A measuring microscope is used to examine the interference pattern. It is found that the average distance between the centers of

To find the volume, we can utilize the ratio of mass to density, as shown by:

volume = mass / density

 

A. when mass = 5.5 kg = 5500 g; density = 1.60 g/cm^3

volume = 5500 g / (1.60 g/cm^3)

resulting in volume = 3,437.5 cm^3

By rounding according to significant digits:

volume = 3,400 cm^3 = 3.4 L

 

B. when mass = 4.9 kg = 4900 g; density = 1.36 g/cm^3

volume = 4900 g / (1.36 g/cm^3)

calculating gives volume = 3,602.94 cm^3

Considering significant digits:

<span>volume = 3,600 cm^3 = 3.6 L</span>

Let T be the force exerted on the rope by her. This force induces tension in the rope, which exerts an upward force on the crates, while the weight of the crate pulls downward. Thus, the net force acting on the crate can be expressed as mg - T, acting in the downward direction. According to Newton's law, we can set up the equation: mg - T = ma. Given that a = 0 (the speed remains constant), this simplifies our equation to mg - T = 0, which leads to T = mg. Therefore, T = 25 x 9.8 = 245 N, indicating that the force she needs to apply is 245 N.

Answer:

a)  τ = i ^ (y - z ) + j ^ (z Fₓ - x ) + k ^ (x - y Fₓ)

b) τ = (-0.189i ^ -5.6 j ^ + 33.978k ^) N m

c) α = (-7.8 10⁻⁴ i ^ - 2.3 10⁻² j ^ + 1.4 10⁻¹ k ^) rad / s²

Explanation:

a) The torque can be expressed as

        τ = r x F

To tackle this equation, using the determinant approach is the most straightforward method

         

The resulting expression is

      τ = i ^ (y - z ) + j ^ (z Fₓ - x ) + k ^ (x - y Fₓ)

b) Now let's compute

     τ = i ^ (0.075 1.4 -0.035 8.4) + j ^ (0.035 2.8 - 4.07 1.4) + k ^ (4.07 8.4 - 0.075 2.8)

     τ = i ^ (- 0.189) + j ^ (-5.6) + k ^ (33,978)

     τ = (-0.189i ^ -5.6 j ^ + 33.978k ^) N m

c) To find angular acceleration, we use

       τ = I α

       α = τ / I

The moment of inertia being a scalar means that only the magnitude of each component changes, orientation remains constant.

           

     α = (-0.189i^  -5.6 j^  + 33.978k^) / 241

     α = (-7.8 10⁻⁴ i ^ - 2.3 10⁻² j ^ + 1.4 10⁻¹ k ^) rad / s²

Answer: The resulting speed is . Option (a) stands as the correct choice. Explanation: Given the context, the potential difference entails calculations linked to speed assessment. If instead accelerated through a different potential difference, the resulting speed will be computed accordingly.

The distinction lies in the fact that the candle emits an emission spectrum, while the book reflects an absorption spectrum. In the case of the book, light is observed from all directions, causing its reflection to be diffuse. Explanation: The light emitted by a candle originates from the heat of the flame, composed of a combination of emissions from a black body at that temperature along with emissions from the chemical elements within the candle. On the contrary, the light reflected off a book cover consists of the incident light spectrum minus the wavelengths that trigger electronic transitions in the cover's elements, resulting in dark areas on the spectrum. Consequently, the difference stems from the candle producing an emission spectrum, whereas the book showcases an absorption spectrum. For a book's cover to reflect light specularly, incident rays would need to reflect uniformly, creating dark areas. However, since light is observed from all directions when reflecting off a book, the result is diffuse reflection.