A 1.0-kg block and a 2.0-kg block are pressed together on a horizontal frictionless surface with a compressed very light spring
1 answer:
Answer:
4. both blocks will both have the same amount of kinetic energy.
Explanation:
When the blocks are released free from the compression force, the spring exerts equal and opposite force on each block but the block with heavier (double) mass will attain slower ( half ) speed as compared to the lighter block according to the law of inertia. This works in synchronization to energy conservation.
Spring force is given as:
where: length of compression in the spring
<u>We know kinetic energy is given by:</u>
Hence the kinetic energy of both the blocks is equal when they are released to move free.
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To develop this problem it is necessary to apply the oscillation frequency-related concepts specifically in string or pipe close at both ends or open at both ends.
By definition the oscillation frequency is defined as
Where
v = speed of sound
L = Length of the pipe
n = any integer which represent the number of repetition of the spectrum (n)1,2,3...)(Number of harmonic)
Re-arrange to find L,
The radius between the two frequencies would be 4 to 5,
Therefore the frequencies are in the ratio of natural numbers. That is
Here f represents the fundamental frequency.
Now using the expression to calculate the Length we have
Therefore the length of the pipe is 1.3m
For the second harmonic n=2, then
Therefore the length of the pipe in the second harmonic is 2.6m
Answer:
(a) 0.115 m
(b) 2.08 x 10^-5 J
Explanation:
mass of bob, m = 81 g = 0.081 kg
The equation of oscillation is given by
θ = 0.068 Cos {9.2 t + Ф}
Now by comparison
The angular velocity
ω = 9.2 rad/s
(a)
where, L be the length of the pendulum
L = 0.115 m
(b) A = L Sinθ
A = 0.115 x Sin 0.068
A = 7.8 x 10^-3 m
Maximum kinetic energy
K = 0.5 x mω²A²
K = 0.5 x 0.081 x 9.2 x 9.2 x 7.8 x 7.8 x 10^-6
K = 2.08 x 10^-5 J