The rod assembly is supported by ball-and-socket joints at A and B . At the instant shown it is rotating about the y axis with an angular velocity $\omega=$5 rad/ s and has an angular acceleration $\alpha=8 \mathrm{rad} / \mathrm{s}^{2} .$ Determine the magnitudes of the velocity and acceleration of point C at this instant. Solve the problem using Cartesian vectors and Eqs. 16-9 and 16-13 .

Find the tension in the Achilles tendon and the force that the tibia exerts on the ankle joint when a person who weighs 750 N supports himself on the ball of one foot. The normal force N=750 N pushes up on the ball of the foot on one side of the ankle joint, while the Achilles tendon pulls up on the foot on the other side of the joint.

A $3 \mathrm{~m}$ pole is supported by a ball-and-socket joint at $A$ and by the cables $C D$ and $C E$. Knowing that the line of action of the $5~\mathrm{kN}$ force forms an angle $\phi=30^{\circ}$ with the vertical $x y$ plane (and is parallel to the $y z$ plane), determine $(a)$ the tension in cables $C D$ and $C E$, $(b)$ the reaction at $A$.

The hip is an extremely stable joint because it has

a) a complete bony socket.

b) a strong articular capsule.

c) supporting ligaments.

d) all of the above

What are the differences between a server socket and a client socket?

A rope of length L is supported at two points, (c, d) and (-c, d). The middle of the rope is located at the point (0, b). The shape of the rope is given by $y=a \cosh \left(\frac{x}{a}\right)+b-a$. Find a.

Two $2 \times 4$-ft plywood panels, each of weight $12 \mathrm{lb}$, are nailed together as shown. The panels are supported by ball-and-socket joints at $A$ and $F$ and by the wire $B H$. Determine $(a)$ the location of $H$ in the $x y$ plane if the tension in the wire is to be minimum, (b) the corresponding minimum tension.

Match each joint with the category of joints that it represents.

$$\begin{matrix} \text{Joint} & \text{Category}\\ \text{Shoulder} & \text{A. Ball-and-socket joint}\\ \text{ } & \text{B. Hinge joint}\\ \text{ } & \text{C. Immovable joint}\\ \text{ } & \text{D. Pivot joint}\\ \text{ } & \text{E. Slightly movable joint}\\ \end{matrix}$$

What type of joint allows you to turn your head? a. ball-and-socket b. hinge c. pivot d. gliding

If the 5-kg plate is released from rest in the horizontal position, what force is exerted on it by the ball-and-socket support at that instant?

Rod $A B$ has a length of $13 \mathrm{~in}$. and is connected by ball-and-socket joints to collars $A$ and $B$ that slide along the two rods shown. Knowing that collar $B$ moves toward point $D$ at a constant speed of $36 \mathrm{~in} . \mathrm{s}$, determine the velocity of collar $A$ when $b=4$ in.

Several rods are brazed together to form the robotic guide arm shown that is attached to a ball-and-socket joint at $O$. Rod $O A$ slides in a straight inclined slot, while rod $O B$ slides in a slot parallel to the $z$ axis. Knowing that at the instant shown $\mathbf{v}_B=(9\mathrm{~in.}/ \mathrm{s}) \mathbf{k}$, determine $(a)$ the angular velocity of the guide arm, $(b)$ the velocity of point $A,(c)$ the velocity of point $C$.

A boom $D E$ is supported by a ball and socket at $D$ and cables $A C$ and $A B$. The boom has a length of $7 \mathrm{~m}$. Determine the tensions in the cables and the socket reactions at $D$. Neglect the weight of the boom.

What are the differences between a server socket and a client socket?