To prevent dust and soot particles from polluting the atmosphere, industry often employs static electric charges in their smokestacks.

Explain the physics principle involved in this application.

In: Physics

2) The Plank radiation law is

I(lambda) = 2 pi h c^{2}/[lambda^{5} (e
^{hc/labda kT} -1)]

take the derivative of this expression with respect to lambda to show

lambda_{max} = hc/(4.965kT).

You may uses 5 - x = 5 e^{-x} is true for x = 4.965.

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The charge at a point in space is q (t) = 0.5 cos (6t) C. What is the current at t = −2 s? At an arbitrary time t?

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A -10.0
nC
point charge and a +20.0
nC
point charge are 15.0
cm
apart on the *
x*-axis.

Part A)

What is the electric potential at the point on the *
x*-axis
where the electric field is zero? Answer in V

Part B)

What is the magnitude of the electric field at the point on
the *
x*-axis,
between the charges, where the electric potential is zero? Answer
in N/C

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An object with total mass m_{total} = 14.6 kg is sitting
at rest when it explodes into three pieces. One piece with mass
m_{1} = 4.7 kg moves up and to the left at an angle of
θ_{1} = 20° above the –x axis with a speed of v_{1}
= 26.8 m/s. A second piece with mass m_{2} = 5.1 kg moves
down and to the right an angle of θ_{2} = 25° to the right
of the -y axis at a speed of v_{2} = 23.5 m/s.

What is the x-component of the velocity of the third piece?

What is the y-component of the velocity of the third piece?

What is the magnitude of the velocity of the center of mass of the pieces after the collision?

Calculate the increase in kinetic energy of the pieces during the explosion.

In: Physics

1. Derive PV^Gamma = constant

2. All adiabatic relations

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An 8000 kg truck traveling with a velocity of 20. 0 m/s in a direction 30 ° south of east and a 6250 kg car traveling with a velocity of 25. 0 m/s 40 ° north of east collide in a perfectly inelastic collision. Find (a) the final speed and (b) the direction of the combined mass. Also, calculate (c) the change in the kinetic energy of the system.

In: Physics

1. Determine the variance in position and momentum,
Δx^{2}=<x^{2}>−<x>^{2} and
Δp^{2}=<p^{2}>−<p>^{2} for the
ground-state SHO and show that they satisfy the Heisenberg
uncertainty relation, (Δx)(Δp)≥ℏ2

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Two cars are approaching each other, one traveling north with a momentum of 3 kg-m/s and one traveling east with a momentum of 4 kg-m/s. The two cars collide and stick together. Right after the collision (choose all that apply)

1. the eastern component of the momentum of the two cars is 4 kg-m/s.

2. the northern component of the momentum of the two cars is 3 kg-m/s.

3. the total momentum of the two cars is 7 kg-m/s

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(a)
A solenoid having an inductance of 6.30μH

is connected in series with a 1.6 kΩ

resistor. If a 14.0V

battery is connected across the pair, What is the current in
units of A

through the resistor at time t=1.0τL

?

(b)A certain elastic conducting material is stretched into a
circular loop of 4.6 cm

radius. It is placed with its plane perpendicular to a uniform
0.5 T

magnetic field. When released, the radius of the loop starts
to shrink at an instantaneous rate of 75.0cm/s

. What emf is induced in the loop at that instant in units of
V

?

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A symmetrical table of height 0.750 m, length 1.55 m, and weight 462 N is dragged across the floor by a force applied to its front edge. The force is directed to the right and upward and makes an angle of 30.0° with the horizontal.

(a) Find the minimum force necessary to drag the table across
the floor. The coefficient of sliding friction between table and
floor is 0.375. 164.45 N

(b) Calculate the normal force and the frictional force on each
leg.

front legs: | normal force | |

frictional force | ||

back legs: | normal force | |

frictional force |

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The formula for length contraction gives the length of an interval on a ruler moving with velocity v relative to an observer as where L is the length of the same interval on a ruler at rest with respect to the observer. By what fraction is the length of a meter stick reduced if its velocity relative to you is measured to be 87 percent of the speed of light?

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Sound with a frequency 710 Hz from a distant source passes through a doorway 1.17 m wide in a sound-absorbing wall.

(a) Find the number of the diffraction minima at listening
positions along a line parallel to the wall.

(b) Find the angular directions of the diffraction minima at
listening positions along a line parallel to the wall. (Enter your
answers from smallest to largest starting with the first answer
blank. Enter NONE in any remaining answer blanks.)

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A 10 g bullet traveling at 350 m/s strikes a 9.0 kg , 1.2-m-wide door at the edge opposite the hinge. The bullet embeds itself in the door, causing the door to swing open. What is the angular velocity of the door just after impact?

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The wạlls of ạn ice chest ạre mạde of 2.00-mm-thick insulạtion
hạving ạ thermạl conductivity 0.00300 W/m∙K. The totạl surfạce ạreạ
of the ice chest is 1.20 m^{2}. The temperạture of the
outside surfạce of the chest is 20.0 °C. The lạtent heạt of fusion
of wạter is 334 kJ/kg.

How mạny hours (time) does it tạke to melt 4.00 kg of ice plạced inside the ice chest?

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