A 1.5 kg solid cylinder (radius = 0.15 m , length = 0.60 m ) is released from rest at the top of a ramp and allowed to roll without slipping. The ramp is 0.80 m high and 5.0 m long.

When the cylinder reaches the bottom of the ramp, what is its total kinetic energy?

When the cylinder reaches the bottom of the ramp, what is its rotational kinetic energy?

When the cylinder reaches the bottom of the ramp, what is its translational kinetic energy?

A solid disk of mass M and radius R is rotating on the vertical axle with angular speed w. Another disk of mass M/2 and radius R, initally not rotating, falls coaxially on the disk and sticks. The rotational velocity of this system after collision is:

w

w/2

2w/3

3w/2

2w

A point charge with a mass of 1.81 ng and a charge of +1.22 uC moves in the x-y plane with a velocity of 3.00 x 104 m/s in a direction 15° above the +x-axis. At time t=0, the point charge enters a uniform magnetic field of strength 1.25 T that points in the +x-direction. Assume that the point charge remains immersed in the uniform magnetic field after time t=0.

a. (5 points) What is the magnitude and direction of the magnetic force that the magnetic field exerts on the point charge at time t=0?

b. (5 points) How does the x-component of the charge’s initial velocity effect the motion of this point charge as it moves through the uniform magnetic field? Does its magnitude change? Does its direction change? Explain your reasoning.

c. (5 points) How does the y-component of the charge’s initial velocity effect the motion of this point charge as it moves through the uniform magnetic field? Does its magnitude change? Does its direction change? Explain your reasoning.

d. (5 points) Use your answers from parts 1b & 1c to explain why the path of this point charge is helical (corkscrew-shaped). Explain your reasoning.

e. (2.5 points) Determine the radius of the circular part of the point charge’s helical path.

Let me know the effectiveness of the death penalty?
Are there alternative punishments that would be more effective than the death penalty?

A 170 g block attached to a spring with spring constant 2.1 N/m oscillates horizontally on a frictionless table. Its velocity is 19 cm/s when x0 = -4.0 cm .

A) What is the amplitude of oscillation?

B) What is the block's maximum acceleration?

C) What is the block's position when the acceleration is maximum?

D) What is the speed of the block when x1 = 3.3 cm ?

Derive the equations for a particle moving near the surface of the earth, given by

?̈= 2? cos ? ?̇

?̈= −2( cos ? ?̇ + ? sin ? ?̇)

?̈= −? + 2? sin ? ?̇

? = v/r; v=velocity; r-radius

where the earth’s rotational speed in the ?̂ direction is ?.

True/False: Because hot water cools down faster than cold water, an ice cube tray filled with hot water will freeze faster than an ice cube tray filled with cold water. Explain your choice.

Hint: Although hot water cools down at a faster rate than cold water, it also has to undergo a larger temperature change. As it cools down, what happens to the rate at which it continues to cool down?

Explain how a mercury thermometer works. A mercury thermometer breaks open and loses its mercury while the thermometer is at a temperature of 20°C. You refill the thermometer with colored ethanol to a level of 20°C. a. At a temperature of 10°C, will the thermometer read a value below, above, or exactly 10°C? Explain. b. At a temperature of 30°C, will the thermometer read a value below, above, or exactly 30°C? Explain.

Einstein and Lorentz, being avid tennis players, play a fast-paced game on a court where they stand 20.0 m from each other. Being very skilled players, they play without a net. The tennis ball has mass 0.0580 kg. You can ignore gravity and assume that the ball travels parallel to the ground as it travels between the two players. Unless otherwise specified, all measurements are made by the two men. Lorentz serves the ball at 80m/s. Einstein slams a return at 1.8 x 10^8 m/s Question: Presuming the force that Einstein impacted to the ball was constant and done over two centimeters, what was this force?

A type of foam ear plug has a 26 dB overall EPA noise reduction rating. Sally wants to sleep on her bus ride and decides to use these earplugs. The noise level inside the bus is 87 dB.
(A) What noise level would she perceive with the ear plugs that have the 26 dB noise reduction?
The reduced noise level would be _________ dB.
(B) A loud rock band produces a sound level of 117 dB at a location near the band. In a work environment, regulations limit exposure to this very loud sound to 30 minutes or less per day. What is the sound intensity of the rock band?
Intensity is __________ W/m².
(C) Using the ear plugs with 26 dB noise reduction, what sound level would she preceive?
She would preceive _________ dB sound level.
(D) What is the sound intensity she hears with the ear plugs?
Sound intensity, after attenuation by ear plugs, is ________ W/m²

The length of a simple pendulum is 0.84 m and the mass of the particle (the "bob") at the end of the cable is 0.23 kg. The pendulum is pulled away from its equilibrium position by an angle of 9.05° and released from rest. Assume that friction can be neglected and that the resulting oscillatory motion is simple harmonic motion.

A bungee jumper of mass 110 kg jumps from a cliff of height 120m. The massless relaxed bungee cord has a length of 15 m. Ignore the height of the body of the jumper. K=125N/m. (a) Find the velocity of the jumper right before the bungee starts to stretch. (b) Find the distance the cord stretches.

Please explain the steps. Thank you!

An electron is confined by some potential energy well centered about the origin, and is represented by the wave function ψ(x) = Axe−x2/L2, where L = 4.48 nm. The electron's total energy is zero. (a) What is the potential energy (in eV) of the electron at x = 0? eV (b) What is the smallest value of x (in nm) for which the potential energy is zero? nm

In the homework, you were asked to calculate the minimum height needed for a roller coaster car to just barely make a circular loop-the-loop. Instead, suppose a roller coaster designer wants the riders to feel their seats pushing back on them with a force equal to their weight when the car is at the inside, top of the loop. What height h should the car be released from if this condition is to be met? Express your answer in terms of R. Ignore friction.  
a. After drawing a free body diagram for a person in the car when the car is at the inside, top of the loop, determine a constraint equation on the square of the speed when the car is at that position. b. Apply conservation of energy to determine the necessary, minimum height h. Express your answer in terms of the radius R of the loop.

2. A rigid disk with radius 2 m is spinning at an angular speed of 8 1/s (or 8 rad/s). A constant angular acceleration is applied that slows downthe disk at a rate of 2 1/s²(or 2 rad/s²).

(i) Calculate the number of revolutions the disk does before coming to a full stop.

(ii) Calculate the centripetal acceleration of a point, positioned at 1 m from the disk rotation axis, at t = 2 s.

(iii) Calculate the tangent speed of a point positioned at the edge of the disk at t = 2 s.

Q: In an elastic collision between two bodies of equal mass, with body 2 initially at rest, body 1 moves off at angle θ relative to the direction of its initial velocity and body 2 at angle φ. The sine of the sum of θ and φ, sin(θ + φ), is equal to.....................

Question options:

a). 0.

b). 0.500.

c). 0.707.

d). 0.866.

e). 1.00.

=> I tried but it's not A or D so maybe someone can help.

=> Answer left is B, C, E