A simple log bridge in a remote area consists of two parallel logs with planks across them. The logs are Douglas fir with average diameter 300 mm. A truck moves slowly across the bridge, which spans 2.5 m. Assume that the weight of the truck is equally distributed between the two logs. Because the wheelbase of the truck is greater than 2.5 m, only one set of wheels is on the bridge at a time. Thus, the wheel load on one log is equivalent to a concentrated load W acting at any position along the span. In addition, the weight of one log and the planks it supports is equivalent to a uniform load of $850\ \mathrm{N} / \mathrm{m}$ acting on the log. Determine the maximum permissible wheel load W based upon (a) an allowable bending stress of 7.0 MPa, and (b) an allowable shear stress of 0.75 MPa.

A ViseGrip ${ }^{\otimes}$ plier-wrench is drawn to scale in the figure. Scale the drawing for dimensions. Find the forces acting on each pin and member of the assembly for an assumed clamping force of $P=4000 \mathrm{~N}$ in the position shown. What force $F$ is required to keep it in the clamped position shown? Note: A similar tool is probably available for inspection in your school's machine shop.

For the problem, identify all the forces acting on the object and draw a free-body diagram of the object. You are driving on the highway, and you come to a steep downhill section. As you roll down the hill, you take your foot off the gas pedal. You can ignore friction, but you can't ignore air resistance.

A long piece of wire with a mass of 0.100 kg and a total length of 4.00 m is used to make a square coil with a side of 0.100 m. The coil is hinged along a horizontal side, carries a 3.40-A current, and is placed in a vertical magnetic field with a magnitude of 0.010 0 T. Find the torque acting on the coil due to the magnetic force at equilibrium.

The deflection curve for a cantilever beam AB is given by the following equation: $v=-\frac{q_{0} x^{2}}{360 L^{2} E I}\left(45 L^{4}-40 L^{3} x+15 L^{2} x^{2}-x^{4}\right)$ (a) Describe the load acting on the beam. (b) Determine the reactions $R_{A}$ and $M_{A}$ at the support.

The force F per unit length of a conducting wire carrying a current I in a magnetic field B is F = I × B. Find the force acting on a circuit whose shape is given by x = sin θ, y = cos θ, $z=\sin \frac{1}{2} \theta$, when current I flows in it and when it lies in a magnetic field B = xi − yj + k.

The drag coefficient of a car at the design conditions of 1 atm, $25^{\circ} \mathrm{C}$, and 90 km/h is to be determined experimentally in a large wind tunnel in a full-scale test. The height and width of the car are 1.25 m and 1.65 m, respectively. If the horizontal force acting on the car is measured to be 220 N, determine the total drag coefficient of this car.

A long, straight wire containing a semicircular region of radius $0.95 \mathrm{~m}$ is placed in a uniform magnetic field of magnitude $2.20 \mathrm{~T}$. What is the net magnetic force acting on the wire when it carries a current of $3.40 \mathrm{~A}$? (what does symmetry tell you about the forces on the upper and lower halves of the semicircular region?)

A rubber ball bounces. We'd like to understand how the bounces. a. A rubber ball has been dropped and is bouncing off the floor. Draw a motion diagram of the ball during the brief time interval that it is in contact with the floor. Show 4 or 5 frames as the ball compresses, then another 4 or 5 frame as it expands. What is the direction of $\vec { a }$ during each of these parts of the motion? b. Draw a picture of the ball in contact with the floor and identify all forces acting on the ball. c. Draw a free-body diagram of the ball during its contact with the ground. Is there a net force acting on the ball? If so, in which direction? d. During contact, is the force of the ground on the ball larger than, smaller than, or equal to the weight of the ball? Use your answers to parts a-c to explain your reasoning.

A 70-kg base runner begins his slide into second base when he is moving at a speed of 4.0 m/s. The coefficient of friction between his clothes and Earth is 0.70. He slides so that his speed is zero just as he reaches the base. How much mechanical energy is lost due to friction acting on the runner?

A force acting on a particle in the $x y$ plane at coordinates $(x, y)$ is given by $\overrightarrow{\boldsymbol{F}}=\left(F_0 / r\right)(y \hat{i}-x \hat{j})$, where $F_0$ is a positive constant and $r$ is the distance of the particle from the origin. Find the work done by this force on a particle that moves once around a circle of radius $5.0 \mathrm{~m}$ that is centered at the origin.

For each underlined word in the following sentences, write the plural above the word. Lunts

Example 1. The $\underline{\text{Lunt}}$ (Lunts), a famous husband and wife acting team, performed in many $\underline{\text{play}}$ (plays) together.

The $\underline{\text{candidate}}$ from both $\underline{\text{party}}$ spoke at the town hall last week.

A prismatic bar with a length $L=3\ \mathrm{ft}$ and cross-sectional area $A=8$ in $^2$ is compressed by an axial centroidal load $P=10\ \text{kips}$. Determine the complete state of stress acting on an inclined section $p q$ that is cut through the bar at an angle $\theta=35^{\circ}$, and show the stresses on a properly oriented stress element.

An air puck of mass $m_1$ is tied to a string and allowed to revolve in a circle of radius $R$ on a frictionless horizontal table. The other end of the string passes through a small hole in the center of the table, and a load of mass $m_2$ is tied to the string. The suspended load remains in equilibrium while the puck on the tabletop revolves. What are
(b) the radial force acting on the puck,