In a test to determine the crushing characteristics of polystyrene packing material, a steel cone of mass $m$ is dropped so that it falls a distance $h$ and then penetrates the material. The resistance $R$ of polystyrene to penetration depends on the cross-sectional area of the penetrating object and thus is proportional to the square of the cone penetration distance $x$, or $R=k x^2$. If the cone comes to rest at a distance $x=d$, determine the constant $k$ in terms of the test conditions and results.

Five kmol of oxygen ($O_{2}$) gas undergoes a process in a closed system from $p_{1}=50\: \mathrm{bar}, T_{1}=170\: \mathrm{K}$ to $p_{2}=25 \mathrm{bar}$, $T_{2}=200 \mathrm{K}$. Determine the change in volume, in $\mathrm{m}^{3}$.

The term __________ refers to a quantity of matter that is homogeneous throughout in both chemical composition and physical structure.

The 80-kg ventilation door OD with mass center at G is held in the open position shown by means of a moment M applied at A to the opening linkage. Member AB is parallel to the door for the $30^{\circ}$ position shown. Determine M.

Helium gas is in a cylinder that has rigid walls. If the pressure of the gas is 2.00 atm, then the root-mean-square speed of the helium atoms is $\mathrm{v}_{\mathrm{rms}}=176 \mathrm{m} / \mathrm{s}$. By how much (in atmospheres) must the pressure be increased to increase the $\mathrm{v}_{\mathrm{rms}}$ of the He atoms by 100 m/s? Ignore any change in the volume of the cylinder.

The small slider A moves with negligible friction down the tapered block, which moves to the right with constant speed v = $v_0$. Use the principle of work-energy to determine the magnitude $v_A$ of the absolute velocity of the slider as it passes point C if it is released at point B with no velocity relative to the block. Apply the equation, both as an observer fixed to the block and as an observer fixed to the ground, and reconcile the two relations.

The bar clamp is being used to clamp two boards together while the glue between them cures. What torque M must be applied to the handle of the screw in order to produce an 80-lb compression between the boards? The $\frac{3}{8}$-in.-diameter single-thread screw has 12 square threads per inch, and the effective coefficient of friction is 0.20. Neglect any friction in the pivot contact at C. What torque M' is required to loosen the clamp?

The 300-Mg jet airliner has three engines, each of which produces a nearly constant thrust of 240 kN during the takeoff roll. Determine the length s of runway required if the takeoff speed is 220 km/h. Compute s first for an uphill takeoff direction from A to B and second for a downhill takeoff from B to A on the slightly inclined runway. Neglect air and rolling resistance.

A ball is released from rest relative to the elevator at a distance $h_1$ above the floor. The speed of the elevator at the time of ball release is $v_0$. Determine the bounce height $h_2$ of the ball (a) if $v_0$ is constant and (b) if an upward elevator acceleration a = g/4 begins at the instant the ball is released. The coefficient of restitution for the impact is e.

A ride at a carnival has four spokes to which pods are attached that can hold two people. The spokes are each 15 m long and are attached to a central axis. Each spoke has mass 200.0 kg, and the pods each have mass 100.0 kg. If the ride spins at 0.2 rev/s with each pod containing two 50.0-kg children, what is the new spin rate if all the children jump of the ride?

A ride at a carnival has four spokes to which pods are attached that can hold two people. The spokes are each 15 $\mathrm{m}$ long and are attached to a central axis. Each spoke has mass $200.0 \mathrm{~kg}$, and the pods each have mass $100.0 \mathrm{~kg}$. If the ride spins at $0.2$ rev/s with each pod containing two $50.0-\mathrm{kg}$ children, what is the new spin rate if all the children jump off the ride?

A boy of mass m is standing initially at rest relative to the moving walkway inclined at the angle $\theta$ and moving with a constant speed u. He decides to accelerate his progress and starts to walk from point A with a steadily increasing speed and reaches point B with a speed $v_r$ relative to the walkway. During his acceleration he generates a constant average force F tangent to the walkway between his shoes and the walkway surface. Write the work-energy equations for the motion between A and B for his absolute motion and his relative motion and explain the meaning of the term muv$_r$. If the boy weighs 150 lb and if u = 2 ft/sec, s = 30 ft, and $\theta$ = 10$^\circ$, calculate the power $P_{rel}$ developed by the boy as he reaches the speed of 2.5 ft/sec relative to the walkway.

A simple pendulum is placed on an elevator, which accelerates upward. If the pendulum is displaced an amount $\theta_0$ and released from rest relative to the elevator, find the tension $T_0$ in the supporting light rod when $\theta$ = 0. Evaluate your result for $\theta_0 = \pi$/2.

Consider the system of previous problem where the mass of the ball is m = 10 kg and the length of the light rod is l = 0.8 m. The ball–rod assembly is free to rotate about a vertical axis through O. The carriage, rod, and ball are initially at rest with $\theta$ = 0 when the carriage is given a constant acceleration $a_O$ = 3 $m/s^2$. Write an expression for the tension T in the rod as a function of $\theta$ and calculate T for the position $\theta = \pi$/2.