A 12-kg cylinder of radius 0.10 m starts at rest and rolls without slipping down a ramp that is 4.5 m long and inclined at 30? to the horizontal. When the cylinder leaves the end of the ramp, it drops 5.0 m to the ground.

At what horizontal distance from the end of the ramp does it land?

A mass of 1.20 kg is attached to a horizontal spring with a spring constant of 125 N/m. It is stretched to a length of 20.0 cm and released from rest.

a) Write down an equation for the position and velocity of the block as a function of time. b) What is the maximum magnitude of acceleration that the block experiences? Is this consistent with Hooke’s Law? c) When the block is to the right of the equilibrium position with a speed of 1.00 m/s to the left, a ball with a mass of 50.0 g and a speed of 10.0 m/s to the right hits (and sticks) to the block. After the collision, the system still oscillates following simple harmonic motion. What is the new amplitude of the system? Hint: Find the position at which the collision occurs, and then find the velocity of the block+ball after the collision. You can find the new amplitude using energy considerations.

A child sits on a merry‑go‑round that has a diameter of 6.00 m. The child uses her legs to push the merry‑go‑round, making it go from rest to an angular speed of 18.0 rpm in a time of 43.0 s. What is the average angular acceleration ?avg of the merry‑go‑round in units of radians per second squared (rad/s2)? ?avg= rad/s2 What is the angular displacement Δ? of the merry‑go‑round, in units of radians (rad), during the time the child pushes the merry‑go‑round? Δ?= rad What is the maximum tangential speed ?max of the child if she rides on the edge of the platform? ?max=

A pair of eyeglasses is designed to allow a person with a far-point distance of 2.21 m to read a road sign at a distance of 22.1 m

Part A Find the focal length required of these glasses if they are to be worn 2.50 cm from the eyes.

f=______ m

Part B Find the focal length required of these glasses if they are to be worn 1.25 cm from the eyes.

f=______ m

A large horizontal circular platform (M=91.7 kg, r=4.16 m) rotates about a frictionless vertical axle. A student (m=76.53 kg) walks slowly from the rim of the platform toward the center. The angular velocity ω of the system is 3.29 rad/s when the student is at the rim.

Find the moment of inertia of platform through the center with respect to the z-axis.

Find the moment of inertia of the student about the center axis (while standing at the rim) of the platform.

Find the moment of inertia of the student about the center axis while the student is standing 1.95 m from the center of the platform.

Find the angular speed when the student is 1.95 m from the center of the platform.

Match the following constellations with the number of days the sun spends in each constellation. One answer is be used twice.

Two charges are placed on the x axis. One of the charges (q₁ = +7.6 µC) is at x₁ = +3.3 cm and the other (q₂ = -18 µC) is at x₂ = +8.9 cm.

(a) Find the net electric field (magnitude and direction) at x = 0 cm. (Use the sign of your answer to indicate the direction along the x-axis.)


(b) Find the net electric field (magnitude and direction) at x = +6.4 cm. (Use the sign of your answer to indicate the direction along the x-axis.)

A very long conducting tube (hollow cylinder) has inner radius a and outer radius b. It carries charge per unit length -a where a is a positive constant with units of C/m. A line of charge lies along the axis of the tube. The line of charge has charge per unit length +a.

Part F

Find the direction of the electric field in terms of a? and the distance r from the axis of the tube for r>b

Find the direction of the electric field in terms of  and the distance  from the axis of the tube for

Part G

What is the charge per unit length on the inner surface of the tube?

Express your answer in terms of the given quantities and appropriate constants.

Part H

What is the charge per unit length on the outer surface of the tube?

Express your answer in terms of the given quantities and appropriate constants.

PLEASE SHOW ALL WORK! Thanks!

A 0.726-kg rope 2.00 meters long lies on a floor. You grasp one end of the rope and begin lifting it upward with a constant speed of 0.710 m/s. Find the position and velocity of the rope's center of mass from the time you begin lifting the rope to the time the last piece of rope lifts off the floor. Plot your results. (Assume the rope occupies negligible volume directly below the point where it is being lifted.)

Are these true or false, and explain why please.


White light shines on a sheet of iron but does not cause electrons to be emitted from it. Once the intensity of the white light is increased enough electrons will start to be emitted from the iron sheet.

The Bohr model provides a successful explanation for the emission spectrum of hydrogen gas.

Determine your grating constant “d” uncertainty by calculating the standard deviation from the 14 values obtained.

Average grading constant (m)-2.8*10^-6

^Rulling (lines/m)=3.6*10⁵

A person walks into a room that has two flat mirrors on opposite walls. The mirrors produce multiple images of the person. Consider only the images formed in the mirror on the left. When the person is 5.40 m from the mirror on the left wall and 6.70 m from the mirror on the right wall, find the distance from the person to the first three images seen in the mirror on the left wall

First image (m)

Second Image (m)

Third image (m)

Consider a circular vertical loop-the-loop on a roller coaster. A car coasts without power around the loop. Determine the difference between the normal force exerted by the car on a passenger with a mass of m at the top of the loop and the normal force exerted by the car on her at the bottom of the loop.

Express your answer in terms of m and the acceleration due to gravity g.

Two boxes with masses m1=5.0 kg and m2=3.0 kg are connected by a massless rope, which is put over a massless, frictionless pulley. The coefficient of kinetic friction between the incline and the boxes is 0.12 and the coefficient of static friction between the incline and the boxes is 0.25.The angles of the inclines with respect to the horizontal are ?=45** and ?2=30**. Use 9.8 m/s^2 for gravity and assume the incline is fixed in space.

a.) Show that the system will have a nonzero acceleration if it is initially at rest. Find the magnitude and direction of acceleration.

b.) If the system moves 1.5 m(in the direction found in part a), what is the work done by: i.) gravity on m1, ii.) the normal force on m1, iii.) friction on m1, iv.) gravity on m2, v.) the normal force on m2, vi.) friction on m2

c.) Using the results from part b, what is the speed of the system after it has moved 1.5 m if it was initially at rest?