A ball, which is initially at rest, starts rotating around a fixed point. The ball has a constant angular acceleration. You need to know that the radial acceleration of the ball aradarad is proportional to ball's angular displacement θ

Find the angular displacement of the ball if its resultant acceleration makes an angle of 40 ∘ with the radial direction?

You must provide a brief description of the obstacle you design, highlighting the physical concepts involved and explicitly stating the relevant formulas that are at work. If there’s a specific strategy that would be most effectively for completing the obstacle, include a description of it. Using: Rotation Thank you so much.

A small block with mass 1.50 kgkg is placed against a light spring that is compressed 0.250 mm. The spring has force constant 50.0 N/mN/m . The block and spring are released from rest, and the block travels along a horizontal surface for which the coefficient of kinetic friction between the block and surface is μkμk = 0.500. When the block has moved 0.250 mm and the spring has reached its equilibrium length, the block loses contact with the spring.

Find the speed of the block at the instant when it leaves the spring?

Calculate the maximum speed of the block during its motion?

Algunos espejos nos dan imágenes reales, virtuales, más grandes, más pequeñas, dependiendo de donde se ubiquen los objetos y de las características del espejo. La amplificación de cierto espejo es 2.5 para algún objeto de 3.0 cm de alto, que está alejado 10 cm del espejo.

1. ¿Cuál es la distancia focal de este espejo y la altura de la imagen?
2. Haga el dibujo, mostrando todas las partes importantes para este espejo, y trace el diagrama de rayos para ubicar la imagen, y enuncie las principales características de la imagen con respecto al objeto.

2a. Confirm that the position and momentum, p=-ℏ ∂/∂x, operators do not commute.

2b. Show how the statement above limits the ability for a state that to be both an eigenstate of position and momentum concurrently.

2c. For an eigenstate where the momentum is zero, show that x than p leads to a result, xp, that is different than that of p then x.

Calculate how far apart an electron and a proton would have to be for their electric force to be equal in magnitude to their gravitational force in a hydrogen atom (a distance of 52.9pm). Give the answer in meters. Then convert meters to light-years given that the speed of light is 2.998*10⁸ m/s and a year is approximately 365.2421 days, and a light year is the distance light travels in one year.

Using the wave functions

for the potential energy step, apply the boundary conditions of ψ and

dψ/dx

to find B' and C' in terms of A', for the potential step when particles are incident from the negative x direction. Evaluate the reflection and transmission coefficients

R=

and

T=

.

( k₀=42 and k₁=12)

It is given that M = 185 kg and R = 1.65 m. What if an inner solid cylinder is cut out from it, with a radius of (1/2)R?

a) What is the moment of inertia around the central axis (as in the example) of this inner cylinder?

b) What is the moment of inertia of the remaining hollow cylinder around the same axis? (Notice that all answers are independent of the length L.)

Two charges, +9 µC and +15 µC, are fixed 1 m apart, with the second one to the right. Find the magnitude and direction of the net force (in N) on a −8 nC charge when placed at the following locations.

(a)

halfway between the two

magnitude ______________ N

(b)

half a meter to the left of the +9 µC charge

magnitude __________ N

(c)

half a meter above the +15 µC charge in a direction perpendicular to the line joining the two fixed charges (Assume this line is the x-axis with the +x-direction toward the right. Indicate the direction of the force in degrees counterclockwise from the +x-axis.)

magnitude__________ N

direction____________ ° counterclockwise from the +x-axis

A -3.00 nC point charge is at the origin, and a second -5.50 nC point charge is on the x-axis at x = 0.800 m.

Q1: Find the net electric force that the two charges would exert on an electron placed at point on the x-axis at x = 0.200 m.

Q2: Find the net electric force that the two charges would exert on an electron placed at point on the x-axis at x = 1.20 m.

Q3: Find the net electric force that the two charges would exert on an electron placed at point on the x-axis at x = -0.200 m.

A 1.20 kg iron cube at 343 K is placed in contact with olive oil at 283 K in a thermally insulated container. The specific heat of iron and oil is 450 J/(kg.K) and 1970 J/(kg.K), respectively. Both matters reach thermal equilibrium at 301.8 K, and there is no phase change and no chemical process in this example. (a) Find the amount of heat transfer for (i) the iron cube, and (ii) the olive oil. (b) Find the total change in entropy of this entire iron-oil system. Does your result validate the 2nd Law of Thermodynamics?

A solid S occupies the region of space located outside the sphere x² + y² + z² = 8 and inside the sphere x² + y² + (z - 2)² = 4. The density of this solid is proportional to the distance from the origin.

• Determine the center of mass of S.
• Is the center of mass located inside the solid S ? Carefully justify your answer.

A thin-walled capillary tube (diameter=5mm, length=1m) carries steam at 100degreesC The capillary is covered by a later of insulation (thermal conductivity=0.10W/mK) and thickness delta. Assume that the heat transfer coefficient in the outside ir is 25W/m2K and its temp is 25degreesC. Compute and plot the steady state heat loss from the tube as a function of the thickness of insulation used for the range 0<delta<2cm

how to solve the curvilinear motion in rocket

Compute the relative probability of finding an electron at the bottom of the conduction band relative to the probability of finding an electron at the top of the valence band in a silicon crystal at a temperature of (a) 3 K and (b) 300 K. Use Fermi-Dirac statistics. Compare your answer with the one given by the Boltzmann equation.