The best laboratory vacuum has a pressure of about 1.00 x 10-18 atm, or 1.01 x 10-13 Pa. How many gas molecules are in 8.57 cm3 in such a vacuum at 298 K?

A 100g ball is tied to a string so that the center its mass hangs 60 cm below the point where the string is tied to a support rod. The ball is pulled aside to a 70° angle with vertical and released. As the string approaches vertical, it encounters a peg at a distance x below the support rod. The string then bends around the peg. If the position of the peg is low enough, the ball will move in a circle wrapping the string around the peg. a. Draw a FBD for the ball. Starting from the definition of work W=F d cos, demonstrate and explain the work done by each of the force on your FBD. b. What is the work done by nonconservative force? What can you say about the total mechanical energy for the ball as it swing and rotate around the support rod and peg. c. What is the smallest value of x for which the ball will move in a circle wrapping the string around the peg? Note: to answer the last question c, first explain what happen to the mechanical energy, gravitational potential energy, kinetic energy, speed, and centripetal force of the ball as you decrease x. Then predict what will happen to the mechanical energy, gravitational potential energy, kinetic energy, speed, and centripetal force when x reaches its minimum value. Set up a mathematical equation that satisfy the condition for minimum x and solve it based on the conditions provided.

A 50.0-g Super Ball traveling at 30.0 m/s bounces off a brick wall and rebounds at 21.0 m/s. A high-speed camera records this event. If the ball is in contact with the wall for 3.05 ms, what is the magnitude of the average acceleration of the ball during this time interval?

A jet plane lands with a speed of 91 m/s and can accelerate at a maximum rate of −5.80 m/s² as it comes to rest. From the instant the plane touches the runway, what is the minimum time needed before it can come to rest?

A tennis player tosses a tennis ball straight up and then catches it after 2.00 s at the same height as the point of release.

(a) what is the acceleration of the ball while it is in flight?

(b) what is the velocity of the ball when it reaches its maximum height?

(c) the initial velocity of the ball and

(d) the maximum height it reaches

Two manned satellites approaching one another at a relative speed of 0.400 m/s intend to dock. The first has a mass of 2.50 ✕ 10³ kg, and the second a mass of 7.50 ✕ 10³ kg. Assume that the positive direction is directed from the second satellite towards the first satellite.

(a) Calculate the final velocity after docking, in the frame of reference in which the first satellite was originally at rest..(m/s)

(b) What is the loss of kinetic energy in this inelastic collision?

(c) Repeat both parts, in the frame of reference in which the second satellite was originally at rest.
final velocity (m/s) and loss of kinetic energy (J).

(d) Explain why the change in velocity is different in the two frames, whereas the change in kinetic energy is the same in both.

What is the difference between a photo-interrupter and an opto-isolator?

A 193 Ω resistor, a 0.750 H inductor, and a 6.00 μF capacitor are connected in series across a voltage source that has voltage amplitude 28.5 V and an angular frequency of 245 rad/s . What is vR at t= 18.0 ms ? What is vL at t= 18.0 ms ? What is vC at t= 18.0 ms ?

In a rainy Summer day you observe a beautiful rainbow. Complete the following statements with greater than, less than, or equal to.

1. The wavelength of the light inside a raindrop is ... the wavelength of the same light in air.

2. The speed of the light inside a raindrop is ... the speed of light in air.

3. The frequency of the light inside a raindrop is ... the frequency of the same light in air.

In the ground state of the Hydrogen atom the energy of the electron is E₀ = -13.61 eV. What is the energy of the electron in the ground state of the He⁺ ion?

What is the energy of the electron in the ground state of the Li⁺⁺ ion?

The electron in the He⁺ ion is excited to the n = 2 principal state. What is the energy of the electron now?

What is the energy of the electron in the Li⁺⁺ ion in the n = 2 principal state?

What is the energy of the electron in the Li⁺⁺ ion in the n = 3 principal state?

Take element Z = 47 from the periodic table. Ionize it 46 times so that there is only one electron left orbiting around the nucleus. What is the ground state energy of the electron?

What is the energy of the electron when it is in the n = 8 principal state in the ion above?

Example 1:  H2O boils at 100ºC and 1 atm.  At what temperature will water boil

if pressure = 500 torr (1 atm / 760 torr) = 0.658 atm?

DvapH = 40.66 kJ mol-1.

Can you please show all steps and equations??? Thank you

A bee is flying down South with a velocity of 10 m/s, the wind is blowing toward the bee at a constant velocity of 3 m/s in the direction of the North-West. How far does the bee travel after 10 sec and at what direction? At what velocity should the bee fly in order to keep itself moving straight toward the South at 5 m/s?

Three particles are fixed on an x axis. Particle 1 of charge q₁ is at x = -a and particle 2 of charge q₂ is at x = +a. If their net electrostatic force on particle 3 of charge Q is to be zero, what must be the ratio q₁/q₂ when particle 3 is at (a) x = +0.754a and (b) x = +1.65a?

What is a good application of an RC circuit? Explain how the RC circuit carries out its function in the application.

A fox fleeing from a hunter encounters a 0.675 m tall fence and attempts to jump it. The fox jumps with an initial velocity of 7.50 m/s at an angle of 45.0°, beginning the jump 1.94 m from the fence. By how much does the fox clear the fence? Treat the fox as a particle.

Particle A and particle B are held together with a compressed spring between them. When they are released, the spring pushes them apart and they then fly off in opposite directions, free of the spring. The mass of A is 5.00 times the mass of B, and the energy stored in the spring was 30 J. Assume that the spring has negligible mass and that all its stored energy is transferred to the particles. Once that transfer is complete, what are the kinetic energies of (a) particle A and (b) particle B?

A 28.5 kg block is being pulled by a force F = 245 N up along a rough incline. The coefficient of kinetic friction between the block and the incline is μk = 0.30. The block is pulled through a distace of 21.0 m. Angle is 33 degrees.

(a) Solve for the magnitude of the normal force FN (in Newtons)? Calculate the work (in Joules) done by the normal force. Pay attention to the angle in the work formula and the sign of work.

(b) What is the magnitude of the kinetic frictional force (in Newtons)? Calculate the work (in Joules) done by the kinetic frictional force. Pay attention to the angle in the work formula and the sign of work.

(c) Calculate the work (in Joules) done by the pulling force F. Pay attention to the angle in the work formula and the sign of work.

(d) The block starts from rest at the bottom of the incline. After it is pulled through a distance of 21.0 m up along the incline, what is its vertical height (in meters), hf? What is its speed (in m/s) after being pulled through 21.0 m?

(e) Add up the works (in Joules) done by all NONCONSERVATIVE Forces:

(e)