A student throws a ball vertically. 2.0 seconds later, it is caught by a friend on a balcony 5.0 m above the point of release. When did the ball first pass the friend on the balcony and how fast was it going at that instant?

1. Given two wave equations, ?1(?, ?) = ? sin(?? − ?? + ?1) and ?2(?, ?) = ? sin(?? − ?? + ?2), what is the linear combination of the two wave equations where both waves have the same wavelength and angular frequency but ? ≠ ? and ?1 ≠ ?2? That is, what is ?1 + ?2 given different amplitudes of oscillation and phase constants? Your answer must be in the form of?3(?, ?) = ? sin(?? − ?? + ?3) where ? is the amplitude of oscillation of the new resultant wave and ?3 is a new phase constant. Be sure to give an expression for ? and ?3. Show how you get to your answer. Do not simply show an end result. Hint: Trigonometric identities will be useful here.

Two identical spaceships, both measuring 100 m at rest are moving in the same direction. In a particular reference frame one spaceship measures 80 m, and the other 60 m. What would be the lengths of the spaceships with respect to each other?

A binary star system consists of two stars, each of mass 2 * 10^30 ??. The initial positions of Star A and Star B are ?⃗?? = 〈−3, −4, 0〉 * 10^9 ? and ?⃗?? = 〈3, 4, 0〉 * 10^9 ? respectively. The magnitude of the gravitational force that one star exerts on another is about 2.7 * 10^30 N.

The initial velocity of Star B is ?⃗?? = 〈−6.5,4.9,0〉*10^4 ? ? . What is the approximate velocity of Star B after a time step of about 1 hour (∆? = 3.6*10^3 ?)?

What is the approximate new position of Star B after a time step of about 1 hour (∆? = 3.6*10^3 ?)?

Pendulum experiment:

1) create a plot of length (x axis) versus average period (y axis). Make sure to clearly label your axes and indicate units.

(2) create a plot of length (x axis) versus (average period)2 (y axis). Add a linear trend line. Record the slope of the best fit line.

(3) recall that the period of an ideal simple pendulum is given by the following relation: T= 2pi sq rt of L/g

squaring both sides of the equation gives us this relation: T^2=4pi^2L/g= 4pi^2/g*L. Using the slope of your T2 versus L plot determine the acceleration due to gravity.

(4) how close is your experimentally determined gravitational acceleration to 9.81m/s^2? What are potential sources for error in this experiment?

(5) for small angles does the pendulums period of oscillation depend in the initial angular displacement from equilibrium? Explain.

(6) why is it a good idea to use a relatively heavy mass in this experiment? What would you say to a colleague that wanted to use only one washer as the pendulum mass?

(7) use the relation of the period of an ideal simple pendulum. = 2pi square rt of L/g to calculate the ratio of the periods of identical pendulums on the earth and on mars. Note the gravitational acceleration on the surface of mars is approx 3.7 m/s^2.

Consider 100 g mass hung from a spring at equilibrium (y = 0). Write the equation of oscillation, and sketch of the mass’ position y(t) for the following situations. Be sure to correctly identify each function drawn.

a) Suppose the mass is displaced upward from the equilibrium position by 10 cm and then released from this position at time t = 0. A period of oscillation of 2 second was observed. Draw this on the first graph.

(b) Suppose the mass is displaced downward by 5 cm and then released from this position at time t = 0. Draw this on the same graph. (

c) Suppose the mass is decreased to 25 g and is allowed to come to its new equilibrium position (which we again call y = 0). It is then displaced upward from the new equilibrium position by 10 cm and then released from this position at time t = 0. Draw this on the second graph. (

d) Suppose you started observing the same oscillation but 0.25 seconds after it was released. Draw this on the same graph. Indicate on the graph the time delay between this oscillation and the previous one.

A long, hollow, cylindrical conductor (inner radius 2.4 mm, outer radius 4.4 mm) carries a current of 45 A distributed uniformly across its cross section. A long thin wire that is coaxial with the cylinder carries a current of 24 A in the opposite direction. What is the magnitude of the magnetic field (a) 1.4 mm, (b) 2.6 mm, and(c) 4.7 mm from the central axis of the wire and cylinder?

three point charges +1 nC +2nC and -3nC are placed in two adjacent vertices and in the center if a square with 3m ling sides. find electric field (magnitude and direction) and electric potential (magnitude and sign) in the empty vertices of the square. find total potential energy of the interaction between charges . find force of interaction between the charges in the vertices.

A copper calorimeter can with mass 0.555kg contains 0.165kg of water and 1.90

If the coefficient of kinetic friction is 0.2, what friction of the total mechanical energy is lost due to frictional forces?

A box of mass 18.0 kg sits at rest on a horizontal surface. The coefficient of kinetic friction between the surface and the box is 0.300. The box is initially at rest, and then a constant force of magnitude FF and direction 39.0 ∘∘ below the horizontal is applied to the box; the box slides along the surface.

A. What is F if the box has a speed of 6.00 m/s after traveling a distance of 8.00 mm? Express your answer with the appropriate units.

B. What is F_B if the surface is frictionless and all the other quantities are the same? Express your answer with the appropriate units.

C. What is F_C if all the quantities are the same as in part A but the force applied to the box is horizontal? Express your answer with the appropriate units.

Superhero physics: a) Choose a height between 1.00 miles and 3.00 miles. How fast would a superhero have to throw a ball straight upwards in order for it to rise this high? Give your answer in both m/s and mph. Assume air resistance is negligible, since at these speeds that's as believable as superheroes are. b) Choose a time between 1.00 minutes and 3.00 minutes. How fast would a superhero have to throw a ball straight upwards in order for it to spend this much time in the air (that is, for it to take that much time to return to their hand)? Give your answer in both m/s and mph. Same assumption. c) Without resorting to further calculations, which of these two balls will be in the air longer? Explain your reasoning, explicitly citing evidence. d) Choose one case, (a) or (b), and calculate the time required for the ball to rise halfway to its highest point, and the time to rise from there to the highest point. Check: see next question. e) Why does it take less time to rise halfway to the highest point than to rise the rest of the way?

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 2.00 times the mass of B, and the energy stored in the spring was 50 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?

How are conversion electrons formed? List all the differences between an internal conversion process and beta decay?

A person with mass m=80 kg is training for pushups. Assume that the distance between the shoulders and the feet is 1.5 m, and the center of mass is at 1 m from the feet. First, he is trying to do a normal pushup. Assuming only vertical forces, what is the force on the arms?After that proved to be too difficult, he tries a modified version, where his arms are on the kitchen counter instead (~92 cm from the ground), which causes his body to form a 450 angle with the ground. What is the force on the arms, and what happens as the person expands their arms?