The child on a swing can be modeled as a simple pendulum. The period of a simple pendulum is given by
What question can a student BEST answer when comparing and contrasting the models?
1 answer:
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Answer:
5.886 J
Explanation:
Given:
The mass of the book is, kg
Height of lift is, m
Acceleration due to gravity is, m/s²
Now, gain in gravitational potential energy is a function of change in position and is given as:
Here, is the change in gravitational potential energy.
Plug in 0.5 kg for , 9.81 for
and 1.2 for
. Solve for
Therefore, the gain in gravitational energy of the book is 5.886 J.
1) 2.17 s
The period of a mass-spring oscillating system is given by
where k is the spring constant and m is the mass attached to the spring. In this problem, we have
k = 25.1 N/m
m = 3.0 kg
Substituting into the equation, we find
2) 0.46 Hz
The frequency of the oscillating system is equal to the reciprocal of the period:
Therefore, by substituting T=2.17 s, we find:
3) 0.13 s
As before, the period of a mass-spring oscillating system is given by
where k is the spring constant and m is the mass attached to the spring. In this part of the problem, we have
k = 25.1 N/m
m = 11 g = 0.011 kg
Substituting into the equation, we find
4) 7.69 Hz
The frequency of the oscillating system is equal to the reciprocal of the period:
Therefore, by substituting T=0.13 s, we find:
5) 1.59 s
Again, the formula for the period of a mass-spring oscillating system is given by
In this part of the problem, we have
k = 25.1 N/m
m = 1.6 kg
Substituting into the equation, we find