Question

A 5.0 kg object suspended on a spring oscillates such that its position x as a function of time t is given by the equation x (t ) = A cos(ωt ), where A = 0.80 m and ω = 2.0 s-1 . What is the magnitude of the maximum net force on the object during the motion?

Answer 1

Answer:

The magnitude of the maximum net force on the object during the motion is 16 newtons.

Explanation:

The position of the mass, measured in meters, within the mass-spring system is:

$x(t) = A\cdot \cos \left(\omega\cdot t \right)$ (1)

Where:

$A$ - Amplitude, measured in meters.

$t$ - Time, measured in seconds.

$\omega$ - Angular frequency, measured in radians per second.

The acceleration function ($\ddot {x} (t)$), measured in meters per square second, is obtained by deriving twice (1) in time:

$\dot {x} (t) = -\omega\cdot A\cdot \sin (\omega\cdot t)$

$\ddot {x} (t) = -\omega^{2}\cdot A\cdot \cos (\omega\cdot t)$ (2)

And the maximum acceleration ($a_{max}$), measured in meters per square second, experimented by the mass is:

$a_{max} = \omega^{2}\cdot A$ (3)

And the maximum net force ($F$), measured in newtons, is:

$F = m\cdot a_{max}$ (4)

If we know that $\omega = 2\,\frac{rad}{s}$, $A = 0.80\,m$ and $m = 5\,kg$, then the maximum net force on the object during the motion is:

$a_{max} = \left(2\,\frac{rad}{s} \right)^{2}\cdot (0.80\,m)$

$a_{max} = 3.2\,\frac{m}{s^{2}}$

$F = (5\,kg)\cdot \left(3.2\,\frac{m}{s^{2}} \right)$

$F = 16\,N$

The magnitude of the maximum net force on the object during the motion is 16 newtons.

Answer 2

The magnitude of the maximum net force on the object during the motion will be 16 newtons.

What is force?

Force is defined as the push or pull applied to the body. Sometimes it is used to change the shape, size, and direction of the body. Force is defined as the product of mass and acceleration. Its unit is Newton.

The given data in the problem is;

m is the mass of  5.0 of object kg

x (t ) = A cos(ωt ),

A is the amplitude=  0.80 m

ω is the frequency= 2.0 s-1 .

F is the  magnitude of the maximum net force=?

The position of the mass is given by the equation;

$x(t)= A cos( \omega t)$]

$\em \dot x= - \omega A sin(\omega t) \\\\ \dot \dot x = - \omega ^2 A cos (\omega t)$

The maximum acceleration is found as;

$\rm a_{max} = \omega ^2 A \\\\ \rm a_{max} = (2) ^2 \times 0.80 \\\\ \rm a_{max} =3.2 \m/sec^2$

The value of net force is found as;

$\rm F= m a_{max} \\\\ \rm F= 5 \times 3.2 \\\\\ \rm F=16\ N$

Hence the magnitude of the maximum net force on the object during the motion will be 16 newtons.

To learn more about the force refer to the link;

https://brainly.com/question/26115859