3a and c someone please help I really don't understand
1 answer:
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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:
a) 35 kPa
d) 140 N
c) 1) Increasing the brake fluid pressure
2) Increasing the slave piston surface area.
Explanation:
The parameters given are;
a) Force applied to the master cylinder piston = 28 N
Cross sectional area of the master cylinder piston = 8 cm² = 8 × 10⁻⁴ m²
The pressure P on the brake fluid is given by the formula for pressure as follows;
The pressure on the brake fluid, P, produced by the master cylinder piston = 35,000 Pa = 35 kPa
b) Given that the area of the slave piston = 40 cm² = 0.004 m², we have from the formula for pressure, P;
Therefore;
Applied force on the slave piston = 4 × 10⁻³ m² × 35,000 N/m² = 140 N
c) The force, F produced by the slave cylinder piston is given by the relation;
F = Pressure × Area
Therefore, the two ways of increasing the force produced by the slave cylinder piston is as follows;
1) Increasing the pressure in the brake fluid by increasing the force exerted by the master cylinder piston
2) Increasing the surface area of the slave piston.