A 0.5 kg ball is dropped from a window. An archer shoots a 0.05 kg arrow to intercept the ball. When the ball is impaled it is traveling at -2 m/s in the y direction, and the arrow is traveling at 35 m/s at an angle of 20 degrees. What is the velocity of the pair after the collision in vector notation, magnitude, and direction? What is the impulse of the arrow?

1. Consider an object on a spring of k=200 N/m whose position is given by x=(5.00 cm)cos(9.90 rad/s). Find: (a) the maximum speed of the object and when this maximum speed first occurs after t=0, (b) the maximum of the acceleration of the object and when the maximum of the magnitude of the acceleration first occurs after t=0, (49.5cm/s 490 cm.s^2), (c) the amplitude and period of motion, (d) the position of the block at t=1.0s, (d) the maximum kinetic energy and potential energy of the spring block system.

Sassbot and Block Ness Monster play roller derby for the Reservoir Dolls, a roller derby team in Madison, Wisconsin. In a particular bout against the Unholy Rollers, another Madison team, Sassbot is playing the position of jammer: she must pass members of the Unholy Rollers in order to score points. Block Ness Monster is playing as a blocker: she must help Sassbot while also stopping the Unholy Rollers’ jammer. During a crucial moment in the bout, Monster sees that Sass, a few feet in front of her, is about to get hit by Skullz B. Kraken, a member of the Unholy Rollers. Monster reaches Sass quickly and pushes her forward, attempting to give Sass a boost of speed so she is out of the Skullz’s reach. Monster pushes Sass straight forward, delivering the push at Sass’s center of mass, her lower back, so that Sass does not experience any rotation due to the push. Neither Monster nor Sass are using their wheels to brake immediately before, during, or after the push, so the outside forces on them are negligible. Monster’s mass is 82 kg. Sass’s mass is 55 kg. Monster’s speed before the push is 2 m·s−1, and Sass’s speed before the push is 0.75 m·s−1. Monster and Sass have found, in previous practice, that the average coefficient of restitution of this sort of push between them is 0.8. The coefficient of restitution is defined as the ratio of the difference in two objects’ velocities after the collision to that of the difference in the objects’ velocities before the collision. e = v2,f − v1,fv2,i − v1,i At the moment Monster finishes her push, Skullz is 0.75 m to the left and 1.1 m in front of Sass. Skullz is moving laterally (to the right) at a speed of 2.15 m·s−1 in her attempt to hit Sass. Sass is moving directly forward after Monster’s push. Will Sass get hit by Skullz or will she get past her in time?

How long will it take Sass to travel forward past Skullz’s position?

from the laue condition explain why we can observe maximal peaks in the amplitude of the diffracted wave

In an attempt to save someone in a vertically falling car Spider-Man spins a web catching the 2000 kg car. The webbing has a spring constant of 22,000 N/m and the car is caught at t = 0 at a distance 0.500 m above equilibrium while it is still falling at a speed of -10.0 m/s. After this, the car goes into vertical SHM.

Wo = 3.32Hz

f = .528Hz

Period (T) = 1.89s

Find:

a) the amplitude

b) the phase angle

c) the time it takes the car to get to its lowest point (? = −?).

Draw an example of, and compare the differences between the three types of static equilibrium

Which of the following is ALWAYS true.

a) An object experiencing a constant negative acceleration has a decreasing momentum.

b) If an object has a constant acceleration, its kinetic energy is changing at a constant rate.

c) If an object has a zero net force acting on it, its kinetic energy is constant.

d) If an object's kinetic energy is constant, there is no net force acting on it.

e) If an object's kinetic energy is increasing there is a positive net force on it.

A bullet (m = 10 g) flies horizontally with an initial speed of v = 500 m/s and then embeds itself in a block of wood (m = 400 g) that is at rest on a flat surface. The surface has a coefficient of kinetic friction μk = 0.4. After the impact, how far does the block of wood slide?

(a) 40 m (b) 800 m (c) 8 m (d) 80 m (e) 20 m

In the worst-case scenario, you've got an elevator with a mass 2420 kg moving a speed 4.29 m/s when it reaches the bottom of the shaft. Your first idea is to put a spring, with spring constant 1.068×10⁴ N/m, at the bottom of the shaft.

a)Assuming the spring obeys Hooke's Law perfectly, how far will it compress to stop the elevator?

b)When the elevator comes to a stop with the spring compressed, what is the net force on the elevator?

c)It's a bit unreasonable to put a spring large enough to compresses this far under every elevator. So you decide to add a clamping mechanism to the walls around the spring, which will provide a friction force of magnitude 1.74×10⁴ N

Now how far does the spring get compressed?

Express your answer with appropriate units.

An insulated container contains 15.0 g of steam at 100C. A mass of 65.0 g of ice at 0.00C is dropped into the container (assume no energy is absorbed by the container).

C = Celsius

a). How much heat is released by the steam when it condenses at 100C? (Qs)

b). How much heat is absorbed by the ice when it melts at 0.00C? (Qi)

c). What is the final temperature of the the water in the container? (T)

Consider the following wavefunctions. For each wavefunction, Normalize it. Find the probability that the particle described by these wavefunctions exists in the region 0

Phi(x) = Ae^(-x^2/3)

Phi(x) = A/(x^2+2)

Muons are unstable subatomic particles with a mean lifetime of 2.2 μs that decay to electrons. They are produced when cosmic rays bombard the upper atmosphere about 10 km above the earth’s surface, and they travel very close to the speed of light. The problem we want to address is why we see any of them at the earth’s surface.What is the greatest distance a muon could travel during its 2.2 μs lifetime?According to your answer in part A, it would seem that muons could never make it to the ground. But the 2.2 μs lifetime is measured in the frame of the muon, and they are moving very fast. At a speed of 0.999c, what is the mean lifetime of a muon as measured by an observer at rest on the earth?

a) An asteroid revolves around the Sun with a mean orbital radius 2.5 times that of Earth’s. Predict the period of the asteroid in Earth years.

(Show all work, including formulas and units for full credit.)

b) Saturn requires 29 years to circle the Sun. Find Saturn’s average distance from the Sun as a multiple of Earth’s average distance from the Sun.

(Show all work, including formulas and units for full credit.)

c) The Moon has a period of 27.3 days and a mean distance of 3.9×10⁵ km from its center to the center of Earth.

i) Use Kepler’s laws to find the period of a (hypothetical) satellite in orbit 8.20×10³ km from the center of Earth.

ii) How far above Earth’s surface is this satellite (Hint: Look up the Earth's diameter online, convert it to the radius, and also to kilometers. Keep in mind that the satellite rotates from the center of the Earth, and the question asks for the height above the surface of the Earth)?

A 15.0 kg object moving in the +x direction at 5.5 m/s collides head-on with a 11.5 kg object moving in the −x direction at 4.0 m/s .

Part A-

Find the final velocity of each mass if the objects stick together.

Express your answers using two significant figures. Enter your answers numerically separated by a comma.

Part B-

Find the final velocity of each mass if the collision is elastic.

Express your answers using two significant figures. Enter your answers numerically separated by a comma.

Part C-

Find the final velocity of each mass if the 15.0 kg object is at rest after the collision.

Express your answers using two significant figures. Enter your answers numerically separated by a comma.

Part D-

Is the result in part C "reasonable"? Explain

Part E-

Find the final velocity of each mass if the 11.5 kg object is at rest after the collision.

Express your answers using two significant figures. Enter your answers numerically separated by a comma.

Part F-

Is the result in part E "reasonable"? Explain.

Part G-

Find the final velocity of each mass if the 15.0 kg object has a velocity of 4.0 m/s in the −x direction after the collision.

Express your answers using two significant figures. Enter your answers numerically separated by a comma.

Part H-

Is the result in part G "reasonable"? Explain

A solid, homogeneous sphere with a mass of m0, a radius of r0 and a density of ρ0 is placed in a container of water. Initially the sphere floats and the water level is marked on the side of the container. What happens to the water level, when the original sphere is replaced with a new sphere which has different physical parameters? Notation: r means the water level rises in the container, f means falls, s means stays the same. Combination answers like 'f or s' are possible answers in some of the cases.

The new sphere has a mass of m < m0 and a radius of r = r0.

The new sphere has a density of ρ > ρ0 and a radius of r = r0.

The new sphere has a mass of m = m0 and a density of ρ > ρ0.