One of the advantages of skates is that they allow you to push against ice, which
typically has low friction. Let’s consider an hockey player on frictionless ice who is
going to shoot a slap shot. The player weighs Mp = 100kg. He is going to fire the
puck, which weighs Mpuck = 0.5kg with a velocity of v = 50(m/s). How fast does the
hockey player recoil in the direction opposite to the puck’s trajectory. If the force he
exerts on the puck occurs over a time, ∆t = 0.1s what is the average force needed to
create the impulse that accelerates the puck to that velocity?

Please explain carefully so that I can understand it!

Two charged metal balls of a different size, radius R1 is bigger than R2, and then connected by a wire. Which ball gets the larger charge? What about charge density? Prove the answer.

Uniqueness theorem

Prove that the solution to the Laplace’s equation in a spatial region is unique if the potential is specified on the surface of the region.

A charge of -2.705 μC is located at (2.830 m , 4.456 m ), and a charge of 1.460 μC is located at (-2.757 m , 0).

Find the electric potential at the origin. the answer to this was 154 V.

Here is the part I dont understand. Need (x,y) coordinates

there is one point on the line connecting these two charges where the potential is zero. Find this point.(x,y)

Express your answers using three decimal places separated by a comma.

Please show work and answer in (x,y)

True/False:

1. Gravity is an example of inverse square behavior.
2. A grindstone is rotating at constant rotational speed. There is a net torque on it.
3. A lever multiplies a force but does not redirect it.
4. On a rotating merry go round one child sits halfway out between the axis and the edge. Another child sits on the edge. Both kids have the same rotational speed.
5. Angular momentum is a vector.

If X, Y and Z are three arbitrary vectors, prove these identities:

a. (X×Y).Z = X.(Y×Z)

b. X×(Y×Z) = (X.Z)Y – (X.Y)Z

c. X.(Y×Z) = -Y.(X×Z)

How can a force (e.g., a muscle force or a gravitational force) produce a translatory and a linear force simultaneously?

1 .Identify type of image represented in the following graphic:

Group of answer choices

Real

Virtual

2. Identify type of image represented in the following graphic:

Group of answer choices

Virtual

Real

3. Identify the direction that the refracted beam will bend:

Group of answer choices

Towards the normal

Away from the normal

4. The capability of a prism that to separate white light into its constituent colors is due to the slight variation of index of refraction as a function of wavelength. This property is referred to as:

Group of answer choices

Dispersion

Funky Colors

Diffusion

Total internal Reflection

5. True or false: A ray of light within a medium of higher index of refraction comes to an interface with a medium of lower index of refraction at an angle greater than the critical angle. There is no light transmitted into the medium of lower index of refraction

Group of answer choices

True

False

6.You are standing exactly halfway between to perfectly parallel mirrors. You see your reflection in the mirror that you are facing, but you notice a second (and many more) reflection that appears even further away.   How much further away is the second reflection image from the first reflection image in the mirror you are facing.

Group of answer choices

10 feet from first reflection

• 1 Light year from first reflection

15 feet from first reflection

5 feet from first reflection

7.(True or false) Parallel rays that pass through a thin lens will be be directed through the lens focal point.

Group of answer choices

True

False

8.(True or false) The law of reflection is mathematically expressed with Snell's law: n 1 sin ⁡ θ 1 = n 2 sin ⁡ θ 2

Group of answer choices

True

False

Suppose a photon is absorbed by the electron in a hydrogen atom in an n= 2 state. What wavelength should the photon have to enable the electron to transition to the n= 4

state? Once the photon is absorbed, what are the various wavelengths of photons that could be emitted by the atom? (Use Bohr approximation).

A 54.0-kg woman stands at the western rim of a horizontal turntable having a moment of inertia of 490 kg · m² and a radius of 2.00 m. The turntable is initially at rest and is free to rotate about a frictionless, vertical axle through its center. The woman then starts walking around the rim clockwise (as viewed from above the system) at a constant speed of 1.50 m/s relative to the Earth. Consider the woman–turntable system as motion begins.

(a) Is the mechanical energy of the system constant?

Yes/No

(b) Is the momentum of the system constant?

Yes/No

(c) Is the angular momentum of the system constant?

Yes/No

(d) In what direction and with what angular speed does the turntable rotate?

Magnitude: ___ rad/s

Direction: Clockwise/Counterclockwise

(e) How much chemical energy does the woman's body convert into mechanical energy of the woman–turntable system as the woman sets herself and the turntable into motion?
___ J

A spherical shell is cut into two halves that remain forming the
sphere, but are electrically isolated from each other at a negligible distance. The nortern hemisphere is at potential +V_0 and the southern hemisphere is at potential -V_0. Obtain the potential V (r, θ, ϕ) inside and outside of the sphere.

Figure out

how to test what happens when the light rays come from underwater. Compare your ideas about why

things look different under water to how light rays appear to “bend.”.

Hydrogen is used in some semiconducting devices to improve their performance. Consider a material in which atomic hydrogen (H) diffuses at 1.8 × 10^-24 m²/s at 329 K.

1) When in use, the device is exposed to a large electric field. If the force on each charged hydrogen nucleus is 10 ^-11 N, use the fluctuation-dissipation relation to find out how fast they drift in the field at 329 K.

Is every galaxy in the universe rotating in the same way as our solar system?