A railroad car moving at a speed of 3.20 m/s overtakes, collides, and couples with two coupled railroad cars moving in the same direction at 1.20 m/s. All cars have a mass of mass 1.10 105 kg. Determine the following.

(a) speed of the three coupled cars after the collision____ (Give your answer to at least two decimal places.) m/s

(b) kinetic energy lost in the collision ___ J

2. A cue ball at rest on a frictionless pool table is hit dead center by a pool stick, giving it an impulse of +0.55 N · s. The ball slides (the combination of hitting the ball dead center and no friction allows this to happen) along the table and makes a head-on elastic collision with another pool ball. If both pool balls have a mass of 0.166 kg, determine the velocity of the second ball the instant after the collision. (Indicate the direction with the sign of your answer.) m/s

A vacuum tube diode consists of concentric cylindrical electrodes, the negative cathode and the positive anode. Because of the accumulation of charge near the cathode, the electric potential between the electrodes is not a linear function of the position, even with planar geometry, but is given by V(x)=Cx4/3 where x is the distance from the cathode and C is a constant, characteristic of a particular diode and operating conditions. Assume that the distance between the cathode and anode is 14.0 mm and the potential difference between electrodes is 200 V

Determine the value of C

Obtain a formula for the electric field between the electrodes as a function of x.

Determine the magnitude of the force on an electron when the electron is halfway between the electrodes

Determine the direction of the force on an electron when the electron is halfway between the electrodes

A wall in a building has a width of 15 m and a height of 3 m. It is made of several layers — a layer of motionless air with an R value of 0.12 K m^2 / W, a 12.4 mm thick layer of gypsum board with a thermal conductivity of 0.17 W/m K, a layer of brick with an R value of 1.7 m^2/ W, and another layer of motionless air with an R value of 0.12 K m^2 / W.

(a) If the temperature inside the building is 27.2 °C and the temperature outside is 33.1 °C, how much power will flow through the wall in steady state?

(b) How much power will flow if we add a layer of foam insulation with an R value of 27.0 K m2/ W?

Earth has a mass of 6.0 x10^24 kg and the moon 7.3 x 10^22 kg. The center of the moon is 238,900 miles from the center of Earth.

The moon goes around the Earth-Moon center of mass with a speed of 2,288 miles per hour (3,683 kilometers per hour).

a.)What is the orbital speed of Earth in the Earth-Moon center of mass frame (total momentum is zero)? Please, give your answer in meters per second.

b.) Using the formula for centripetal force, what is the force of gravity exerted by the Earth on the Moon?

c.) Using the formula for centripetal force, what is the force of gravity exerted by the Moon on Earth?

A baseball has a mass of 3kg and is thrown off a roof with a horizontal velocity of 55m/s with a drag coefficient of 33Ns/m.

The baseball falls for 5s before hitting the ground, what the horizontal and vertical velocity?

How far did the ball travel both vertically and horizontally?

If the bat was thrown off the roof with a horizontal velocity of 13m/s and has a mass of 15kg, what is the bats drag coefficient if it take’s 5s to hit the ground?

What is the best way to design an argon laser that emits at 501.7 nm?

From t = 0 to t = 4.66 min, a man stands still, and from t = 4.66 min to t = 9.32 min, he walks briskly in a straight line at a constant speed of 1.66 m/s. What are (a) his average velocity vavg and (b) his average acceleration aavg in the time interval 1.00 min to 5.66 min? What are (c) vavg and (d) aavg in the time interval 2.00 min to 6.66 min?

A child bounces in a harness suspended from a door frame by three elastic bands.

(a) If each elastic band stretches 0.200 m while supporting a 6.35-kg child, what is the force constant for each elastic band? (N/m)

(b) What is the time for one complete bounce of this child? (s)

(c) What is the child's maximum velocity if the amplitude of her bounce is 0.200 m? (m/s)

what produces a torque on the boat and what effect does it have on the boat?

In the figure here, a red car and a green car move toward each other in adjacent lanes and parallel to an x axis. At time t = 0, the red car is at x_r = 0 and the green car is at x_g = 222 m. If the red car has a constant velocity of 25.0 km/h, the cars pass each other at x = 43.0 m. On the other hand, if the red car has a constant velocity of 50.0 km/h, they pass each other at x = 76.3 m. What are (a) the initial velocity and (b) the (constant) acceleration of the green car? Include the signs.

Please show how to Graph the Vector Sets. And Solve for it analytically.

Part A: Experimental Determination of the Equilibrant-

1. Obtain three sets of vectors, two sets of two and one set of three.
2. Use a scale of 1 cm = 10 g. For example, a vector of magnitude 5 cm would be represented by a hanging mass of 50g (5 cm x 10 g/1 cm = 50 g). Record each set of vectors below.

3. Record the value of the equilibrant, mass and angle.

Equilibrant: 142       g @     225      _ for set 1 (Vectors A and B)
Equilibrant:  166              g @  200         _ for set 2 (Vectors A and B)
Equilibrant:     76           g @    60        _ for set 3 (Vectors A, B and C)

Part B: Graphical Determination of Equilibrant-

1. Using the first set of vectors, graphically add the two vectors (using graph paper) to find the resultant.
2. From the resultant, determine the equilibrant. Refer to page 41.
3. Record your results:

Equilibrant:   g @ _ for set 1 (Vectors A and B)
Equilibrant:    g @ _ for set 2 (Vectors A and B)
Equilibrant:   g @ _ for set 3 (Vectors A, B and C)

Part C: Analytical (Mathematical) Addition of Vectors-

1. Calculate the x and y components of each of your vectors and record in the following table.
2. Calculate the magnitude and direction of the resultant R and equilibrant E.