A. What are the three longest wavelengths for standing waves on a 240-cm-long string that is fixed at both ends?
1 answer:
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Answer:
the angular acceleration of the gate is approximately 1.61
Explanation:
Recall the formula that connects the net torque with the moment of inertia of a rotating object about its axis of rotation, and the angular acceleration (similar to Newton's second law with net force, mass, and linear acceleration):
In our case, both forces contribute to the same direction of torque, so we can add their torques up and get the net torque on the gate:
Now we use this value to obtain the angular acceleration by using the given moment of inertia of the rotating gate:
r
Answer:
a) w = - , b) W = - ½ m_woman R² (1 + m_woman R / I²) v²
Explanation:
a) To solve this exercise, let's use the conservation of angular momentum.
We define a system formed by the table and the woman, therefore the torques are internal and the moment is conserved
initial instant. Before starting to move the woman
L₀ = 0
final instant. After starting to move
L_f = I w + m v r
the moment is preserved
L₀ = L_f
0 = Iw + m v r
w = - (1)
the direction of the angular velocity is opposite to the direction of the linear velocity, that is, counterclockwise
b) for this part we use the relationship between work and kinetic energy
W = ΔK
in this case the initial speed is zero and the final speed of the table, using the relationship between linear and angular variables
v = w r
we substitute
W = 0 - ½ I_total w²
I_total = I + m_{woman} R²
W = - ½ (I + m_woman R²) ( ) ²
W = - ½ (m_woman² R² + m_woman³ R³ / I²) v²
W = - ½ m_woman R² (1 + m_woman R / I²) v²