Physics, 24.07.2019 06:30 caldonjoshhsms2061

An air-track cart is attached to a spring and completes one oscillation every 5.67 s in simple harmonic motion. at time t = 0.00 s the cart is released at the position x = +0.250 m. what is the position of the cart when t = 29.6

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The cart is moving by simple harmonic motion, and its position at time t is described by
$x(t) = A \cos (\omega t)$
where
A is the amplitude of the oscillation
$\omega$ is the angular frequency

The amplitude of the oscillation corresponds to the maximum displacement of the spring, which corresponds to the initial position where the spring was released:
A=0.250 m

The period of the motion is T=5.67 s, and the angular frequency is related to the period by
$\omega = \frac{2 \pi}{T}= \frac{2 \pi}{5.67 s} =1.11 rad/s$

Therefore now we can calculate the position of the system at the time t=29.6 s:
$x(29.6 s)=(0.250 m)\cos ((1.11 rad/s)(29.6 s))=+0.033 m$

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.

Answer from: Quest

The purpose of a lab is to do your "expirements" the importance of the topic is so you can now what the story is about and the last one is because no one is me with my question ( what is 3 over 4 x - 9 = 27 maybe you can )

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