An electron in a vacuum chamber is fired with a speed of 7400 km/s toward a large, uniformly charged plate 75 cm away. The elect
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The thermal expansion of the materials allows to find the deflection of the bimetallist strip is Δy = 3.48 cm
given paramers
* Bimetallic brass / steel tape
* Initial temperature, room temperature T = 20ºC
* Final temperature, boiling water = 100ºC
* initial length L₀ = 222mm (1cm / 10mm) = 22.2cm
* thickness of bimetallic tape e = 0.036 inch (2.54 cm/1 inch) = 0.0914 cm
to find
* perpendicular deviation or deflection (Δy)
Thermal expansion is the phenomenon of change in the length of a body due to the change in temperature, due to the increase in the length of the atomic and molecular bonds, macroscopically it is described by
ΔL = α L₀ ΔT
ΔL and ΔT are the variation of the length and temperature respectively, L₀ is the initial length and α the coefficient of expansion ends.
In this case we have a strip formed by two materials with different coefficient of thermal expansion,
Brass α_{brass} = 19 10⁻⁶ ºC⁻¹
Steel α_{steel} = 11 10⁻⁶ ºC⁻¹
In the attached we can see a diagram of the process, as the temperature increases, the material with greater thermal expansion lengthens more, so the system must curve towards the center of the material with less
thermal expansion. Let's find the length of the strip for each material
brass L_{f brass} - L₀ = α_{brass} L₀ ΔT
Steel L_{f steel} - L₀ = \alpha_{steel} L₀ ΔT
Note that the initial length is the same for the two materials and that the strip is in thermal equilibrium at room temperature.
If we assume that we have an arc of circumference, we can write the length of the arc
θ = L / r
where θ is the angle in radines, L the length of the arc and r the radius of curvature, let's write this equation for each material
brass L_{f \ brass} =θ r₁
steel L_{f \ steel} = θ r₂
we substitute in our equations
θ r₁ - L₀ = α_{brass} L₀ ΔT
θ r₂ - L₀ = α_{steel} L₀ ΔT
let's subtract the two equations
θ (r₁- r₂) = L₀ ΔT (α_{brass} - α_{steel})
the thickness of the strip is
e = r₁ -r₂
θ =
we calculate
θ =
θ = 0.155 rad
Let's use trigonometry to find the perpendicular deflection
tan θ = Δy / L₀
Δy = L₀ tan θ
Δy = 22.2 tan 0.155
Δy = 3.48 cm
Using the thematic expansion of the two materials we find the deflection of the bimetallist strip is 3.38 cm
Learn more about thermal expansion here: brainly.com/question/18717902
Answer:
The rotational inertia of the pendulum around its pivot point is .
Explanation:
The angular frequency of a physical pendulum is measured by the following expression:
Where:
- Angular frequency, measured in radians per second.
- Mass of the physical pendulum, measured in kilograms.
- Gravitational constant, measured in meters per square second.
- Straight line distance between the center of mass and the pivot point of the pendulum, measured in meters.
- Moment of inertia with respect to pivot point, measured in
.
In addition, frequency and angular frequency are both related by the following formula:
Where:
- Frequency, measured in hertz.
If , then angular frequency of the physical pendulum is:
From the formula for the physical pendulum's angular frequency, the moment of inertia is therefore cleared:
Given that ,
,
and
, the moment of inertia associated with the physical pendulum is:
The rotational inertia of the pendulum around its pivot point is .