If the strip is 29 mm long, how far is the maximum deviation of the strip from the straight orientation? (The deviation is measured from the straight orientation from the interface of the two strips.)Radius of curvature is 53.7 m
For a circular arc of a strip with length L (when straight), the deflection d is given by
(L/2)^2 = d*(2R-d)
The maximum deflection is in the middle. Solve for d.
I got two positive answers...one is really small and one is big, which one do i choose?
The one that is closest to
d = L^2/(8*R)
2R-d is nearly the same as 2R, for small deflections
An aluminum vessel with a volume capacity of 510 cm3 is filled with water to the brim at 20.0°C. The vessel and contents are heated heated to 45.5°C. During the heating process, will the water spill over the top (in this case the answer would be positive), will there be more room for water to be added (the answer would be negative), or will the water level remain the same? Calculate the volume of water that will spill over or that could be added.
An aluminum vessel with a volume capacity of 570 cm3 is filled with water to the brim at 20.0°C. The vessel and contents are heated heated to 58.9°C. During the heating process, will the water spill over the top (in this case the answer would be positive), will there be more room for water to be added (the answer would be negative), or will the water level remain the same? Calculate the volume of water that will spill over or that could be added.
An aluminum vessel with a volume capacity of 310 cm3 is filled with water to the brim at 20.0°C. The vessel and contents are heated heated to 44.9°C. During the heating process, will the water spill over the top (in this case the answer would be positive), will there be more room for water to be added (the answer would be negative), or will the water level remain the same? Calculate the volume of water that will spill over or that could be added.
To find the maximum deviation of the strip from the straight orientation, we need to calculate the deflection caused by the curvature of the curved surface.
The key concept here is the relationship between the curvature (radius of curvature) of the surface and the deflection caused by it. This relationship is defined by the formula:
Deflection = (Curvature * Length^2) / (2 * Radius of Curvature)
Let's plug in the values we have:
Length of the strip (L) = 29 mm = 0.029 m
Radius of curvature (R) = 53.7 m
Now we can calculate the maximum deviation (D) using the formula:
D = (Curvature * Length^2) / (2 * Radius of Curvature)
D = (R * L^2) / (2 * R)
D = (0.029^2 * 53.7) / (2 * 53.7)
D = 0.029^2 / 2
D ≈ 0.00041965 m
Therefore, the maximum deviation of the strip from the straight orientation is approximately 0.00041965 meters.