A cylindrical rod of mass M. length L and radius R has two cords wound around it whose ends are ato the ceiling as shown. The rod is held horizontally with the two cords vertical. When the rod s mecase
cords unwind the rod rotates. Find the tension in the cords as they unwind.
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Answer:
T = mg/6
Explanation:
Draw a free body diagram (see attached). There are two tension forces acting upward at the edge of the cylinder, and weight at the center acting downwards.
The center rotates about the point where the cords touch the edge. Sum the torques about that point:
∑τ = Iα
mgr = (1/2 mr² + mr²) α
mgr = 3/2 mr² α
g = 3/2 r α
α = 2g / (3r)
(Notice that you have to use parallel axis theorem to find the moment of inertia of the cylinder about the point on its edge rather than its center.)
Now, sum of the forces in the y direction:
∑F = ma
2T − mg = m (-a)
2T − mg = -ma
Since a = αr:
2T − mg = -mαr
Substituting expression for α:
2T − mg = -m (2g / (3r)) r
2T − mg = -2/3 mg
2T = 1/3 mg
T = 1/6 mg
The tension in each cord is mg/6.
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stratus clouds
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They are uniform and flat, producing a gray layer of cloud cover which may be precipitation-free or may cause periods of light precipitation or drizzle.
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Considering the definition of density, the density of the old coin is 8.92 .
It is neccesary to know that density is defined as the property that matter, whether solid, liquid or gas, has to compress into a given space.
In other words, Density is a quantity that allows us to measure the amount of mass in a certain volume of a substance, that is, density is the relationship between the mass of a substance and the volume it occupies.
Mathematically, the expression for the calculation of density is the quotient between the mass of a body and the volume it occupies:
In this case, you know:
- mass= 26.76 g
- volume= 3 cm³
Replacing in the definition of density:
Solving:
density= 8.92
The density of the old coin is 8.92 .
Learn more about density:
Density = mass/volume
26.76/3 = 8.92
The density is 8.92
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