In an apartment building, water is traveling up inside a pipe that has a constant cross-sectional area.

(A.) Which of the following statements about this situation are true? Choose the two correct statements.

As the water rises¸ it slows down

As the water rises¸ its speed stays the same

As the water rises¸ the pressure drops

As the water rises¸ the pressure stays the same

(B.) The flow from a 2 cm diameter shower head pipe is 5 liters per minute. What is the speed of the water exiting the pipe? _______ m/s

(C.) The shower head above is in a fourth floor apartment, 15 meters above the main pipe in the building basement. The main pipe in the basement is 10 cm in diameter. What must the water speed be in the main pipe? ______ m/s

(D.) A fourth floor apartment is 15 meters above the main pipe in the building basement. The flow from a 2 cm diameter shower head pipe is 5 liters per minute. The main pipe in the basement is 10 cm in diameter. What must the pressure (in kPa) in the main pipe in the basement be in order to generate that flow on the fourth floor? Take g to be 9.8 N/kg and atmospheric pressure to be 101.3 kPa.
_______ kPa

(A.) A "healthy" systolic (during heart contraction, the high number in 120/80) blood pressure is typically 120 mmHg. What is this in Pascals? (Take the density of mercury to be 14 g/ml and the acceleration due to gravity to be 10 m/s^2) _____ Pa

I tried converting mmHg to atm (760mmHg = 1atm) and then converting atm to Pa (1 atm = 101325 Pa) and got 15998.6842 Pa, but this answer was incorrect.

(B.) Blood flows through the aorta, and the rest of the body, at a rate of 5 liters per minute.

If the aorta has a diameter of 2 cm, what is the speed of the blood flowing through it? _____ m/s

(C.) Given that the blood flow through the body is 5 liters per minute, estimate the number of capillaries there are in the body using the following. Assume the diameter each capillary is 10 micrometers and the speed of blood through them is 0.03 cm/s

(D.) During a ventricle contraction, the average pressure pushing blood into the aorta is 100 mmHg. What is this pressure in Pascals? (use the density of mercury at 14 g/ml and the acceleration due to gravity of 10 m/s^2)

______ Pa

(E.) During a contraction, the heart pumps 75 ml of blood into the Aorta. Given the pressure above, how much work is done (in Joules) on the blood by the heart during a contraction?

(F.) Assuming a heart rate of 60 beats per minute, how many Calories (kilocalories) are burned just circulating blood during a day. (Take the approximation of 4 Joules per calorie.)

A 62.0-kg boy and his 36.0-kg sister, both wearing roller blades, face each other at rest. The girl pushes the boy hard, sending him backward with a velocity 3.10 m/s toward the west. Ignore friction.

(a) Describe the subsequent motion of the girl.

She will move west, in the same direction as her brother, with a speed 3.10 m/s.She will move east, directly away from her brother with a speed 6.89 m/s.    She will move east, directly away from her brother with a speed 5.34 m/s.She will move east, directly away from her brother with a speed 1.55 m/s.

(b) How much potential energy in the girl's body is converted into mechanical energy of the boy–girl system?
J

(c) Is the momentum of the boy–girl system conserved in the pushing-apart process?

YesNo    

(d) If so, explain how that is possible considering there are large forces acting. (If momentum is not conserved, enter "Momentum is not conserved.")

This answer has not been graded yet.

(e) If so, explain how that is possible considering there is no motion beforehand and plenty of motion afterward. (If momentum is not conserved, enter "Momentum is not conserved.")

a) A block of Aluminum has a density of 2700 kg/m^3 and a mass of 63 grams. The block is tied to one end of a string and the other end of the string is tied to a force scale. The block is allowed to hang in the air from the string. Calculate the force which will be registered on the scale.

b) The block remains tied to the string but is now completely submerged in a container of water. The block is not touching the sides or bottom of the container. Calculate the force which will be registered on the scale.

c) The block is raised so that it is only 39% submerged in the water. Calculate the force which will be registered on the scale.

In the absence of air resistance, a projectile that lands at the elevation from which it was launched achieves maximum range when launched at a 45∘ angle. Suppose a projectile of mass m is launched with speed v0 into a headwind that exerts a constant, horizontal retarding force F⃗ wind =−Fwindi^.

By what percentage is the maximum range of a 0.600 kg ball reduced if Fwind = 0.100 N ?

Express your answer with the appropriate units.

A rope of negligible mass hangs vertically on each side of a pulley. The pulley, which has mass 1.00 kg and radius 20 cm, can be modeled as a thin uniform cylinder. One end of the rope is tied to a box of mass 10.00 kg; this box is resting on the ground. The other end of the rope dangles freely. Then a 15.00 kg monkey, who is initially standing on a ledge 2.00 m above the floor, grabs the freely hanging rope and (starting from rest) accelerates down to the ground. As the monkey descends, the box rises. What is the monkey's speed when it reaches the floor?

A small solid sphere of mass M₀, of radius R₀, and of uniform density ρ₀ is placed in a large bowl containing water. It floats and the level of the water in the dish is L. Given the information below, determine the possible effects on the water level L, (R-Rises, F-Falls, U-Unchanged), when that sphere is replaced by a new solid sphere of uniform density.

R F U R or U F or U R or F or U  The new sphere has radius R < R₀ and mass M = M₀

R F U R or U F or U R or F or U  The new sphere has mass M = M₀ and density ρ < ρ₀

R F U R or U F or U R or F or U  The new sphere has radius R = R₀ and mass M > M₀

R F U R or U F or U R or F or U  The new sphere has density ρ = ρ₀ and radius R < R₀

R F U R or U F or U R or F or U  The new sphere has density ρ < ρ₀ and radius R > R₀

R F U R or U F or U R or F or U  The new sphere has density ρ = ρ₀ and radius R > R₀

Use chemical potentials to explain the driving force for the spontaneous mixing of gases or liquids

A flywheel with a radius of 0.390 m starts from rest and accelerates with a constant angular acceleration of 0.670 rad/s2. Compute the magnitude of the tangential acceleration, the radial acceleration, and the resultant acceleration of a point on its rim at the start. Compute the magnitude of the tangential acceleration, the radial acceleration, and the resultant acceleration of a point on its rim after it has turned through 60.0 ∘. Compute the magnitude of the tangential acceleration, the radial acceleration, and the resultant acceleration of a point on its rim after it has turned through 120 ∘.

Starting from the one-dimensional motion equation x=Xo + vt

prove that v^2 = Vo^2 + 2a(X-Xo)

If you could eplain as well why/ how each step in the problem proves the equation, this would be greatly helpful.

Thank you!

Show that setting the 4-divergence of current four vector equal to zero gives the equation of continuity.

A 960-kg satellite orbits the Earth at a constant altitude of 95-km.

(a) How much energy must be added to the system to move the satellite into a circular orbit with altitude 193 km?


(b) What is the change in the system's kinetic energy?

(c) What is the change in the system's potential energy?

A marble rolls down an incline, and when it’s halfway down it’s going at 1.12 m/s. Find (a) its starting height and (b) its speed at the bottom.

A bucket of water of mass 16.0 kg is suspended by a rope wrapped around a windlass, that is a solid cylinder with diameter 0.320 m with mass 13.0 kg . The cylinder pivots on a frictionless axle through its center. The bucket is released from rest at the top of a well and falls a distance 10.6 m to the water. You can ignore the weight of the rope.

What is the tension in the rope while the bucket is falling?

Take the free fall acceleration to be g = 9.80 m/s2 .

With what speed does the bucket strike the water?

Take the free fall acceleration to be g = 9.80 m/s2 .

What is the time of fall?

Take the free fall acceleration to be g = 9.80 m/s2 .

While the bucket is falling, what is the force exerted on the cylinder by the axle?

Take the free fall acceleration to be g = 9.80 m/s2 .