Why is the principle of periodic motion used in pendulum and quartz clocks?
1 answer:
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Answer:
(a) 34.6429J
(b) -1.57 m
(c) 4.71 m
Explanation:
The derivative of the potential energy with respect to the position is equal to the negative of the force, so:
Then, if we integer both sides, we get:
∫dU = -∫(7x - 11)dx
we know that U is equal to 26 J when x is zero, so:
Finally, the equation for the potential energy is:
Therefore, the maximum positive potential energy is the energy when x is equal to 11/7. That is because the equation of U is the equation of a parable, and the vertex in a parable is given by:
Where b is the number beside x and a is the number beside , Then, the value of maximum U is:
On the other hand, the negative and positive values of x where the potential energy is equal to zero is calculated as:
if we solve this using the quadratic equation, we get:
Finally, the negative and positive values of x where the potential energy is equal to zero are -1.5747 and 4.7175 respectively.