A 11.4-kg block rests on a horizontal table and is attached to one end of a massless, horizontal spring. By pulling horizontally on the other end of the spring, someone causes the block to accelerate uniformly and reach a speed of 4.08 m/s in 1.13 s. In the process, the spring is stretched by 0.231 m. The block is then pulled at a constant speed of 4.08 m/s, during which time the spring is stretched by only 0.0543 m. Find (a) the spring constant of the spring and (b) the coefficient of kinetic friction between the block and the table.
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A solid, homogeneous sphere with a mass of m0, a radius of r0 and a density of ρ0 is placed in a container of water. Initially the sphere floats and the water level is marked on the side of the container. What happens to the water level, when the original sphere is replaced with a new sphere which has different physical parameters?
Notation: r means the water level rises in the container, f means falls, s means stays the same.
1. The new sphere has a density of ρ = ρ0 and a
radius of r < r0.
2. The new sphere has a mass of m > m0 and a density
of ρ = ρ0.
3. The new sphere has a radius of r > r0 and a mass
of m = m0.
4. The new sphere has a mass of m = m0 and a density
of ρ > ρ0.
5. The new sphere has a radius of r = r0 and a density
of ρ > ρ0.
6. The new sphere has a mass of m > m0 and a radius
of r = r0.
7. The new sphere has a density of ρ < ρ0 and a
radius of r > r0.
8. The new sphere has a radius of r < r0 and a mass
of m > m0.
9. The new sphere has a density of ρ > ρ0 and a mass
of m < m0.
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The mass of the moon is 7.34 × 1022 kg, and its radius is about 1.74 × 106 m
(a) What is the value of “gmoon”, that is, the acceleration of gravity for a falling object near the surface of the moon?
(b) What is the escape speed (from the moon) for an object on the surface of the moon?
(c) What is the escape speed from the earth for an object that is as far from the earth as the orbit of the moon?
(d) At some point between the earth and the moon, an object would be pulled with equal strength towards both bodies. How far from the earth is that point?
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Why are there very few helium (and deuterium) nuclei a hundredth of a second after the big bang? Select all the statements that are both correct and relevant.
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At this point in time there are so few protons in the universe that we can't create deuterium or helium. |
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The temperature is so high that any created would quickly be destroyed in a collision |
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Any created would quickly decay away |
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Any created would be broken apart by high energy photons |
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Lots of high energy collisions are happening which would break apart any that were created. |
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The collisions are not of high enough energy to create any of them. There is no way to create any of them. |
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At this point in time there are so few protons in the universe that we can't create deuterium or helium. |
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At this point in time there are no free electrons to combine with protons. |
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At this point in time there are not enough muons to create deuterium or helium. |
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None of the above |
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A mass is moving at 10 m/s in the +x direction and it collides in a perfectly elastic collision with a mass of 2 kg moving in the -x direction. The collision takes places in 0.21 seconds and after the collision the mass that was moving in the +x direction is moving in the -x direction at 9 m/s and the mass that was moving in the -x direction is moving in the +x direction at 13 m/s. What is the magnitude of the average force, in Newtons, on the first mass which was originally moving in the +x direction before the collision?
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The mass of a meteor with a radius of 1 km is about 9 x 1012 kg. The mass of a meteor also is proportional to the cube of its radius. Suppose a meteor with a radius of 8.8 km is moving at 1.7 x 104 m/s when it collides inelastically with the Earth. The Earth has a mass of 5.97 x 1024 kg and assume the Earth is stationary. The kinetic energy lost by the asteroid in this collision will be transferred to non-conservative work in heating the atmosphere and physically destroying the place where it lands. The Tsar Bomb, the largest atomic bomb ever tested, released 2.1 x 1017 J of energy. (Which, by the way, is 1000's of times more energy compared to the atomic bombs dropped in World War II.) How many MILLIONS of equivalent Tsar Bombs is the kinetic energy lost of this meteor?
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1) A diver of mass 43.0kg stands on the end of a uniform diving board over the water. The board is 7.00m long and has a mass of 75kg. The end of the board opposite the diver is attached to the platform. The bounce of the board is adjusted by a roller underneath that can be moved back and forth. The roller is 2.80 m from the fixed end of the board. a) What are the magnitude and the direction of the force on the board due to the roller? Show your work and explain your reasoning. b) What are the magnitude and the direction of the force on the board due to the diver? Assume the diver is stationary and the board is not bouncing. Show your work and explain your reasoning
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Please provide an example of a damped harmonic oscillator. They are more common than undamped or simple harmonic oscillators. What do you think there is any harmonic motion in the physical world that is not damped harmonic motion? Try to make a list of five examples of undamped harmonic motion and damped harmonic motion. Which list was easier to make? Why are the group of the peoples in general ordered to “route step” (walk out of step) across a bridge?
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What is the smallest number of whole logs (density = 735 kg/m³, radius = 0.077 m, length = 2.91 m) that can be used to build a raft that will carry 3 people, each of whom has a mass of 76.0 kg?
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A plank of length l = 2m is hinged at one end to a wall. The other end is being (temporarily) supported by a worker who is holding it up with his hand, keeping the plank horizontal. The plank has a mass of 20kg, and there is also a toolbox of mass 5kg sitting on it, 50cm away from the worker (1.5 m away from the wall). (a) Draw a free body diagram and an extended free-body diagram for the plank. (b) What are the magnitudes of (1) the upwards force exerted by the worker on the plank and (2) the force at the hinge?(c) If the worker were to let go of the plank, what would its angular acceleration be as it starts swinging down? The moment of inertia is I = 1Ml2. (Note: assume the toolbox stops pressing down on the plank immediately. This is a good approximation, as you shall see below.)(d) Consider a point on the plank located immediately below the toolbox. As the plank swings, this point moves in a circle of radius 1.5 m. What is its linear (tangential) acceleration as it starts going down, and how does it compare to the acceleration of gravity?
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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.
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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.
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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
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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?
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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.)
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