A solid, homogeneous sphere with a mass of m₀, a radius of r₀ and a density of ρ₀ is placed in a container of water. Initially the sphere floats and the water level is marked on the side of the container. What happens to the water level, when the original sphere is replaced with a new sphere which has different physical parameters? (Answer choices per question: rises, falls, stays the same, rises or stays the same, falls or stays the same)
1. The new sphere has a mass of m < m₀ and a radius of r = r₀.

2. The new sphere has a density of ρ > ρ₀ and a radius of r = r₀.

3. The new sphere has a mass of m = m₀ and a density of ρ > ρ₀.

**Please explain how you got the answers also :) Thank you!

An air bubble at the bottom of a lake 32.0m deep has a volume of 1.00 cm3.

If the temperature at the bottom is 2.2 ?C and at the top 20.2 ?C, what is the radius of the bubble just before it reaches the surface?

The lab experiment is repeated with the same two glass plates but with a different human hair. The sodium vapor lamp is replaced by a monochromatic light source that produces light of wavelength

The separation between adjacent dark fringes is measured to be 0.485 mm. Calculate the diameter of the hair. (The length of the plates is 12.0 cm.)

(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.)

. Block A and Block B start from rest on a horizontal track. An ideal string pulls cart A with a constant force of 25 N, causing both of the carts to move together as they accelerate. The coefficient of kinetic friction between the blocks and the track is 0.10. Block A= 4.0kg and Block B= 1.0kg (pulled horizontally) Determine the magnitude of each individual force that acts on Block A and each individual force that acts on Block B.

1.) Give the three mathematical definitions of conservative forces?

2.) Explain what the expression "Inertial force" means? and why are inertial forces not really forces?

3.) For pulley-type simple machines specifically, the ideal mechanical advantage is equal to ____?

4.) for ramp-type simple machines specifically, the ideal mechanical advantage is equal to ____?

The great pyramid of Giza consits of approximately 2 million stones, each weighing 1.5 tons ( 3000 lbs). The pyramid is 450 ft high and has a square base measuring 750 ft. Find the work rquired to lift the stones into place from ground level.

Would I use the integral of w=f*d; w=3000*x from 0 to 450? Do I need to do something with the square base and its volume?

Answer is 675,000,000,000 ft-lb

Thermal Storage Solar heating of a house is much more efficient if there is a way to store the thermal energy collected during the day to warm the house at night. Suppose one solar-heated home utilizes a concrete slab of area 13 m2 and 29 cm thick.

If the density of concrete is 2400 kg/m3, what is the mass of the slab?

The slab is exposed to sunlight and absorbs energy at a rate of 1.4 ×107J/h for 10 h. If it begins the day at 25 ∘C and has a specific heat of 750 J/(kg⋅K), what is its temperature at sunset?

Model the concrete slab as being surrounded on both sides (contact area 26 m2) with a 1.7-m-thick layer of air in contact with a surface that is 5.0 ∘C cooler than the concrete. At sunset, what is the rate at which the concrete loses thermal energy by conduction through the air layer?

Model the concrete slab as having a surface area of 24 m2 and surrounded by an environment 5.0 ∘C cooler than the concrete. If its emissivity is 0.93, what is the rate at which the concrete loses thermal energy by radiation at sunset?

A uniform steel rod has mass 0.300 kg and length 40.0 cmand is horizontal. A uniform sphere with radius 8.00 cm and mass 0.700 kg is welded to one end of the bar, and a uniform sphere with radius 6.00 cm and mass 0.580 kg is welded to the other end of the bar. The centers of the rod and of each sphere all lie along a horizontal line.

Part A

How far is the center of gravity of the combined object from the center of the rod?

Express your answer with the appropriate units. Enter negative value if the center of gravity is toward the 0.700 kg sphere and positive value if the center of gravity is toward the 0.580 kg sphere.

A uniform spherical shell of mass M = 2.0 kg and radius R = 13.0 cm rotates about a vertical axis on frictionless bearings (see the figure). A massless cord passes around the equator of the shell, over a pulley of rotational inertia I = 1.92×10^-3 kg m² and radius r = 4.0 cm, and its attached to a small object of mass m = 4.0 kg. There is no friction on the pulley's axle; the cord does not slip on the pulley. What is the speed of the object after it has fallen a distance h = 1.1 m from rest: Use work - energy considerations.

A uniform stationary ladder of length L = 4.2 m and mass M = 19 kg leans against a smooth vertical wall, while its bottom legs rest on a rough horizontal floor. The coefficient of static friction between floor and ladder is μ = 0.38. The ladder makes an angle θ = 53° with respect to the floor. A painter of mass 8M stands on the ladder a distance d from its base.

a. Find the magnitude of the normal force N, in newtons, exerted by the floor on the ladder.

b. Find an expression for the magnitude of the normal force NW exerted by the wall on the ladder.

c. What is the largest distance up the ladder dmax, in meters, that the painter can stand without the ladder slipping?

Lecture 4. Interfacial phenomena and membranes

• How are proteins positioning themselves on the surface of membranes?
• What are liposomes, how are they prepared and for what purposes are they used?
• Which factors of phospholipids are important in determining the fluidity of membranes?
• What are the differences between the phospholipids?
• What are the causes of structural bending of the membrane

A 6 (mu Coulomb) point charge is located at the origin and a - 2.5 (mu Coulomb) point charge is located 1m to the right along the X-axis. Determine the point (besides infinity) at which the electric field is 0.

Please show steps and explaination. Thanks in advance!

Two carts with masses 250. g and 200. g are free to slide without friction on a horizontal airtrack.  The 250.g cart is pushed against a spring, compressing it by 3.00 cm, then released.  It slides towards the initially stationary 200 g mass and collides with it.  After the collision the 200. g mass has a forward velocity of 0.450 m/s and the 250. g mass has a forward velocity of 0.250 m/s.
a)  What was the velocity of the 250. g cart just before the collision?
b)  What was the spring constant?

A cue ball traveling at 7.77 m/s makes a glancing, elastic collision with a target ball of equal mass that is initially at rest. The cue ball is deflected so that it makes an angle of 30.0° with its original direction of travel.

(b) Find the speed of each ball after the collision.