You are holding a shopping basket at the grocery store with a 1.24-kg carton of cereal at the left end of the basket. The basket is 0.61 m long. Where should you place a 1.9-kg

gallon of milk, relative to the left end of the basket, so that the center of mass of your groceries is at the center of the basket?

Hello ! I'm studying for a test tomorrow and looking for steps on how to do this.

A spherical shell has in inner radius R_i and an outer radius R_o. Within the shell, a total charge Q is uniformly distributed.

Calculate:

a) the charge density within the shell (if you cannot get this answer, you can proceed without it).

b) the electric field strength E(r) outside the shell (r > R_o).

c) the electric field strength inside the shell (r< R_i).

d) the electric field within the shell (R_i < r < R_o)

e) show that your solutions match both inner and outer boundaries

f) Draw a graph E versus r.

Cosmic acceleration and dark energy

Q: How do we measure the changes in the expansion rate?

Q: What is a standard candle? Why are supernovae useful as standard candles?

Q: What is so bizarre about the universe accelerating? What are the possible explanations for this? Which solution is the least radical?

Q: Why is dark energy invoked to explain the accelerated expansion?

The maximum distance from the Earth to the Sun (at aphelion) is 1.521 1011 m, and the distance of closest approach (at perihelion) is 1.471 1011 m. The Earth's orbital speed at perihelion is 3.027 104 m/s. Ignore the effect of the Moon and other planets. (a) Determine the Earth's orbital speed at aphelion. m/s (b) Determine the kinetic and potential energies of the Earth

C) A 0.315 kg bird flying along at 6.5 m/s sees a 0.019 kg insect heading straight toward it with a speed of 23 m/s (as measured by an observer on the ground, not by the bird). The bird opens its mouth wide and enjoys a nice lunch. What is the bird's speed immediately after swallowing the insect? Answer in m/s

D) A 2.6 kg block slides along a frictionless surface at 1 m/s. A second block, sliding at a faster 5.9 m/s, collides with the first from behind and sticks to it. The final velocity of the combined blocks is 2.9 m/s. What was the mass of the second block? Answer in kg

An airplane is dropping an aid package in a remote area. The plane is moving horizontally at speed v0 and the package lands a horizontal distance L from where it was released by the plane. a) Find the time it takes for the package to land. b) Find the altitude of the plane. c) Find the velocity (vector) of the package when it lands. d) Find the speed of the package when it lands. Write your results in terms of v0, L, and g. Check the units/dimensions for each answer.

Describe the difference between photoablation and plasma-induced ablation. Discuss the advantages and disadvantages of these interaction mechanisms for refractive corneal surgery.

A bullet with a mass m b = 13.1 g is fired into a block of wood at velocity v b = 245 m/s. The block is attached to a spring that has a spring constant k of 205 N/m. The block and bullet continue to move, compressing the spring by 35.0 cm before the whole system momentarily comes to a stop. Assuming that the surface on which the block is resting is frictionless, determine the mass of the wooden block.

The picture below shows an isolated system with a fairly massive wheel at one end, attached via its axle to a long shaft, like a bike tire on a bike frame, but the bike frame is merely a low mass 'truss.' At the other end of this long shaft is a mass of roughly the same magnitude as the wheel, so the center of gravity (CG) is roughly in the middle of the shaft. This mass is fixed to the shaft with no rotation possible. The assembly is floating motionless in 'space', with no contact to anything else.

Diagram of apparatus

If a motor on the 'truss' causes the wheel to spin in one direction, the truss would begin to spin in the other direction about the common center of mass. The net angular momentum would thus be zero both before and after the spinning commences. The wheel and the truss would rotate in the same plane. The actual rotation rate of each part is dependent upon the individual masses, wheel radius, and the length of the shaft. It is getting complex, but so far easy enough to envision in general.

Now, place into the 'truss' a mechanism that causes this long shaft to rotate on its long axis (which would be perpendicular to the spin axis) while it is still undergoing the above rotation relative to the wheel. Upon rotation at this new joint, a force is applied to the axle of the spinning wheel (and of course to the mass at the other end of the truss, too) causing each part to try to turn in the opposite direction. Given that the net angular momentum is still zero, the vector sum of the individual parts (the spinning wheel and the body as a whole rotating around its CG) must be equal and opposite. I cannot envision the result, however, nor do I have the background to derive the equations of motion of this 'whirly gig.' The best I can imagine is that the plane of overall rotation should change, with the plane of the wheel's rotation changing in the opposite direction. This would seem to result in a state where the wheel is no longer spinning in the same plane as the overall assembly, but that would seem unsustainable and perhaps unstable. How can the behavior of this system be understood?

3. Two ice skaters collide on the ice. A 39.6-kg skater moving South at 6.21 m/s collides with a 52.1-kg skater

moving East at 4.33 m/s. The two skaters entangle and move together across the ice. Determine the magnitude

and direction of their post-collision velocity (answer: 3.64 m/s at 42.5 degrees)

Please provide a detailed diagram

A man stands on the roof of a building of height 15.7m and throws a rock with a velocity of magnitude 26.3m/s at an angle of 25.0? above the horizontal.

1) Calculate the maximum height above the roof reached by the rock.

answer: y=___ m

2) Calculate the magnitude of the velocity of the rock just before it strikes the ground.

answer: v=___m/s

3) Calculate the horizontal distance from the base of the building to the point where the rock strikes the ground.

answer: x=___ m

A Bottle of compressed nitrogen is used in your laboratory to flush the CVD furnace. If you received the 20-liter bottle at room temperature (25°C) and 10 MPa. After the slow release of nitrogen (isothermal), estimate the pressure if you have disbursed 1 kg.

* 2 points

4 MPa

5 MPa

5.6 MPa

4.4 MPa

Other:

Treat the two channel Young