A bowling ball rolls without slipping up a ramp. If the speed at the bottom of the ramp is 2.85 m/s and the height of the ramp is 0.525 m, what is the speed of the ball at the top of the ramp?

A long time ago, in a galaxy far, far away, electric charge had not yet been invented, and atoms were held together by gravitational forces. Compute the Bohr radius (a₀) and the

n = 5 to n = 2

transition energy

(E₅ − E₂)

in a gravitationally bound hydrogen atom.

A weightlifter works out at the gym each day. Part of her routine is to lie on her back and lift a 41 kg barbell straight up from chest height to full arm extension, a distance of 0.55 m .

1. How much work does the weightlifter do to lift the barbell one time?

2. If the weightlifter does 25 repetitions a day, what total energy does she expend on lifting, assuming a typical efficiency for energy use by the body (25%).

3. How many 430 Calorie donuts can she eat a day to supply that energy? Express your answer using two significant figures.

The wave function for hydrogen in the 1s state may be expressed as ψ(r) = Ae−r/a0. Determine the normalization constant A for this wave function. (Use the following as necessary: a0.)

A pendulum clock in an elevator ticks with a period of T=1.7 s when the elevator is at rest. The elevator starts to move and the period increases to Tnew = 1.87 s.

1. How is the elevator moving? Select the correct answer:

a) accelerating, upward

b) accelerating, downward

c) constant speed, upward

d) constant speed, downward

2. Identify the correct acceleration for the elevator. You must show your work to get credit for your selection.

a) 1.7 m/s^2

b) -0.89 m/s^2

c) 2.06 m/s^2

d) 0.89 m/s^2

e) -1.7 m/s^2

You attach a 100-g puck to a string and let the puck glide in a circle on a horizontal, frictionless air table. The other end of the string passes through a hole at the center of the table. You pull down on the string so that the puck moves along a circular path of radius 0.50 m. It completes one revolution in 6.0 s.

If you pull harder on the string so the radius of the circle slowly decreases to 0.40 m, what is the new period of revolution?

Tf =

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