A man with mass m₁ = 59 kg stands at the left end of a uniform boat with mass m₂ = 163 kg and a length L = 3.5 m. Let the origin of our coordinate system be the man’s original location as shown in the drawing. Assume there is no friction or drag between the boat and water.

1)What is the location of the center of mass of the system?

2)If the man now walks to the right edge of the boat, what is the location of the center of mass of the system?

3)After walking to the right edge of the boat, how far has the man moved from his original location? (What is his new location?)

4)After the man walks to the right edge of the boat, what is the new location the center of the boat?

5)Now the man walks to the very center of the boat. At what location does the man end up?

A tube of air open at only one end is vibrating in the 5th harmonic from a tuning fork of frequency 120 Hz placed at the open end. If this tube of air were to vibrate at its fundamental frequency, what frequency, in Hz, tuning fork would be needed at the open end

Descirbe what energy transformations and/or transfers are occuring in the following activities. Add enough detail to justify your answer.

A) Chemical energy to thermal energy followed by work done.

B) Kinetic energy to potential energy with no change in thermal energy.

   \(\int_{0}^{\pi}e^xsinx dx\) with n=6 subdivisions

1) Find the exact value of the integral

2) Approximate the integral using the trapezoidal rule, midpoint rule and simpson rule.

3) Find the errors using each of these rules

4) For each of these rules, show how large n should be, to be within .0001 of the actual answer.

A 19.0-kg cannonball is fired from a cannon with muzzle speed of 1 150 m/s at an angle of 35.0° with the horizontal. A second ball is fired with the same initial speed at an angle of 90.0°. Let y = 0 at the cannon.

(a) Use the isolated system model to find the maximum height reached by each ball.

(b) Use the isolated system model to find the total mechanical energy of the ball–Earth system at the maximum height for each ball.

Two clever kids from Kentucky use a huge spring with spring constant k= 890 N/m to launch their sled at the top of a 9.5 m high hill. The mass of kids plus the sled is 80 kg. The brilliant kids are able to compress the spring 2.6 m.

a. Determine their speed at the bottom of the hill. Neglect friction. Use conservation of energy.

b. What fraction of their final kinetic energy was initially stored in the spring?

c. Now assume that the surface of the snow is not frictionless and has a coeficcient of kinetic friction uk=0.100. Determine their speed at the bottom of the hill. Assume that the slope has an average incline of 60 degree.

Please show your work clearly and write step by step solution including numeric substitutions and etc. To make it easier, please do this in paper and include the pictures. thanks

Give an example of an experiment to determine the focal length of a concave lens.

(Note that such a lens cannot project a real image onto a screen by itself, so you will need to use a two-lens system). List all materials use and describe how/why the experiment works.

You are touring a distant planet on which the magnitude of the gravitational acceleration is 65% of that near the earth's surface. For a little adrenaline, you decide to jump off a precipice 500m above the planet's surface. After 5 seconds of free fall, you ignite the jet pack on your back, changing your acceleration to some new, constant value for the rest of your fall. If you reach the surface 26 seconds after ingiting the jet pack, with what speed do you land?

Force Table: If the center ring were to have considerable mass, what effect would it have on the experiment?

In a mall, a shopper rides up an escalator between floors. At the top of the escalator, the shopper turns right and walks 9.26 m to a store. The magnitude of the shopper's displacement from the bottom of the escalator to the store is 16.0 m. The vertical distance between the floors is 5.40 m. At what angle is the escalator inclined above the horizontal?

Hubble's constand and age of the universe question

please show the working out for both parts

Your 64-cmcm-diameter car tire is rotating at 3.8 rev/s when suddenly you press down hard on the accelerator. After traveling 240 mm, the tire's rotation has increased to 6.5 rev/s.

What was the tire's angular acceleration? Give your answer in rad/s2rad/s2.

Express your answer with the appropriate units.

1. Uncle Iroh’s just made a mass M of tea, but it comes off the kettle too hot at a temperature T_hot. Zuko’s asleep, but will scold his uncle if he sees him drinking, so Iroh wants to cool the tea to T_drink< T_hot as quickly as possible. He has a bunch of ice cubes with side length 2l at temperature T_ice<273 K< T_{drink. (assume tea off of kettle is all liquid.)}

The mass-specific heat of the ice is c_{m ice}; the water and tea both have mass-specific heat c_{m water}. The density of ice is ρ in units of mass per volume, and the mass-specific latent heat of melting of the ice is ∆H_m.

a) Assume the tea and ice cubes are completely isolated from the environment. How

many ice cubes must Iroh put in the tea to get it to T_drink ?

b) Some physicist tells you that ice cools tea at a rate

P ∝ A, (1)

where A is the total exposed surface area of the ice. To speed up the process, you decide to cut the ice cubes each into 8 equally sized smaller cubes (by making three cuts on each large cube). If τ_{no cut} is the time it takes to cool the tea without splitting the cubes, and τ_cut is the time it takes using the split cubes, what is the ratio τ _cut/ τ_{no cut}?

c)Given your answers so far, can Iroh cool the tea using the ice much faster than

the environment could? What should his strategy be to cool the tea as quickly as

possible?

A 200 Ω resistor is in series with a 8.50×10⁻² H inductor and a 0.540 μF capacitor.

part A: Compute the impedance of the circuit at a frequency of f1 = 500 Hz and at a frequency of f2 = 1000 Hz .

Enter your answer as two numbers separated with a comma.

part b: In each case, compute the phase angle of the source voltage with respect to the current.

Enter your answer as two numbers separated with a comma.

part c: State whether the source voltage lags or leads the current at a frequency 500 Hz .

part d: State whether the source voltage lags or leads the current at a frequency 1000 Hz .