A solid cylinder, mass of 15 kg, is on a hill that is inclined at a 45 degree angle. If it rolls down the hill without slipping find:

1. The acceleration of the cylinder

2. The force of friction acting on the cylinder

3. The minimum possible coefficient of friction

Explain.

What is Bloch theorem and Kramers theorem and can you take each example showing the theorem clearly?

A 2.5 mm -diameter sphere is charged to -4.5 nC . An electron fired directly at the sphere from far away comes to within 0.34 mm of the surface of the target before being reflected.

Part A) What was the electron's initial speed?

Part B) At what distance from the surface of the sphere is the electron's speed half of its initial value?

Part C) What is the acceleration of the electron at its turning point?

write a detailed essay on energy and power. your essay should include the types of energy and the laws associated with them (500-1500 words)

please make it computer typing thanks

1 Rank the following in terms of increasing momentum:

A 10,000 kg train car at rest

A 100 kg person running at 5 m/s

A 1200 kg car going 15 m/s

A 15 kg meteor going at a speed of 1000 m/s

2 Rank the following in terms of increasing kinetic energy:

A 1200 kg car going 15 m/s

A 10,000 kg train car at rest

A 15 kg meteor going at a speed of 1000 m/s

A 100 kg person running at 5 m/s

3 Ben (55 kg) is standing on very slippery ice when Junior (25 kg) bumps into him. Junior was moving at a speed of 8 m/s before the collision and Ben and Junior embrace after the collision. Find the speed of Ben and Junior as they move across the ice after the collision. Give the answer in m/s. Describe the work you did to get the answer.  

A box of mass M is pushed a distance L across a level floor by a constant applied force P. The coefficient of kinetic friction between the box and the floor is μ. Assuming the box starts from rest, express the final velocity vf of the box in terms of M, L, P, μ, and g.

A child m = 30 kg runs at vi = 5 m/s tangentially to a small playground merry-go-round, aiming at the edge with idea of jumping on and spinning around. The merry-go-round has mass 80 kg, radius 1m, and can be modeled as a thin solid disk.

1. What is the angular speed of the merry-go-round after the child jumps on?

2. After the merry-go-round turns through 270◦ , the child jumps off the merry-go-round radially and tumbles away at vf = 0.75 m/s. What is the angular speed of the merry-go-round after the child jumps off?

3. What force was applied to allow the child to change his or her linear momentum (comparing before and after interacting with the merry-go-round)?

A football player runs for a distance d1 = 8.55 m in 1.33 s, at an angle of θ = 62.1degrees to the 50-yard line, then turns left and runs a distance d2 = 10.68 m in 2.19 s, in a direction perpendicular to the 50-yard line. The diagram shows these two displacements relative to an xy coordinate system, where the x axis is parallel to the 50-yard line, and the y axis is perpendicular to the 50-yard line. What angle, in degrees, does the displacement make with the y axis? (Note that the angle θ was given as measured from the x axis rather than the y axis.)

Originally, light is unpolarized. It then travels through 3 polarizers: the first with its transmission axis aligned vertical, the next at a 30 degree angle to the vertical and the last aligned at a 45 degree angle to the vertical (tilted the same direction as the first with respect to the vertical). The original intensity of light is 4 W/m2.

1-What is the intensity of light after the second polarizer?

2-What is the intensity of light after the third polarizer?

3-If the second polarizer is aligned at a 45 degree angle to the vertical (just like the third), what is the final intensity of light after the third polarizer?

4- If the second polarizer is aligned at a 45 degree angle to the vertical (but in the other direction), what is the final intensity of light after the third polarizer?

There is a well near your house with a 20kg cylindrical spool (with a radius of 0.5m), wrapped with rope, upon which you attach a 5kg bucket. you let the bucket fall into the well from rest. 10s later, you can hear the bucket hit the water at the botttom. A) Determine the tension in the string B) what is the linear acceleration of the bucket? C) What is the angular acceleration of the spool? D)How much torque was required to make the spook spin at this acceleration? E)How far does the bucket ravel when it reaches the water? F)Through how many radians does the spool spin in this time? G)What is the final angular velocity of the spool? H) What is the final linear velocity of the spool?

A truck travels uphill with constant velocity on a highway with a 7.5° slope. A 30-kg package sits on the floor of the back of the truck and does not slide, due to a static frictional force. During an interval in which the truck travels 405 m, find the following.

(a) What is the net work done on the package? (J)

(b) What is the work done on the package by the force of gravity? (J)

(c) What is the work done on the package by the normal force? (J)

(d) What is the work done on the package by the friction force? (J)

Rolling Sphere in a Hemisphere

Must answer both parts

A small sphere, with radius 2.9 cm and mass 6.0 kg, rolls without slipping on the inside of a large fixed hemisphere with radius 1.00 m and a vertical axis of symmetry. It starts at the top from rest. What is its kinetic energy of the sphere at the bottom?

What fraction of its kinetic energy at the bottom (in percent) is associated with rotation about an axis through its center of mass?

1. A 3.0cm tall object is located 5.0cm from a converging lens that has a focal length of 10.0cm. What is the magnification of the image?

a. M= 0.500

b. M= -0.500

c.M= 2.0

d. M= -2.0

e. none of the above

2. A bird is flying above the water when it spots a fish a few meters ahead in a direction about 30 degrees below the horizontal (the bird is not directly over the fish). The bird is hungry, and dives towards the water. In order to catch the fish, the bird should aim ____

a. above where the fish appears.

b. below where the fish appears.

c.precisely where the fish appears.

3.  A convex mirror forms an image of a real object. Which of the following statements is true?

a.The image is real, upright and larger than the object.

b. The image is real, upright, and smaller than the object.

c. The image is virtual, upright and larger than the object.

d. The image is virtual, upright and smaller than the object.

e. The image is virtual, upright, and can be larger or smaller than the object

A circular steel wire 3.00 m long must stretch no more than 0.25 cm when a tensile force of 860 N is applied to each end of the wire. What minimum diameter is required for the wire? I just really need a clear explanation of how to figure out Young's Modulus of steel.