a.) Two identical particles of charge 3 μμC and mass 6 μμg are initially at rest and held 3 cm apart. How fast will the particles move when they are allowed to repel and separate to very large (essentially infinite) distance?

b) Now suppose that the two particles have the same charges from the previous problem, but their masses are different. One particle has mass 6 μμg as before, but the other one is heavier, with a mass of 48 μμg. Their initial separation is the same as before. How fast are the particles moving when they are very far apart? [Enter the heavier particle's final speed in the first box and the lighter particle's final speed in the second box.]

A car is to be hoisted by elevator to the fourth floor of a parking garage, which is 48 ft above the ground. Part A If the elevator can accelerate at 0.8 ft/s2, decelerate at 0.3 ft/s2, and reach a maximum speed of 8 ft/s, determine the shortest time to make the lift, starting from rest and ending at rest.

Indicate which statements are true or false

Only very small objects have an associated wave function.

Electrons show interference effects like waves.

The quantization of frequencies is specific to quantum physics.

Light can display particle properties,

Quantum effects are only visible at microscopic scales.

In nature, is mechanical energy always conserved (yes or no) why?

When the potential difference between the plates of a capacitor is halved, the magnitude of the electric energy stored in the capacitor U:

a. is 2U b. is U/2 c. remains the same d. is U/4

EXPLAIN.

A cylindrical aluminum pipe of length 1.42 m has an inner radius of 1.60 ×10^-3 m and an outer radius of 3.39 ×10^-3 m. The interior of the pipe is completely filled with copper. What is the resistance of this unit? (Hint: Imagine that the pipe is connected between the terminals of a battery and decide whether the aluminum and copper parts of the pipe are in series or in parallel.)

A charge 4.98 nC is placed at the origin of an xy-coordinate system, and a charge -1.99 nC is placed on the positive x-axis at x = 4.01 cm . A third particle, of charge 6.05 nC is now placed at the point x = 4.01 cm , y = 2.98 cm .

a. Find the x-component of the total force exerted on the third charge by the other two.

b. Find the y-component of the total force exerted on the third charge by the other two.

c. Find the magnitude of the total force acting on the third charge.

d. Find the direction of the total force acting on the third charge. (THETA)

A batted baseball is hit with a velocity of 44 m/s, starting from an initial height of 4 m. Find how high the ball travels in two cases:

(a) a ball hit directly upward and

(b) a ball hit at an angle of 69° with respect to the horizontal.

Also, find how long the ball stays in the air in each case.

case a:

case b:

4.2.2 What is an RC Circuit?

Recall that the capacitance is defined as the proportionality constant between the total charge accumulated by a capacitor and the voltage difference across the circuit

Q = C△V (4.2)

In this equation, the charge Q is expressed in Coulomb (C), the voltage △V, in volts (V) and the capacitance C in farads (F).

In this lab you will study both the charging and discharging process of an RC circuit. During the charging process, an electrical EMF source accumulates charges on each side of the parallel plate capacitor. During the discharging process, the capacitor releases all its charges into the circuit (which now does not contain the battery). Capacitors charge and discharge exponentially in time. During the discharge of a capacitor, the instantaneous voltage △Vc between the ends of the capacitor also drops and is given by △Vс = △Vmax*e^(-t/τ) (4.3) where △Vmax is the maximum voltage across the capacitor, i.e. the voltage to which thecapacitor was initially charged, t is the time and τ is the time constant given by τ= Req*Ceq (4.4) where Req and Ceq are, respectively, the equivalent resistance and capacitance to which we can reduce the circuit. Although the theoretical discharge time is in nite, in practice we consider that the discharge is over when the voltage at the bounds of the capacitor is at 1% of its maximal value.

Answer the following questions in the Results section: Assuming the voltage, when completely charged, is set to V₀ = 1 and by considering the variables τ for time constant and t for time, what are the equations for of charging and discharging? Support your answer by physical arguments

A rocket takes off vertically from the launchpad with no initial velocity but a constant upward acceleration of 2.25 m/s2 . At 15.4s after blastoff, the engines fail completely so the only force on the rocket from then on is the pull of gravity (free fall). a) What is the maximum height the rocket will reach above the launchpad? b) How fast is the rocket moving at the instant before it crashes onto the launchpad? c) How much longer after the engines fail does it take for the rocket to crash on the launchpad?

1.   A boy pushes a load of 1260 N at a constant speed up a 25° inclined plane onto a platform 1.0 m high. If the boy’s maximum force is 300 N parallel to the plane and the coefficient of kinetic friction is 0.4, what must be the length of the plane?

1. Boltzmann statistics are used to find the distribution or distribution of the velocity of Inert gas at any temperature. If D (v) is the velocity distribution of inert gas at T, then the probability that atoms (or Molecules) of inert gas have velocity in the dv range is equal to D (v) dv, where
D (v) dv = 4π (m / 2πkT) ^ 3⁄2 (v ^ 2) e ^ (- mv2⁄2kT) dv

2.1 Draw the graph between D (v) and v when the inert gas has a temperature of 1000 K (Recommended: Use a program such as Mathematica) to explain. Graph style
2.2 In the Thermosphere atmosphere, which is 100 - 150 km above the earth, the temperature is around 1000 K. Find the probability
Is that the nitrogen gas molecules will escape from gravity. In which the molecules must be faster than the velocity From the earth's surface, which is equal to 11 km / s (recommended: for integration D (v) dv, use the program For example Mathematica)
2.3 The lunar surface velocity is 2.4 km / s. Find the probability that the nitrogen gas molecules will escape from the force. Gravity of the moon And explain that Why does the moon have no atmosphere? (Recommended: set the temperature of the moon's surface to equal1000 K)

Two wires separated by 2 meters are carrying current in the same direction. One carries a current of 2 amps and the other carries a current of 3 amps. For the following, show all work starting with the equations at the top of the first page and/or explain your reasoning. Do NOT simply write down a formula specifically derived for this problem.

1. Find the force on the wire carrying the 3-amp current. In which direction does it point?

2. Find the force on the wire carrying the 2-amp current. In which direction does it point?

3. Will the wires attract each other or repel?

A charge q1 of +3.0 x10^-6C is held at (-12, 0) (cm) . Another charge q2 of the same magnitude is held at (12,0). The third charge q3 is held at (0,8) = -6x10^16C

a) What is the magnitude of the net force on charge q1 and q2

b) If q3 were to be released what direction and angle will it move in

c) At what point on the plane would a charge q4 of +15x 10^-6 be placed so that net force is 0

6.) A 'Newton's Cradle' consists of 7 identical metal balls which are free to swing back and forth. When two are pulled back and then released, they stop after colliding elastically with the other 5 balls. The two balls on the other end then swing upwards with the same speed as the first two balls. Using the conservation of momentum and mechanical energy, explain why only two balls move afterwards. Use words and/or equations to explain your answer.