Pythagorean Theorem and Pendulums

In summary: The maximum speed of the 100 g pendulum mass is when it has a length of 100 cm and an amplitude of 50 cm.
  • #1
Soley101
37
0

Homework Statement


Calculate the maximum speed of the 100 g pendulum mass when it has a length of 100 cm and an amplitude of 50cm. sorry my computer won't access the other thread. i don't know any other laws of conservations of energy or trig very well. also, when the pendulum as an amplitude of 50 cm , how does this lend me knowledge.




Homework Equations


pythagorean theorem (i would like to use this).
a=9.8 m/s2
what does amplitude mean, the pendulums height, or how far the pendulum is from its maximum speed point


The Attempt at a Solution


max of pendulum is at bottom.
pendulum starts gainig speed of a from top till reaches bottom.
 
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  • #2
Soley101 said:
Calculate the maximum speed of the 100 g pendulum mass when it has a length of 100 cm and an amplitude of 50cm.
I assume that this means the pendulum mass reaches a height of 50cm above the lowest point.

Hint: Consider conservation of mechanical energy.
 
  • #3
you cannot solve this problem without using pythagorean theorem, so don't worry :smile:
the amplitude of a pendulum is the displacement of the bob from the equilibrium position. it is not the arc length or anything, it is the displacement.

first draw a figure and call one of the distances you don't know x
then write the others in terms of x

then, u will need to solve a quadratic which u will form by using pythagorean theorem. and u will get 2 values for x. which one do you think is more reasonable to use?

when u get x, construct an equation concerning conservation of energy. think about what the maximum speed impilies

then solve your equation to get the max. speed
 
  • #4
Doc Al said:
I assume that this means the pendulum mass reaches a height of 50cm above the lowest point.

the amplitude of a pendulum is defined to be the displacement from the equilibrium position
 
  • #5
esalihm said:
the amplitude of a pendulum is defined to be the displacement from the equilibrium position
Good point! :wink:
 
  • #6
Soley101 did u get the answer?
 

What is the Pythagorean Theorem?

The Pythagorean Theorem is a fundamental principle in mathematics that states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. It is often written as a^2 + b^2 = c^2, where a and b are the lengths of the legs of the triangle and c is the length of the hypotenuse.

How is the Pythagorean Theorem used in pendulums?

In pendulums, the Pythagorean Theorem is used to calculate the length of the pendulum based on the period of its swing. The period of a pendulum is the time it takes for one complete swing, and it is directly proportional to the square root of its length. This relationship is derived from the Pythagorean Theorem, as the length of the pendulum is one of the sides in a right triangle formed by the pendulum's swing.

What is a simple pendulum?

A simple pendulum is a theoretical model used to study the behavior of pendulums. It consists of a point mass (known as the pendulum bob) suspended by a massless string or rod. The motion of a simple pendulum is governed by the laws of motion and the principles of conservation of energy, and it is often used to demonstrate the principles of harmonic motion.

What factors affect the period of a pendulum?

The period of a pendulum is affected by several factors, including the length of the pendulum, the mass of the pendulum bob, and the amplitude (the angle at which the pendulum is released). The period is also affected by external factors such as air resistance, friction, and the strength of the gravitational field.

What is the relationship between the Pythagorean Theorem and simple harmonic motion?

The relationship between the Pythagorean Theorem and simple harmonic motion is that the motion of a simple pendulum follows a sinusoidal pattern, which can be described using the sine function. The Pythagorean Theorem is used to derive the equations of motion for a simple pendulum, which are then used to calculate the position, velocity, and acceleration of the pendulum at any given time. This relationship helps us understand the fundamental principles of harmonic motion and its connection to the Pythagorean Theorem.

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