Physics, 30.06.2021 02:10 mangustaylor

A simple pendulum takes 2.00 s to make one compete swing. If we now triple the length, how long will it take for one complete swing

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Answer from: andyboehm7411

3.464 seconds.

Explanation:

We know that we can write the period (the time for a complete swing) of a pendulum as:

$T = 2*\pi*\sqrt{\frac{L}{g} }$

Where:

$\pi = 3.14$

L is the length of the pendulum

g is the gravitational acceleration:

g = 9.8m/s^2

We know that the original period is of 2.00 s, then:

T = 2.00s

We can solve that for L, the original length:

$2.00s = 2*3.14*\sqrt{\frac{L}{9.8m/s^2} }\\\\\frac{2s}{2*3.14} = \sqrt{\frac{L}{9.8m/s^2}}\\\\(\frac{2s}{2*3.14})^2*9.8m/s^2 = L = 0.994m$

So if we triple the length of the pendulum, we will have:

L' = 3*0.994m = 2.982m

The new period will be:

$T = 2*3.14*\sqrt{\frac{2.982m}{9.8 m/s^2} } = 3.464s$

The new period will be 3.464 seconds.

Answer from: Quest

less than one you can't create energy

Answer from: Quest

force is based upon mass and acceleration.the statement is not always true.

it can be explained from newton's second law of motion.

as per newton's second law of motion the rate of change of momentum is directly proportional to the applied force and takes place along the direction of force.

mathematically it can be written as -

$f\alpha \frac{dp}{dt}$

⇒ $f= k \frac{dp}{dt}$

here k is the proportionality constant whose value is 1.

$f=\frac{dp}{dt}$

$f= \frac{d[mv]}{dt}$

$f= m\frac{dv}{dt} +v\frac{dm}{dt}$

$f=ma+v\frac{dm}{dt}$ [a is the acceleration=dv/dt]

hence we see that force not only depends on mass and acceleration but also on velocity and rate of change of mass. force f will depend on mass and acceleration only when mass is constant.

hence the statement that force is based upon mass and acceleration is false.

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