A 34-kg child on an 18-kg swing set swings back and forth through small angles. If the length of the very light supporting cable
1 answer:
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Consider two aluminum rods of length 1 m, one twice as thick as the other. If a compressive force F is applied to both rods, their lengths are reduced by and
, respectively.The ratio ΔLthick rod/ΔLthin rod is:
a.) =1
b.) <1
c.) >1
Answer:
The ratio is less than 1 i.e option B is correct
Explanation:
The Young Modulus of a material is generally calculated with this formula
Where is the stress =
is the strain =
Making Strain the subject
now in this question we are that the same tension was applied to both wires so
would be constant
Hence
for the two wire we have that
Looking at young modulus formula
Now we are told that a comprehensive force is applied to the wire so for this question
is constant
And given that the length are the same
so
Now we are told that one is that one rod is twice as thick as the other
So it implies that one would have an area that would be two times of the other
Assuming that
So
From the question the length are equal
So
Hence the ratio is less than 1
Answer:
b. 29.2 rev/min
Explanation:
- Assuming no external torques acting during the process, total angular momentum must be conserved, as follows:
- The initial angular momentum L₀, can be expressed as follows:
where I₀ = initial moment of inertia = moment of inertia of the disk +
moment of inertia of the cylinder and ω₀ = initial angular velocity =
30.0 rev/min.
- Replacing by the values, we get:
⇒ L₀ = I₀* ω₀ = 0.2009 kg*m² * 30.0 rev/min = 6.027 kg*m²*rev/min
- The final angular momentum can be written as follows:
where If = final moment of inertia = moment of the inertia of the solid
disk + moment of inertia of the clay flattened on a disk, and ωf = final
angular velocity.
- Replacing by the values, we get:
⇒ Lo =Lf = If*ωf
- Replacing (2) in (1), and solving for ωf, we get: