Two boys are sliding toward each other on a frictionless, ice-covered parking lot. Jacob, mass 45 kg, is gliding to the right at 7.95 m/s, and Ethan, mass 31.0 kg, is gliding to the left at 10.9 m/s along the same line. When they meet, they grab each other and hang on. (a) What is their velocity immediately thereafter? magnitude m/s direction (b) What fraction of their original kinetic energy is still mechanical energy after their collision? % (c) That was so much fun that the boys repeat the collision with the same original velocities, this time moving along parallel lines 1.02 m apart. At closest approach, they lock arms and start rotating about their common center of mass. Model the boys as particles and their arms as a cord that does not stretch. Find the velocity of their center of mass. magnitude m/s direction (d) Find their angular speed. rad/s (e) What fraction of their original kinetic energy is still mechanical energy after they link arms? % (f) Why are the answers to parts (b) and (e) so different? This answer has not been graded yet.

A nonconducting disk has a radius R, carries a uniform surface charge density s, and rotates with angular speed w.

(a) Consider an annular strip that has radius ?, width ??, and charge ??. Show that the

current produced by this strip is ?? = ?????.

(b) Show that the net magnetic field at the center of the disk is ?)???⁄2.

(c) Find the magnetic field on the axis of the disk, a distance z from the center.

An approximately spherical, black asteroid (emissivity equal to one) of diameter 2km is orbiting the sun at a distance from the sun 10 times larger than the distance from the sum to the earth

a) What is the tempature of this asteroid?

b) What is the wavelength of radiation it emits with maximum intersity?

c) What rediation intersity emitted by the asteroid would be observed on Earth (when the asteroid makes its closet approach, assuming a circular orbit)?

Solar constant (solar power per unit area measured above the earth's atmosphere is 1400 W/m^2).

Distance from the Sun to the Earth is 1.5*10^11m

A cylinder of radius 4.09 cm and a spherical shell of radius 7.47 cm are rolling without slipping along the same floor. The two objects have the same mass. If they are to have the same total kinetic energy, what should the ratio of the cylinder\'s angular speed to the spherical shell\'s angular speed be?

The Moon orbits Earth in a nearly circular orbit that lasts 27.32 days.

1) Determine the distance from the surface of the Moon to the surface of Earth in Mm. (Express your answer to three significant figures.)

A planet orbits a star with an orbital radius of 1 AU. The star has a mass that is 1.60 times our own Sun's mass.

2) Determine the time for one revolution of the planet around the star in years. (Express your answer to three significant figures.)

A 4.5 kg box slides down a 4.2-m -high frictionless hill, starting from rest, across a 2.3-m -wide horizontal surface, then hits a horizontal spring with spring constant 480 N/m . The other end of the spring is anchored against a wall. The ground under the spring is frictionless, but the 2.3-m-long horizontal surface is rough. The coefficient of kinetic friction of the box on this surface is 0.26.

What is the speed of the box just before hitting the spring? How far is the spring compressed? Including the first crossing, how many complete trips will the box make across the rough surface before coming to rest?

An 95.0 kg spacewalking astronaut pushes off a 620 kg satellite, exerting a 80.0 N force for the 0.600 s it takes him to straighten his arms.

How far apart are the astronaut and the satellite after 1.50 min ?

A clock pendulum, made of aluminum, has a period of 1.00 s s and is accurate at 8.0°C. If the clock is used in a climate where the temperature averages 36.0°C what correction is necessary at the end of a 40 day period to the time given by the clock?

Explain the 3 Emissive flat-panel devices: electroluminescent, plasma display and field-emission display with detail to the use of phosfur if used

In words, explain the Lawson criterion and its significance. a)One needs high densities for extended time periods to produce enough energy for fusion reactions to break even. b)One needs high densities for short time periods to produce enough energy for fusion reactions to break even. c)One needs low densities for extended time periods to produce enough energy for fusion reactions to break even. d)One needs low densities for short time periods to produce enough energy for fusion reactions to break even

2. The heat capacity of one mole of aluminum at low temperature (below 50 K) follows the form

CV = aT+bT³

where a = 0.00135 J/K² and b = 2.48×10^-5 J/K⁴. (The first term comes from the free electrons and the second term is due to lattice vibrations.) Use this expression to derive a formula for the molar entropy of aluminum as a function of temperature, assuming that the entropy at 0 K is zero. Finally, determine the ratio of the multiplicity of a mole of aluminum at 10 K to its value at 1 K.

3. In order to take a nice warm bath, you mix 50 liters of hot water at 55 ◦C with 25 liters of cold water at 10 ◦C. Assume that the tub is insulated fiberglass that thermally isolates the water. You can also assume that the mixing happens quickly enough that energy is not lost to the air through the open surface of the water.

(a) How much heat is involved in warming the water?

(b) How much entropy did you create?

why orthogonal components are useful for science?

Charge q = + 15 nC is uniformly distributed on a spherical shell that has a radius of 120 mm.

1. What is the magnitude of the electric field just outside the shell? (Express your answer with the appropriate units.)

2. What is the magnitude of the electric field just inside the shell? (Express your answer with the appropriate units.)

3. What is the direction of the electric field just outside and just inside the shell?

4. What is the electrostatic potential just outside the shell, relative to zero at infinity? (Express your answer with the appropriate units.)

5. What is the electrostatic potential just inside the shell, relative to zero at infinity? (Express your answer with the appropriate units.)

6. What is the electrostatic potential at the shell's center? (Express your answer with the appropriate units.)

7. What is the electric field magnitude at the shell's center? (Express your answer with the appropriate units.)

In this experiment, we have claimed to measure the speed of sound in air. To do this, we have used an audible frequency sweep. Why can we claim that the speed of sound will be the same over the bandwidth of the sweep? Is this assertion justified based on your results from experiment 2? Hint: Consider how sound (longitudinal pressure waves) propagate in a medium. (5 pts)

A woman of mass m = 58.9 kg sits on the left end of a seesaw—a plank of length L = 4.04 m, pivoted in the middle.

(a) First compute the torques on the seesaw about an axis that passes through the pivot point. Where should a man of mass M = 69.9 kg sit if the system (seesaw plus man and woman) is to be balanced?
1.702m (Correct)

(b) Find the normal force exerted by the pivot if the plank has a mass of m_pl = 12.8 kg.
1387.68N (Correct)

(c) Repeat part (a), but this time compute the torques about an axis through the left end of the plank.
1.65m (Correct)

QUESTION: Suppose a 27.8-kg child sits 0.73 m to the left of center on the same seesaw as the problem you just solved in the PRACTICE IT section. A second child sits at the end on the opposite side, and the system is balanced.

(a) Find the mass of the second child 10.05 kg?

(b) Find the normal force acting at the pivot point.____N?