A wheel accelerates uniformly from rest to an angular speed of 25 rad/s in 10 s.(a) Find the angular acceleration of the wheel.

Response:

a) 318.2 W/m^2

b) 2.5 x 10^-4 J

c) 1.55 x 10^-8 v/m

Reasoning:

The laser power P = 1 mW = 1 x 10^-3 W

duration t = 250 ms = 250 x 10^-3 s

Taking a beam diameter of 2 mm = 2 x 10^-3 m

therefore

the beam's cross-sectional area A = = (3.142 x )/4

A = 3.142 x 10^-6 m^2

a) The intensity I = P/A

where P refers to the laser's power

and A represents the beam's cross-sectional area

I = ( 1 x 10^-3)/(3.142 x 10^-6) = 318.2 W/m^2

b) The total energy delivered E =Pt

where P is the beam's power

and t is the exposure duration

E = 1 x 10^-3 x 250 x 10^-3 = 2.5 x 10^-4 J

c) The peak electric field can be computed as

E =

where I signifies the beam's intensity

and E is the electric field

c is the speed of light = 3 x 10^8 m/s

= 8.85 x 10^9 m kg s^-2 A^-2

E = = 1.55 x 10^-8 v/m

To tackle this question, we know the following:

1 Albert equals 88 meters.

1 A = 88 m.

Initially, we square both sides of the equation:

(1 A)^2 = (88 m)^2

1 A^2 = 7,744 m^2

<span>Since 1 acre equals 4,050 m^2, let’s divide both sides by 7,744 to find out how many acres match this value:</span>

1 A^2 / 7,744 = 7,744 m^2 / 7,744

(1 / 7,744) A^2 = 1 m^2

Then multiply both sides by 4,050.

(4050 / 7744) A^2 = 4050 m^2

0.523 A^2 = 4050 m^2

<span>Thus, one acre is approximately 0.52 square alberts.</span>

Response: a) 0.04 kW = 40 W

b) 0.05

Explanation:

A)

The thermal efficiency of the power cycle is calculated as Input / Output

Input = 10 kW + 14,400 kJ/min which translates to 10 kW + 14,400 kJ/(60s) = 10 kW + 14,400/60 kW.

Output equals 10 kW

Thus, Thermal Efficiency = Output / Input = 10 kW / 250 kW = 0.04 kW = 40 W

B)

Maximum Thermal Efficiency of the power cycle is defined as 1 - T1/T2

where T1 = 285 Kelvin

and T2 = 300 Kelvin

Thus, Maximum Thermal Efficiency = 1 - T1/T2 = 1 - 285/300 = 0.05

<span>None of the provided options presents an accurate statement. The third choice is nearly correct,
yet it can be considered misleading.

The pencil seems broken due to light bending away from a straight path
when it transitions from air to water.</span>

The answer is:

Details are as follows:

According to the problem, we have

The combined mass of A and B is 60kg

A's speed is 2m/s

B's speed is 1m/s

The mass of the bag is 5kg

Typically, the momentum of astronaut A along with the bag is defined by

To prevent a collision, astronaut A should maintain a speed that is either equal to or less than astronaut B's speed

Thus, the minimum speed astronaut A should achieve corresponds to that of astronaut B, which is 1

Consequently,