Physics, 15.04.2020 04:18 sbush5231

A weight of 50.0 N is suspended from a spring that has a force constant of 210 N/m. The system is undamped and is subjected to a harmonic driving force of frequency 11.5 Hz, resulting in a forced-motion amplitude of 4.00 cm. Determine the maximum value of the driving force.

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Answer from: bessieyounger1211

The maximum value of the driving force is 1044.01 N.

Explanation:

Given that,

Weight of the object, W = 50 N

Force constant of the spring, k = 210 N/m

The system is undamped and is subjected to a harmonic driving force of frequency 11.5 Hz.

Amplitude, A = 4 cm

We need to find the maximum value of the driving force. The force is given by the product of mass and maximum acceleration as :

$F=mA\omega^2$ .....(1)

A is amplitude

m is mass,

$m=\dfrac{W}{g}\\\\m=\dfrac{50}{10}\\\\m=5\ kg$

$\omega$ is angular frequency

Angular frequency is given by :

$\omega=2\pi f\\\\\omega=2\pi \times 11.5\\\\\omega=72.25\ rad/s$

Equation (1) becomes :

$F=5\times 0.04\times 72.25^2\\\\F=1044.01\ N$

So, the maximum value of the driving force is 1044.01 N.

Answer from: Quest

he made 11 calls in one day

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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A weight of 50.0 N is suspended from a spring that has a force constant of 210 N/m. The system is un...

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