A heat engine does $650 \mathrm{~J}$ of work and dumps $1270 \mathrm{~J}$ of heat to its cold reservoir. What's its efficiency?

the interference pattern on a screen $1.0 \mathrm{~m}$ behind an 800 lines $/ \mathrm{mm}$ diffraction grating. What is the wavelength (in nm) of the light?

An object is located in air 5 cm from the vertex of a concave surface made of glass with a radius of curvature 20 cm. Where does the image form by refraction and what is its magnification? Use $n_{air}$= 1 and $n_{glass}$ = 1.5 .

A coin is placed $13.0 \text{ cm}$ from the axis of a rotating turntable of a variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of $38.0\text{ rpm}$ (revolutions per minute) is reached, at which point the coin slides off. What is the coefficient of static friction between the coin and the turntable?

When an earthquake occurs, two types of sound waves are generated and travel through the earth. The primary, or P, wave has a speed of about 8.0 km/s and the secondary, or S, wave has a speed of about 4.5 km/s. A seismograph, located some distance away, records the arrival of the P wave and then, 78 s later, records the arrival of the S wave. Assuming that the waves travel in a straight line, how far is the seismograph from the earthquake?

How much work is required to compress 5.00 mol of air at $20.0^{\circ} \mathrm{C}$ and 1.00 atm to one-tenth of the original volume (a) by an isothermal process? (b) What If? How much work is required to produce the same compression in an adiabatic process? (c) What is the final pressure in part (a)? (d) What is the final pressure in part (b)?

The length of nylon rope from which a mountain climber is suspended has an effective force constant of

$$1.40 × 10^4 N/m.$$

(a) What is the frequency at which he bounces, given his mass plus and the mass of his equipment are 90.0 kg? (b) How much would this rope stretch to break the climber's fall if he free-falls 2.00 m before the rope runs out of slack? (Hint: Use conservation of energy.) (c) Repeat both parts of this problem in the situation where twice this length of nylon rope is used.

A 3.00-kg block is connected to two ideal horizontal springs having force constants $\mathrm { k } _ { 1 } = 25.0 \mathrm { N } / \mathrm { cm }$ and $\mathrm { k } _ { 2 } = 20.0 \mathrm { N } / \mathrm { cm }$. The system is initially in equilibrium on a horizontal, frictionless surface. The block is now pushed 15.0 cm to the right and released from rest. What is the maximum speed of the block? Where in the motion does the maximum speed occur?

The turnbuckle is tightened until the tension in the cable AB equals 2.4 kN. Determine the vector expression for the tension T as a force acting on member AD. Also find the magnitude of the projection of T along the line AC.

The angular acceleration of a wheel is $\alpha = 6.0t^4-4.0t^2$, with α in radians per second-squared and t in seconds. At time $t = 0$, the wheel has an angular velocity of $+2.0\text{~ rad/s}$ and an angular position of $+1.0 \text{~rad}$. Write expressions for the angular velocity $(\text{rad/s})$.

A Carnot engine is operated between two heat reservoirs at temperatures of $520 \mathrm{~K}$ and $300 \mathrm{~K}$.
(b) How much mechanical work is performed by the engine during each cycle?

A Carnot engine is operated between two heat reservoirs at temperatures of 520 K and 300 K. (a) If the engine receives 6.45 kJ of heat energy from the reservoir at 520 K in each cycle, how many joules per cycle does it discard to the reservoir at 300 K? (b) How much mechanical work is performed by the engine during each cycle? (c) What is the thermal efficiency of the engine?

A slit 0.360 mm wide is illuminated by parallel rays of light that have a wavelength of 540 nm. The diffraction pattern is observed on a screen that is 1.20 m from the slit. The intensity at the center of the central maximum $\left(\theta=0^{\circ}\right)$ is $I_{0}$. (a) What is the distance on the screen from the center of the central maximum to the first minimum? (b) What is the distance on the screen from the center of the central maximum to the point where the intensity has fallen to $I_{0}/2$?

A swift blow with the hand can break a pine board. As the hand hits the board, the kinetic energy of the hand is transformed into elastic potential energy of the bending board; if the board bends far enough, it breaks. Applying a force to the center of a particular pine board deflects the center of the board by a distance that increases in proportion to the force. Ultimately the board breaks at an applied force of 800 N and a deflection of 1.2 cm. a To break the board with a blow from the hand, how fast must the hand be moving? Use 0.50 kg for the mass of the hand. b. If the hand is moving this fast and comes to rest in a distance of 1.2 cm, what is the average force on the hand?