq 60^{\circ}$: T, $A_{y}, A_{z}, B_{x}, B_{y}, \text { and } B_{z}$. The hinge at A cannot exert an axial thrust. Assume all hinge force components to be in the positive coordinate directions. Friction at D is negligible.

Consider a shell and tube heat exchanger in a milk pasteurizing unit in which the milk flowing is to be heated from $20^\circ C$ by hot water initially at $140^\circ C$ and flowing at a rate of 5 kg/s. The milk flows through 30 thin-walled tubes with an inside diameter of 20 mm with each tube making 10 passes through the shell. The average convective heat transfer coefficients on the milk and water side are $450 W/m^2 \cdot K$ and $1100 W/m^2 \cdot K,$ respectively. In order to complete the pasteurizing process and hence restrict the microbial growth in the milk, it is required to have the exit temperature of milk attain at least $70^\circ C.$ As a design engineer, your job is to decide upon the shell width (tube length in each pass) so that the milk exit temperature of $70^\circ C$ can be achieved. One of the design requirements is that the exit temperature of hot water should be at least $10^\circ C$ higher than the exit temperature of milk.

The centric force P is applied to a short post as shown. Knowing that the stresses on plane a-a are $\sigma=-15 ksi$ and $\tau=5 ksi$, find

(a) the angle $\beta$ that plane a-a forms with the horizontal. (b) the maximum compressive stress in the post.

The centric force P is applied to a short post as shown. Knowing that the stresses on plane $a-a$ are $\sigma=-15 \mathrm{ksi}$ and $\boldsymbol{\tau}=5 \mathrm{ksi}$, determine (a) the angle $\beta$ that plane $a-a$ forms with the horizontal, (b) the maximum compressive stress in the post.

A tank initially contains 100 gal of brine in which there is dissolved 20 lb of salt. Starting at time t = 0, brine containing 3 lb of dissolved salt per gallon flows into the tank at the rate of 4 gal/min. The mixture is kept uniform by stirring and the well-stirred mixture simultaneously flows out of the tank at the same rate. (a) How much salt is in the tank at the end of 10 min? (b) When is there 160 lb of salt in the tank?

Pressurized water $\left(p_{\mathrm{in}}=10 \text { bar, } T_{\mathrm{in}}=110^{\circ} \mathrm{C}\right)$ enters the bottom of an L=10-m-long vertical tube of diameter D=100 mm at a mass flow rate of m=1.5 kg/s. The tube is located inside a combustion chamber, resulting in heat transfer to the tube. Superheated steam exits the top of the tube at $p_{\mathrm {out }}=7 \mathrm { bar }$, $T_{\mathrm{out}}=600^{\circ} \mathrm{C}$. Determine the change in the rate at which the following quantities enter and exit the tube: (a) the combined thermal and flow work, (b) the mechanical energy, and (c) the total energy of the water. Also, (d) determine the heat transfer rate, q. Hint: Relevant properties may be obtained from a thermodynamics text.

The initially stationary 12-kg block is subjected to the time-varying force whose magnitude $P$ is shown in the plot. The $30^{\circ}$ angle remains constant. Determine the block speed at $(a) t=1 \mathrm{~s}$ and (b) $t=4 \mathrm{~s}$.