A parallel-plate capacitor made of circular plates of radius 65 cm separated by 0.30 cm is charged to a potential difference of 800 Volts by a battery. Then a sheet of mylar is pushed between the plates, completely filling the gap between them. How much additional charge flows from the battery to one of the plates when the mylar is inserted?

Two identical containers are open at the top and are connected at the bottom via a tube of negligible volume and a valve that is closed. Both containers are filled initially to the same height of 1.00 m, one with water, the other with mercury, as the drawing indicates. The valve is then opened. Water and mercury are immiscible. Determine the fluid level in the left container when equilibrium is reestablished.

A positively charged particle is held at the center of a spherical shell. The figure gives the magnitude E of the electric field versus radial distance r. The scale of the vertical axis is set by E_s = 8.0

For each of the pairs of objects below, decide which object has the larger moment of inertia, selecting from the following answers: A) the first B) the second C) neither D) can't tell E.g., if the answer for the first pair is B and for the rest, D, enter BDDDDD. The objects are of uniform density. Unless otherwise indicated, the flat objects rotate about an axis perpendicular to the plane in which they lie.

1.(A) A thin circular sheet of material of radius a/sqrt(2) rotating about its centre, or (B) a thin square sheet of the same material of side a, also rotating about its centre.

2.(A) A thin square sheet of material of side a rotating about its centre, or (B) a thin sheet of the same material in the form of an equilateral triangle of side a, also rotating about its centre.

3.(A) A thin circular sheet of material of radius a/2 rotating about a tangent, or (B) a thin square sheet of the same material of side a, rotating about its lower edge.

4.(A) A rod of mass m and length ℓ rotating about its centre, or (B) a rod of mass m and length 2ℓ, also rotating about its centre.

5.(A) A sphere rotating about its axis, or (B) the same sphere rotating about a parallel axis, tangent to the surface.

6.(A) A cylindrical shell rolling on a table, or (B) a solid cylinder of identical mass and size, also rolling.

We observe a glancing collision between two billiard balls of the same mass. The first ball is incident at a speed of 6.36 m/s, strikes the second ball (initially at rest) and moves off with a speed of 5.54 m/s at an angle of 29.5

If an object is projected at a given angle and speed, how long does it take to reach its maximum height?

Please explain in simplest terms and give an example using units given.

A satellite in a circular orbit around the earth with a radius 1.011 times the mean radius of the earth is hit by an incoming meteorite. A large fragment (m = 81.0 kg) is ejected in the backwards direction so that it is stationary with respect to the earth and falls directly to the ground. Its speed just before it hits the ground is 361.0 m/s. Find the total work done by gravity on the satellite fragment. RE 6.37·103 km; Mass of the earth= ME 5.98·1024 kg.

An asteroid is discovered to have a tiny moon that orbits it in a circular path at a distance of 151 km and with a period of 43.0 h. The asteroid is roughly spherical (unusual for such a small body) with a radius of 15.9 km.
a) Find the acceleration of gravity at the surface of the asteroid.

b) Find the escape velocity from the asteroid.

A plane flies at 1.75 times the speed of sound. Its sonic boom reaches a man on the ground 1.00 min after the plane passes directly overhead. What is the altitude of the plane? Assume the speed of sound to be 330 m/s.

An unstable particle with a mass equal to 3.34x10^-27 kg is initially at rest. The particle decays into two fragments that fly off with velocities of 0.981c and -0.863c, respectively. Find the masses of the fragments. (Hint: Conserve both mass-energy and momentum.)

m = 0.981c = _______kg

m = -0.863c = ______kg

U22P1 In the reflection and refraction lab a beam of white light is passed through a prism at an angle of 30 and separated into a spectrum. The red portion of the spectrum is measured to be at an angle of 52 and the blue at 55 . What is the index of refraction for each color?

nred = ________

nblue = _______ What is the velocity of the blue light as it passes through the prism.

vblue prism = ___________

A 0.200-kg block on a smooth horizontal surface gains a speed of 28.2 cm/s when it is released from rest at the free end of a spring that is compressed by 3.20 cm. The block is then connected to the free end of the spring to form a mass-spring system.

What is the spring constant? (A) 15.5 N/m; (B) 16.5 N/m; (C) 17.5 N/m; (D) 18.5 N/m; (E) 19.5 N/m.

What is the period of this harmonic oscillator? (A) 0.413 s; (B) 0.513 s; (C) 0.613 s; (D) 0.713 s; (E) 0.813 s.

What happens to the period if the mass of the block is doubled? (A) No change; (B) Doubled; (C) Increased by 40%; (D) Decreased by 40%; (E) Quadrupled.

Two tugboats pull a disabled supertanker. Each tug exerts a constant force of 1.9×10⁶ N, one an angle 10 ∘ west of north and the other an angle 10 ∘ east of north, as they pull the tanker a distance 0.87 km toward the north.

What is the total work they do on the supertanker?

Express your answer in joules.