Plot the magnitude of the resultant R of the three forces as a function of $\theta$ for $0 \leq \theta \leq 360^{\circ}$ and determine the value of $\theta$ which makes the magnitude R of the resultant of the three loads (a) a maximum and (b) a minimum. Record the magnitude of the resultant in each case. Use values of $\phi=75^{\circ} \text { and } \psi=20^{\circ}$.

Fill in the blank with the most appropriate metric unit $(\mathrm{kg}, \mathrm{g}, \mathrm{mg}$, or metric ton). A carrot has a mass of $75$______

Compression member AB is used to hold up the 325 X 500-mm rectangular plate. If the compressive force in the member is 320 N for the position shown, determine the magnitude of the projection of this force (as it acts at point A) along diagonal OC.

A slender rod of mass $m_{1}$ is welded to the horizontal edge of a uniform semicylindrical shell of mass $m_{2}$. Determine an expression for the angle $\theta$ with the horizontal made by the diameter of the shell through $m_{1}$.

Water at 1000 kPa and $250^{\circ} \mathrm{C}$ is brought to saturated vapor in a piston/cylinder assembly with an isotherm process. Find the specific work and heat transfer. Estimate the specific work form the area in the P-v diagram and compare it to the correct value.

Draw the vectors using the scale indicated.

Displacement $145 \mathrm{mi}$ at $60^{\circ}$ north of east $\qquad$length $=\underline{\qquad}$ in.

Knowing that the speed of car $A$ was $75 \mathrm{mi} / \mathrm{h}$ and that the time elapsed from the first collision to the stop at $P$ was $2.4 \mathrm{~s}$, determine the coordinates of the utility pole $P$.

An agricultural mechanic tries to loosen a nut on a tractor wheel with a wrench that is $32.5 \mathrm{~cm}$ long. If the torque required to loosen the nut is $55.0 \mathrm{~N} \mathrm{~m}$, how much force must she apply to the wrench?

Can you arrange a pulley system containing 10 pulleys and obtain a mechanical advantage of 12 ? Why or why not?

The throttle-control lever OA rotates in the range $0 \leq \theta \leq 90^{\circ}$. An internal torsional return spring exerts a restoring moment about O given by M = K( $\theta+\pi / 4$), where K = 500 ${N} \cdot \mathbf{m} {m} / {r a d}$ and $\theta$ is in radians. Determine and plot as a function of $\theta$ the tension T required to make the net moment about O zero. Use the two values d = 60 mm and d = 160 mm and comment on the relative design merits. The effects of the radius of the pulley at B are negligible.

Fill in the blank with the most appropriate metric unit $(\mathrm{kg}, \mathrm{g}, \mathrm{mg}$, or metric ton). A truckload shipment of copper pipe has a mass of $900$_____.

Fill in the blank (where necessary, rounding to three significant digits): $0.55 \mathrm{~s}$ =_____ $\mu$$\mathrm{s}$

Fill in the blank (where necessary, rounding to three significant digits): $25 \mathrm{~kg}$ =__________$\mathrm{g}$

Draw the vectors using the scale indicated.

Displacement $21 \overline{0} \mathrm{mi}$ at $45^{\circ}$ south of west $\qquad$length $=\underline{\qquad}$ in.