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grin007 [14]
4 years ago
11

Define Mechanical energy. Using an example of the pendulum, explain how kinetic and potential energy relate to the mechanical en

ergy at different positions.
Physics
1 answer:
mamaluj [8]4 years ago
5 0

It has previously been mentioned that there is a relationship between work and mechanical energy change. Whenever work is done upon an object by an external force (or nonconservative force), there will be a change in the total mechanical energy of the object. If only internal forces are doing work (no work done by external forces), then there is no change in the total amount of mechanical energy. The total mechanical energy is said to be conserved. In this part of Lesson 2, we will further explore the quantitative relationship between work and mechanical energy in situations in which there are no external forces doing work.

The quantitative relationship between work and the two forms of mechanical energy is expressed by the following equation:

<span>KEi + PEi + Wext = KEf + PEf</span>

The equation illustrates that the total mechanical energy (KE + PE) of the object is changed as a result of work done by external forces. There are a host of other situations in which the only forces doing work are internal or conservative forces. In such situations, the total mechanical energy of the object is not changed. The external work term cancels from the above equation and mechanical energy is conserved. The previous equation is simplified to the following form:

<span>KEi + PEi = KEf + PEf</span>

In these situations, the sum of the kinetic and potential energy is everywhere the same. As the potential energy is increased due to the stretch/compression of a spring or an increase in its height above the earth, the kinetic energy is decreased due to the object slowing down. As the potential energy is decreased due to the return of a spring to its rest position or a decrease in height above the earth, the kinetic energy is increased due to the object speeding up. We would say that energy is transformed or changes its form from kinetic energy to potential energy (or vice versa); yet the total amount present is conserved - i.e., always the same.

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4 0
3 years ago
Ml(d^2θ/dt^2) =-mgθ
Nata [24]

The equation of motion of a pendulum is:

\dfrac{\textrm{d}^2\theta}{\textrm{d}t^2} = -\dfrac{g}{\ell}\sin\theta,

where \ell it its length and g is the gravitational acceleration. Notice that the mass is absent from the equation! This is quite hard to solve, but for <em>small</em> angles (\theta \ll 1), we can use:

\sin\theta \simeq \theta.

Additionally, let us define:

\omega^2\equiv\dfrac{g}{\ell}.

We can now write:

\dfrac{\textrm{d}^2\theta}{\textrm{d}t^2} = -\omega^2\theta.

The solution to this differential equation is:

\theta(t) = A\sin(\omega t + \phi),

where A and \phi are constants to be determined using the initial conditions. Notice that they will not have any influence on the period, since it is given simply by:

T = \dfrac{2\pi}{\omega} = 2\pi\sqrt{\dfrac{g}{\ell}}.

This justifies that the period depends only on the pendulum's length.

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3 years ago
A marble, a bowling ball, a basketball, and a baseball are rolling across the floor at 1.0 m/s. Which one has the greatest kinet
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Answer: A Bowling Ball

Explanation:

A body possess kinetic energy due to virtue of its motion. It depends on the mass of the body and the speed with which it is travelling.

K.E = 0.5 mv²

K.E. ∝ m

It is given that the marble, bowling ball, basketball and baseball all are rolling with the same speed. This means that the greatest energy would be possessed by the body having greatest mass.

On an average the mass of a marble is about 50 g, mass of a bowling ball is 750 g, mass of baseball is 150 g and mass of basketball is 600 g. Since the mass of a Bowling ball is the greatest, it would possess the greatest kinetic energy.

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I believe the answer is D
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If the resistance of an electric circuit is 12 ohms and the voltage in the circuit is 60 V, the current flowing through the circ
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The formula for calculating the current flowing in a circuit is:
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