A beam of light traveling in an unknown material encounters a boundary with flint glass (n = 1.66). If the critical angle for total internal reflection is $32^{\circ}$, what is the index of refraction of the unknown material?

A beetle sits near the rim of a turntable that rotates without friction about a vertical axis. The beetle then begins to walk toward the center of the turntable. As a result, does the angular speed of the turntable increase, decrease, or stay the same?

The ability to hear a pin drop is the sign of sensitive hearing. Suppose a 0.55-g pin is dropped from a height of 28 cm, and the pin emits sound for 1.5 s when it lands. Assuming that all of the mechanical energy of the pin is converted to sound energy and that the sound radiates uniformly in all directions, find the maximum distance from which a person can hear the pin drop. (This is the ideal maximum distance, but atmospheric absorption and other factors will make the actual maximum distance considerably smaller. Recall that the minimum intensity of sound a human can hear is $10^{-12} \mathrm{W} / \mathrm{m}^{2}$.)

As a 0.43-kg soccer ball rolls on a grassy field, its speed decreases from 4.9 m/s to zero in 3.1 s. What is the average force exerted by the grass on the ball?

A 9.0-V battery is connected in series with four resistors $(220 \Omega, 510 \Omega, 330 \Omega, \text { and } 160 \Omega)$. (a) How much current is supplied by the battery? (b) What is the potential difference across the $330-\Omega$ resistor?

When you touch a piece of metal and a piece of wood that are both at room temperature, the metal feels cooler. Why?

When you lift a bowling ball with a force of 82 N, the ball accelerates upward with an acceleration $a.$ If you lift with a force of92 N, the ball's acceleration is $2 a$. Find (a) the weight of the bowling ball and (b) the acceleration $a$.

Light is refracted as it travels from point A in substance 1 to point B in substance 2. If the index of refraction is 1.33 for substance 1 and 1.51 for substance 2, how much time does it take light to go from A to B assuming that it travels 331 cm in substance 1 and 151 cm in substance 2?

Three resistors $(65 \Omega, 550 \Omega, \text { and } 320 \Omega)$ are connected in parallel. (a) Is the equivalent resistance of these resistors greater than, less than, or equal to $65 \Omega$? Explain. (b) What is the equivalent resistance of the three resistors?

A hollow pipe is cooled. Does the cylindrical volume within the pipe increase, decrease, or stay the same?

Water flows through a pipe with a speed of 2.1 m/s. Find the flow rate in kg/ s if the diameter of the pipe is 3.8 cm.

Object 1 has a moment of inertial $I$ and an angular speed $\omega$. Object 2 has a moment of inertia equal to $2 I$. What angular speed must object 2 have if its angular momentum is to be the same as the angular momentum of object 1?

When a 0.15-kg baseball is struck by a bat, its velocity changes from -12 m/s to 27 m/s in a certain direction. (a) What is the impulse delivered to the ball? (b) If the bat is in contact with the ball for $3.4 \times 10^{-3} \mathrm{s}$, s, what is the force it exerts on the ball?

Two cars move directly toward one another in a parking lot. Car 1 has a mass of 1600 kg and a speed of 1. 5 m/s in the positive direction. Car 2 has a mass of 2100 kg and a speed of 1.4 m/s in the negative direction. (a) What is the total momentum of the two cars? (b) What speed should car 2 have for the total momentum of the two cars to be zero?