A weight is attached to a spring suspended from a beam. At time t = 0, it is pulled down to a point 7 cm above the ground and released. After that, it bounces up and down between its minimum height of 7 cm and a maximum height of 25 cm, and its height h(t) is a sinusoidal function of time t. It first reaches a maximum height 1.4 seconds after starting.

(b) What are the mean, amplitude, phase shift and period for this function? (Use a phase shift with an absolute value less than the period.)

(c) Give four different possible values for the phase shift. (Enter your answers as a comma-separated list.)

(d) Write down a formula for the function h(t) in standard sinusoidal form; i.e. as in the equation shown below.

h(t) = A sin (2pi/B (t-C)) + D

(e) What is the height of the weight after 4.2 seconds?

Q10. Assume that the Earth is orbiting the sun in a perfectly circular orbit. If the Earth is hit by a huge meteorite but its orbiting angular momentum is not changed (this can be the case if the hit is along the radial direction of the orbit), what would be the change in Earth’s orbit?

A. No change

B. Earth would move in a circular orbit with a larger radius

C. Earth would move in a circular orbit with a smaller radius

D. Earth’s orbit would not change, but its period is lengthened

E. Earth’s orbit would become elliptical

Three children are riding on the edge of a merry‑go‑round that has a mass of 105 kg and a radius of 1.70 m . The merry‑go‑round is spinning at 24.0 rpm. The children have masses of 22.0, 28.0, and 33.0 kg. If the 28.0 kg child moves to the center of the merry‑go‑round, what is the new angular velocity in revolutions per minute? Ignore friction, and assume that the merry‑go‑round can be treated as a solid disk and the children as point masses. final angular velocity: rpm

A white billiard ball with mass m_w = 1.5 kg is moving directly to the right with a speed of v = 3 m/s and collides elastically with a black billiard ball with the same mass m_b = 1.5 kg that is initially at rest. The two collide elastically and the white ball ends up moving at an angle above the horizontal of θ_w = 30° and the black ball ends up moving at an angle below the horizontal of θ_b = 60°.

1)

What is the final speed of the white ball?
m/s

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2)

What is the final speed of the black ball?
m/s

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3)

What is the magnitude of the final total momentum of the system?
kg-m/s

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4)

What is the final total energy of the system?
J

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A railroad freight car rolls on a track at 2.65 m/s toward two identical coupled freight cars, which are rolling in the same direction as the first, but at a speed of 1.20 m/s. The first reaches the second two and all couple together. The mass of each is 2.30 ✕ 10⁴ kg.

(a) What is the speed (in m/s) of the three coupled cars after the first couples with the other two? (Round your answer to at least two decimal places.)

(b)Find the (absolute value of the) amount of kinetic energy (in J) converted to other forms during the collision.

A block of mass m1 = 1.60 kg initially moving to the right with a speed of 4.00 m / s on a track
horizontal without friction and collides with a spring attached to a second block of mass m2 = 2.10 kg that initially
moves to the left with a speed of 2.50 m / s. The spring constant is 600 N / m.
a) Find the speeds of the two blocks after the collision.
b) During the collision, at the instant when block 1 moves to the right with a speed of 3.00 m / s, determine the
speed of block 2.
c) Determine the distance that the spring is compressed at that instant.

Describe the evidence for a supermassive black hole at the center of our Galaxy.

a) How did interstellar extinction mislead astronomers into believing that we are at the center of our galaxy?

b) Describe how Harlow Shapley proved that the Sun is not at the center of our galaxy.

Imagine you are a punter on a football team and the coach tells you to give your players a chance to get down the field. With which angle with the horizontal would you punt the ball? Explain. A. 15 degrees B. 45 degrees C. 65 degrees D. It doesn't matter.

When you hold an insect at the near point of your eye it subtends an angle of 5.00 10-3 rad. Determine the maximum angular size of the insect when viewed through a magnifying glass (simple magnifier) that has a focal length of 8.70 cm.

explain how the process of doping is attained to achieve extrinsic semiconductors with different electrical properties ?

describe how the energy gap of a semiconductor is different from that of insulator and conductor .

Suppose a charge of -2.40 µC is at the origin and a charge of 3.10 µC is at the point (0, 3.00) m.

(a) Find the electric potential at (4.00, 0) m, assuming the electric potential is zero at infinity. What is electric potential? What factors affect the size of the electric potential at a particular point?

(b) Find the work necessary to bring a 4.10 µC charge from infinity to the point (4.00, 0) m.

A stone is dropped at t = 0. A second stone, with twice the mass of the first, is dropped from the same point at t = 234 ms.
How far below the release point is the center of mass of the two stones at t = 326 ms? (Neither stone has yet reached the ground.)

How fast is the center of mass of the two-stone system moving at that time?

Briefly describe how the distance traveled by the football might be different if the landing height was different than the release (kicking) height?