The New England Merchants Bank Building in Boston is 152 m high. On windy days it sways with a frequency of 0.15Hz , and the acc
eleration of the top of the building can reach 2.5% of the free-fall acceleration, enough to cause discomfort for occupants.
What is the total distance, side to side, that the top of the building moves during such an oscillation?
What is the total distance, side to side, that the top of the building moves during such an oscillation?
1 answer:
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Refer to the diagram shown below.
m = the mass of the medal
T = the tension in the string
g = 9.8 m/s²
Part (a)
The inertial force, F, tends to move the medal away from the windshield when the vehicle accelerates to the right.
Answer: The medal leans away from the windshield.
Part (b)
For force balance,
T cos(15°) = mg
0.9659 T = 9.8m
T = 10.1457m N
Also,
F = Tsin(15°) = 10.1457m*0.2588 = 2.6257m N
The inertial force is equal to the accelerating force, therefore
the acceleration, a, is given by
(2.6257m N) = (m kg)*(a m/s²)
a = 2.6257 m/s²
Answer: 2.626 m/s²
m = the mass of the medal
T = the tension in the string
g = 9.8 m/s²
Part (a)
The inertial force, F, tends to move the medal away from the windshield when the vehicle accelerates to the right.
Answer: The medal leans away from the windshield.
Part (b)
For force balance,
T cos(15°) = mg
0.9659 T = 9.8m
T = 10.1457m N
Also,
F = Tsin(15°) = 10.1457m*0.2588 = 2.6257m N
The inertial force is equal to the accelerating force, therefore
the acceleration, a, is given by
(2.6257m N) = (m kg)*(a m/s²)
a = 2.6257 m/s²
Answer: 2.626 m/s²
The definition of gravitational potential energy would gravitate allows to find the answers for the energy of each object on the highest rung of the ladder are:
a) expression for gravitational potential energy is
b) Energy value
* Body 1 U_p = 82 J
* Body 2 U_p = 38.6 J
* Body 3 18.5 J
The gravitational potential energy is a configuration energy that represents the amount of work that the system can do for a given configuration, its expression is
Where is the gravitational potential energy, m the mass of the body and Δy the difference in height.
In this case it indicates that the minimum height is at the bottom and is equal to zero, the steps of a ladder have a height of approximately y = 15 cm = 0.15 m
They indicate the mass of the bodies are m₁ = 3.10 kg, the mass of the body 2 m₂ = 1.46 kg , the mass of the third object is not observed, suppose it is m₃ = 0.7 kg.
They indicate that the body is placed on the last step, suppose it is a standard 18-step ladder, therefore the total height is
y = # _ steps y_each step
y = 18 0.15
y = 2.70 m
the gravitational potential energy to the capacity of the body is
body 1
= m₁ g Δy₁
U_p = 3.10 9.8 (2.70 -0)
U_p = 82 J
body 2
U_p = 1.46 9.8 ( 2.7-0)
U_p = 38.6 J
body 3
U_pUp = 0.70 9.8 (2.7-0)
U_p = 18.5 J
In conclusion, using the definition of gravitational potential energy, we can find the answers for the energy of each object on the highest rung of the ladder are;
a) expression for gravitational potential energy is
b) Energy value
* Body 1 U_p = 82.0 J
* Body 2 U_p = 38.6 J
* Body 3 U_p = 18.5 J
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