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Alborosie
3 years ago
5

Do y’all know what A is?! I really need help!

Physics
1 answer:
Naily [24]3 years ago
6 0
It is the crest/peak.
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Block with mass m =7.6 kg is hung from a vertical spring. when the mass hangs in equilibrium, the spring stretches x = 0.29 m. w
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1) 256.9 N/m

The force applied to the spring is equal to the weight of the block hanging on the spring:

F=mg=(7.6 kg)(9.8 m/s^2)=74.5 N

And the spring constant can be found by using Hook's law, because we know that the displacement caused by this force is x = 0.29 m:

F=kx\\k=\frac{F}{x}=\frac{74.5 N}{0.29 m}=256.9 N/m

2) 1.08 Hz

The angular frequency of oscillation of the spring is given by the formula:

\omega=\sqrt{\frac{k}{m}}=\sqrt{\frac{256.9 N/m}{7.6 kg}}=5.81 rad/s

And the frequency of oscillation is given by:

\omega=2\pi f\\f=\frac{2 \pi}{\omega}=\frac{2\pi}{5.81 rad/s}=1.08 Hz

3) 2.19 m/s

The velocity at time t of the block is given by:

v=v_0 cos (\omega t)

where

v_0 = 4.4 m/s is the initial velocity of the block

\omega=5.81 rad/s is the angular frequency

t is the time

Substituting t=0.36 s, we find the speed of the block at that time:

v(0.36 s)=(4.4 m/s) ( cos ((5.81 rad/s)(0.36 s)) = -2.18 m/s

And the negative sign means that the direction of the velocity is upward (because the initial velocity was downward)

4) 25.6 m/s^2

The maximum acceleration is given by:

a_0 = \omega^2 A

where A is the amplitude of the oscillation.

We can find the amplitude by using the law of conservation of energy: in fact, the kinetic energy at the equilibrium point must be equal to the elastic potential energy at the point of maximum displacement:

K=U\\\frac{1}{2}mv_0^2 = \frac{1}{2}kA^2\\A=\sqrt{\frac{mv_0^2}{k}}=\sqrt{\frac{(7.6 kg)(4.4 m/s)^2}{256.9 N/m}}=0.76 m

So, the maximum acceleration is

a_0 = \omega^2 A=(5.81 rad/s)^2 (0.76 m)=25.6 m/s^2

5) 95.1 N

The magnitude of the net force acting on the block is given by the difference between the weight and the restoring force of the spring:

F=mg-kx

First, we need to find the position x at t=0.36 s, which is given by

x(t)=A sin(\omega t)=(0.76 m)(sin ((5.81 rad/s)(0.36 s))=0.66 m

And so, the net force is

F=(7.6 kg)(9.8 m/s^2)-(256.9 N/m)(0.66 m)=-95.1 N

And the negative sign means the direction of the force is upward.

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3 years ago
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