A ski starts from rest and slides down a 30 ∘ incline 70 m long.

A)If the coefficient of friction is 0.075, what is the ski's speed at the base of the incline?

B)If the snow is level at the foot of the incline and has the same coefficient of friction, how far will the ski travel along the level? Use energy methods.

A 0.130-kg cube of ice (frozen water) is floating in glycerine. The gylcerine is in a tall cylinder that has inside radius 3.20 cm . The level of the glycerine is well below the top of the cylinder.

f the ice completely melts, by what distance does the height of liquid in the cylinder change?

Express your answer with the appropriate units.

Does the level of liquid rise or fall? That is, is the surface of the water above or below the original level of the gylcerine before the ice melted?

The Ads side of the AdS/CFT correspondence is a model of quantum gravity in 5 dimensional antidesitter space. What can it say about quantum gravity in our 4-spacetime dimensions? Or is it just a toy model to better our understanding of quantum gravity as a whole?

Under normal conditions, you are just barely able to lift a mass of 91 kg. Your friend drops a box of volume 7 m³ into a lake. If you are just able to lift it to the surface (so that it is still completely submerged), what is the mass of the box?

A.) 1 L of oxygen gas has a temperature of 0

One model for the length of a person's ACL (L_ACL, in millimeters) relates it to the person's height (h, in centimeters) with the linear function

L_ACL = 0.4606h ? 41.29.

Age, gender, and weight did not significantly influence the relationship.

(a) If a basketball player has a height of 2.37 m, how long is his ACL?
1    cm

(b) If a pressure of

8 ? 10⁶ N/m²

is applied to his ligament, how much will it stretch?
2    cm

Three ideal polarizing filters are stacked, with the polarizing axis of the second and third filters at 29.0? and 55.0?, respectively, to that of the first. If unpolarized light is incident on the stack, the light has intensity 75.0W/cm2 after it passes through the stack.

1. If the incident intensity is kept constant, what is the intensity of the light after it has passed through the stack if the second polarizer is removed?

Two ice skaters, Daniel (mass 69.2 kg) and Rebecca (mass 50.1 kg) are practicing. Daniel stops to tie his shoelace and, while at rest, is struck by Rebecca, who is moving at12.7 m/s before she collides with him. After the collision, Rebecca has a velocity of magnitude 6.8 m/s at an angle of 50.1° from her initial direction. Both skaters move on the frictionless, horizontal surface of the rink.

(a) What are the magnitude and direction of Daniel's velocity after the collision?
m/s

(b) What is the change in total kinetic energy of the two skaters as a result of the collision?

Often times during volcano eruptions the clouds have large static charge buildups that cause lightning to happen. If a rock is ejected by the volcano and it flies to a height of 1795 m, and the clouds have a charge concentration of +40.0 C at a height of 3400 m and ?40.0 C at a height of 1000 m, what is the electric field at the ejected rock?

A spring with spring constant 20 N/m hangs from the ceiling. A ball is attached to the spring and allowed to come to rest. It is then pulled down 8.5 cm and released. The ball makes 28 oscillations in 18 s seconds.

A) What is its the mass of the ball?​

B) What is its maximum speed?​

The free oscillations of a mechanical system are observed to have a certain angular frequency ?₁. The same system, when driven by a force F₀cos?t, has a power resonance curve whose angular frequency width, at half-maximum power, is ?₁/5.

(a) At what angular frequency does the maximum power input occur?

(b) What is the Q of the system?

(c) The system consists of a mass m on a spring of spring constant k. In terms of m and k, what is the value of the constant b in the resistive term -bv?

At a steam power plant, steam engines work in pairs, the heat output of the first one being the approximate heat input of the second. The operating temperatures of the first are 770 ∘C and 460 ∘C, and of the second 435 ∘C and 280 ∘C.

A) If the heat of combustion of coal is 2.8×107J/kg, at what rate must coal be burned if the plant is to put out 860 MW of power? Assume the efficiency of the engines is 65% of the ideal (Carnot) efficiency

B)Water is used to cool the power plant. If the water temperature is allowed to increase by no more than 4.5∘C, estimate how much water must pass through the plant per hour.