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.  

A coil is wrapped with 226 turns of wire on the perimeter of a circular frame (of radius 70 cm). Each turn has the same area, equal to that of the frame. A uniform magnetic field is directed perpendicular to the plane of the coil. This field changes at a constant rate from 22 mT to 61 mT in 79 ms. What is the magnitude of the induced average E in the coil, over the time interval 79 ms during which the field changes? Answer in units of V.

A 5 kg pully has a string round around it and a force of 1.0 N pulls down on the string. The pully is frictionless, 10 cm in radius, and is a uniform disk. The pully is initially at rest.

A) What is the torque of the pully?

B) What is the angular acceleration of the pully?

C) How many times will the pully rotate in 3.0 seconds?

D) What will the pully's angular velocity be after 3.0 seconds?

A 2.00 m long metal wire is formed into a square and placed in the horizontal xy-plane. A uniform magnetic field is oriented 30 degrees above the horizontal with a strength of 0.344 T. What is the magnetic flux through the square due to this field?

Two identical metal spheres attract each other with a force of 7.00 × 10−6 N when they are 3.00 cm apart. The spheres are then touched together and then removed to the original separation where now a force of repulsion of 2.00 × 10−6 N is observed. What is the charge on each sphere after touching and before touching?

A home run is hit in such a way that the baseball just clears a wall 16 m high, located 122 m from home plate. The ball is hit at an angle of 33° to the horizontal, and air resistance is negligible. (Assume that the ball is hit at a height of 1.0 m above the ground.)

What is the initial speed of the ball?

How long does it take the ball to reach the wall?

What is the velocity of the ball (x and y-component)?

What is the speed of the ball when it reaches the wall?

A stopper on a string is swung horizontally over a student’s head. The other end of the string is connected to a 0.200 kg mass that remains stationary. If the stopper completes 20 revolutions in 5.5 seconds with a radius of 0.75 m, then what is the mass of the stopper? Hint: In order to be in equilibrium, the vertical weight of the mass in N, needs to equal the centripetal force of the stopper. To find the velocity of the stopper, you will need to multiply the circumference it would travel by how many revolutions it has made, and divide that by the time

Two small loudspeakers emit sound waves of different frequencies equally in all directions. Speaker A has an output of 1.30 mW, and speaker B has an output of 1.90 mW. Two speakers A and B are represented as points which serve as the centers of concentric circles representing sound waves emanating from the speakers. The concentric circles about speaker A are spaced more closely together than the concentric circles about speaker B. The points lie along a horizontal line, and speaker A is 5.00 m to the left of speaker B. A vertical line is drawn that intersects the horizontal line at a distance of 3.00 m from the left speaker and 2.00 m from the right speaker. Point C lies along this vertical line at a distance of 4.00 m above the point of intersection. (a) Determine the sound level (in decibels) at point C in the figure if only speaker A emits sound. (Enter your answer to at least one decimal place.) dB (b) Determine the sound level (in decibels) at point C in the figure if only speaker B emits sound. (Enter your answer to at least one decimal place.) dB (c) Determine the sound level (in decibels) at point C in the figure if both speakers emit sound. (Enter your answer to at least the nearest dB.) dB/Users/crystaldawnmcclendon/Desktop/14-p-064.gif