A bullet with a mass m b = 11.5 g is fired into a block of wood at velocity v b = 265 m/s. The block is attached to a spring that has a spring constant k of 205 N/m. The block and bullet continue to move, compressing the spring by 35.0 cm before the whole system momentarily comes to a stop. Assuming that the surface on which the block is resting is frictionless, determine the mass of the wooden block. From left to right, a bullet of mass m subscript b has a velocity of v subscript b with a velocity vector pointing directly to the right. The vector points toward a block that is attached on its right face to a spring of force constant k. The other end of the spring is attached to a fixed, vertical surface. mass of wooden block: kg

3. (a) An outfielder fields a baseball 280 ft away from home plate and throws it directly to the catcher with an initial velocity of 100 ft/s. Assume that the velocity v(t) of the ball after t seconds satisfies the di↵erential equation dv dt = 1 10 v because of air resistance. How long does it take for the ball to reach home plate? (Ignore any vertical motion of the ball.) (Instructor’s hint: Recall that a di↵erential equation of the form dv/dt = kv has solution v(t) = v(0)ekt.) (b) The manager of the team wonders whether the ball will reach home plate sooner if it is relayed by an infielder. The shortstop can position himself directly between the outfielder and home plate, catch the ball thrown by the infielder, turn, and throw the ball to the catcher with an initial velocity of 105 ft/s. The manager clocks the relay time of the shortstop (catching, turning, throwing) at half a second. How far from home plate should the shortstop position himself to minimize the total time for the ball to reach home plate? Should the manager encourage a direct throw or a relayed throw? What if the shortstop can throw at 115 ft/s? (Instructor’s hint: Let x represent the distance between the shortstop and home plate, then find an expression for the time it takes that ball to reach home plate as a function of x. It is also helpful to use a variable w to represent the shortstop’s throwing velocity, since you can then substitute the di↵erent given values in place of w.) (c) For what throwing velocity of the shortstop does a relayed throw take the same time as a direct throw

Please answer part b

A point charge q2 = -1.9 μC is fixed at the origin of a co-ordinate system as shown. Another point charge q1 = 4.5 μC is is initially located at point P, a distance d1 = 6.6 cm from the origin along the x-axis

1) What is ΔPE, the change in potenial energy of charge q₁ when it is moved from point P to point R, located a distance d₂ = 2.6 cm from the origin along the x-axis as shown?

2) The charge q2 is now replaced by two charges q3 and q4 which each have a magnitude of -0.95 μC, half of that of q2. The charges are located a distance a = 1.6 cm from the origin along the y-axis as shown. What is ΔPE, the change in potential energy now if charge q1 is moved from point P to point R?

3)What is the potential energy of the system composed of the three charges q1, q3, and q4, when q1 is at point R? Define the potential energy to be zero at infinity.

4)The charge q4 is now replaced by charge q5 which has the same magnitude, but opposite sign from q4 (i.e., q5 = 0.95 μC). What is the new value for the potential energy of the system?

5)Charges q3 and q5 are now replaced by two charges, q2 and q6, having equal magnitude and sign (-1.9μC). Charge q2 is located at the origin and charge q6 is located a distance d = d1 + d2 = 9.2cm from the origin as shown. What is ΔPE, the change in potential energy now if charge q1 is moved from point P to point R?

a) An electron with 10.0 eV kinetic energy hits a 10.1 eV potential energy barrier. Calculate the penetration depth.

b) A 10.0 eV proton encountering a 10.1 eV potential energy barrier has a much smaller penetration depth than the value calculated in (a). Why?

c) Give the classical penetration depth for a 10.0 eV particle hitting a 10.1 eV barrier.

1.a)What is corona discharge?

b)Why engineers avoid sharp extensions in high voltage wires?

c)What is a capacitor and capacitance?

d)What is capacitor good for?

For the definitions please include the equations to:

A:Give a definition of the torque as a vector. Briefly describe torque.

B: Give a definition of the angular acceleration. Briefly describe angular acceleration.

C: Give a definition of the moment of inertia.

City A is located 40° N, 10° W. City B is located 40° N, 20° E. Assume the Earth is a perfect sphere with a radius of 6371km.

Calculate the short distance between city A and city B along the 40° N parallel.

Calculate the shortest distance (on curved Earth surface) between city A and the equator. π = 3.141

The coefficients of static and kinetic friction between a 50 kilogram box and a horizontal surface are 0.60 and 0.40, respectively. (a) What is the acceleration of the object if a 250 newton horizontal force is applied to the box? (b) What if the applied force is 350 N?

Assume a satellite communication system based upon a highly elliptical polar orbit approximately centered over the Atlantic Ocean. Communication is to be maintained between a U.S. station and one in the United Kingdom. The frequency of operation is a 435-MHz uplink and 145-MHz downlink.

Discuss the type of antennas that might be used for both uplink and downlink. What are the implications—pros and cons—of each type? Will tracking or positioning equipment be needed? If so, for which types of antennas? Will communication ever be interrupted; if so, when?

A ball is released from the top of the building and reaches the ground after 5 seconds (15 points). a) What is the velocity of the ball when it hits the ground? b) What is the height of the building? c) How much the ball falls in the last 2 seconds of the motion?

At a distance of 60.0km from a radio station antenna the electric-field amplitude is 8.70�10^?2V/m

Part B

Assuming that the antenna radiates equally in all directions (which is probably not the case), what is the total power output of the station? in W

Part C

At what distance from the antenna is the electric-field amplitude equal to half the value given? in km

At the equator, the earth’s field is essentially horizontal; near the north pole, it is nearly vertical. In between, the angle varies. As you move farther north, the dip angle, the angle of the earth’s field below horizontal, steadily increases. Green turtles seem to use this dip angle to determine their latitude. Suppose you are a researcher wanting to test this idea. You have gathered green turtle hatchlings from a beach where the magnetic field strength is 50 μT and the dip angle is 56∘. You then put the turtles in a 2.0 m diameter circular tank and monitor the direction in which they swim as you vary the magnetic field in the tank. You change the field by passing a current through a 100-turn horizontal coil wrapped around the tank. This creates a field that adds to that of the earth.

A.) In what direction should current pass through the coil, to produce a net field in the center of the tank that has a dip angle of 62∘ ? [ANSWER: CLOCKWISE]
B.) What current should you pass through the coil, to produce a net field in the center of the tank that has a dip angle of 62∘ ?

Please show step-by-step solution. Thank you!

A potter is making a spherical vase on a potter’s wheel. The vase has a mass of 0.8 kg and a radius of 4.0 cm and the potter’s wheel has a mass of 20.0 kg and a radius of 20.0 cm. The vase is centered on the wheel. While working on the vase, the wheel and vase rotate at 1 revolution every four seconds. When finished with the vase, the potter slows the wheel (and vase) by applying a normal force at the edge of the wheel. If she brings the wheel to a complete stop in 30 s and the coefficient of friction between her hands and the wheel is 0.45, what is the magnitude of the normal force between each hand and the wheel.

6. Use the periodic chart to fill in all the missing items so as to make the nuclear decays complete. I.e., specify completely (i.e. including subscripts and superscripts) Z and X in each of the two separate reactions below.

92^238U + 0^1 n --> 57^140La + Z + 2 0^1n

88^226Ra --> X + 2^4 He