The $1360-\mathrm{kg}$ car travels along a straight road of increasing grade whose vertical profile is given by the equation shown. The magnitude of the car's velocity is a constant $100 \mathrm{~km} / \mathrm{h}$. When $x=200 \mathrm{~m}$, what are the $x$ and $y$ components of the total force acting on the car (including its weight)?

Strategy: You know that the tangential component of the car's acceleration is zero. You can use this condition together with the equation for the profile of the road to determine the $x$ and $y$ components of the car's acceleration.

A mass is placed on a frictionless, horizontal table. A spring (k = 100 N/m), which can be stretched or compressed, is placed on the table. A 5.00-kg mass is attached to one end of the spring, the other end is anchored to the wall. The equilibrium position is marked at zero. A student moves the mass out to x = 4.0 cm and releases it from rest. The mass oscillates in SHM. (a) Determine the equations of motion. (b) Find the position, velocity, and acceleration of the mass at time t = 3.00 s.

A $500-\mathrm{g}$ collar can slide without friction on the curved rod $B C$ in a horizontal plane. Knowing that the undeformed length of the spring is $80 \mathrm{~mm}$ and that $k=400\ \mathrm{kN} / \mathrm{m}$, determine $(a)$ the velocity that the collar should be given at $A$ to reach $B$ with zero velocity, (b) the velocity of the collar when it eventually reaches $C$.

End A of the link has a downward velocity $v_A$ of 2 m/s during an interval of its motion. For the position where $\theta=30^{\circ}$ determine the angular velocity $\omega$ of AB(200m) and the velocity $v_G$ of the midpoint G of the link. Solve the relative-velocity equations, first, using the geometry of the vector polygon and, second, using vector algebra.

Suppose nuclei must be within a distance of $3 \mathrm{fm}$ for the strong force to become effective. What temperature is required in order to initiate fusion of ${ }^2 \mathrm{H}$ and ${ }^3 \mathrm{H}$ ? Assume a thermal energy of $\frac{3}{2} k T$ per nucleon.

Squid use jet propulsion for rapid escapes. A squid pulls water into its body and then rapidly ejects the water backward to propel itself forward. A 1.5 kg squid (not including water mass) can accelerate at $20 \mathrm { m } / \mathrm { s } ^ { 2 }$ by ejecting 0.15 kg of water. a. What is the magnitude of the thrust force on the squid? b. What is the magnitude of the force on the water being ejected? c. What acceleration is experienced by the water?

A 0.30-kg puck, initially at rest on a frictionless horizontal surface, is struck by a 0.20-kg puck that is initially moving along the x-axis with a velocity of 2.0 m/s. After the collision, the 0.20-kg puck has a speed of 1.0 m/s at an angle of $\theta = 53 ^ { \circ }$ to the positive x-axis. Find the fraction of kinetic energy lost in the collision.

A tank contains 11.0 g of chlorine gas $\left(\mathrm{Cl}_{2}\right)$ at a temperature of $82^{\circ} \mathrm{C}$ and an absolute pressure of $5.60 \times 10^{5}$ Pa. The mass per mole of $\mathrm{Cl}_{2}$ is 70.9 g/mol. (a) Determine the volume of the tank. (b) Later, the temperature of the tank has dropped to $31^{\circ} \mathrm{C}$ and, due to a leak, the pressure has dropped to $3.80 \times 10^{5}$ Pa. How many grams of chlorine gas have leaked out of the tank?

What is the angular position in radians of the minute hand of a clock at (a) 5:00, (b) 7:15, and (c) 3:35?

Carbon dioxide $\left(\mathrm{CO}_2\right)$ modeled as an ideal gas flows through the compressor and heat exchanger shown in figure. The power input to the compressor is $100 \mathrm{~kW}$. A separate liquid cooling water stream flows through the heat exchanger. All data are for operation at steady state. Stray heat transfer with the surroundings can be neglected, as can all kinetic and potential energy changes. Determine (a) the mass flow rate of the $\mathrm{CO}_2$, in $\mathrm{kg} / \mathrm{s}$, and (b) the mass flow rate of the cooling water, in $\mathrm{kg} / \mathrm{s}$.

A pen contains a spring with a spring constant of 250 N/m . When the tip of the pen is in its retracted position, the spring is compressed 5.0 mm from its unstrained length. In order to push the tip out and lock it into its writing position, the spring must be compressed an additional 6.0 mm. How much work is done by the spring force to ready the pen for writing? Be sure to include the proper algebraic sign with your answer.

A discus thrower starts from rest and begins to rotate with a constant angular acceleration of $2.2 \mathrm{rad} / \mathrm{s}^2$. How many revolutions does it take for the discus thrower's angular speed to reach $6.3 \mathrm{rad} / \mathrm{s}$ ?

The two barges shown here are coupled by a cable of negligible mass. The mass of the front barge is $2.00 \times 10^3 \mathrm{~kg}$ and the mass of the rear barge is $3.00 \times 10^3 \mathrm{~kg}$. A tugboat pulls the front barge with a horizontal force of magnitude $20.0 \times 10^3 \mathrm{~N}$, and the frictional forces of the water on the front and rear barges are $8.00 \times 10^3 \mathrm{~N}$ and $10.0 \times 10^3 \mathrm{~N}$, respectively. Find the horizontal acceleration of the barges and the tension in the connecting cable.

For an ideal gas $C_{V}$ and $C_{p}$ are different because of the work W associated with the volume change for a constant-pressure process. To explore the difference between $C_{V}$ and $C_{p}$ for a liquid or a solid, consider the process in which 5.00 mol of ethanol is warmed from 10.0$^{\circ} \mathrm{C}$ to 60.0$^{\circ} \mathrm{C}$ while the applied pressure remains a constant 1.00 atm. The molar mass of ethanol is M=46.1 g/mol. What is the mass of 5.00 mol of ethanol?