SOMEONE PLEASE HELP FAST

A spring has a 12 cm length. When a 200-g mass is hung from the spring, it extends to 27 cm. The hanging mass were pulled downwa

BartSMP [9]

Answer:

The equation of the time-dependent function of the position is $x(t)=5\cos(8.08t)$

(b) is correct option.

Explanation:

Given that,

Length = 12 cm

Mass = 200 g

Extend distance = 27 cm

Distance = 5 cm

Phase angle =0°

We need to calculate the spring constant

Using formula of restoring force

$F=kx$

$mg=kx$

$k=\dfrac{mg}{x}$

$k=\dfrac{200\times10^{-3}\times9.8}{(27-12)\times10^{2}}$

$k=13.06\ N/m$

We need to calculate the time period

Using formula of time period

$T=2\pi\sqrt{\dfrac{m}{k}}$

Put the value into the formula

$T=2\pi\sqrt{\dfrac{0.2}{13.6}}$

$T=0.777\ sec$

At t = 0, the maximum displacement was 5 cm

So, The equation of the time-dependent function of the position

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

Put the value into the formula

$x(t)=5\cos(2\pi\times f\times t)$

$x(t)=5\cos(2\pi\times\dfrac{1}{T}\times t)$

$x(t)=5\cos(2\pi\times\dfrac{1}{0.777}\times t)$

$x(t)=5\cos(8.08t)$

Hence, The equation of the time-dependent function of the position is $x(t)=5\cos(8.08t)$

8 0

3 years ago

Why do you think the sickle cell allele is still common in tropical regions?

Ugo [173]

Sickle-cell disease is common in tropical and sub-tropical regions because being a carrier, carrying a single sickle-cell mutation (sickle cell trait), affords some resistance to malaria.

8 0

3 years ago

A military helicopter on a training mission is flying horizontally at a speed of 90.0 m/s when it accidentally drops a bomb (for

Elena-2011 [213]

Answer:

1) 10.1 s 2) 909 m 3) 90.0 m/s 4) -99m/s 5) just over the bomb.

Explanation:

1)

In the vertical direction, as the bomb is dropped, its initial velocity is 0.
So, we can find the time required for the bomb to reach the earth, applying the following kinematic equation for displacement:

$\Delta y = \frac{1}{2}*a*t^{2} (1)$

where Δy = -500 m (taking the upward direction as positive).
a=-g=-9.8 m/s²
Replacing these values in (1), and solving for t, we have:

$t =\sqrt{\frac{2*\Delta y}{-g}} = \sqrt{\frac{2*(-500m)}{-9.8m/s2}} = 10.1 s$

The time required for the bomb to reach the earth is 10.1 s.

2)

In the horizontal direction, once released from the helicopter, no external influence acts on the bomb, so it will continue moving forward at the same speed. that it had, equal to the helicopter.
As the time must be the same for both movements, we can find the horizontal displacement just as the product of this speed times the time, as follows:

$x = v_{0x} * t = 90.0 m/s * 10.1 s = 909 m.$

3)

The horizontal component of the bomb's velocity is the same that it had when left the helicopter. i.e. 90 m/s.

4)

In order to find the vertical component of the bomb's velocity just before it strikes the earth, we can apply the definition of acceleration, remembering that v₀ = 0, as follows:

$v_{f} = -g*t = -9.8 m/s2*10.1 s = -99 m/s$

5)

If the helicopter keeps flying horizontally at the same speed, it will be always over the bomb, as both travel horizontally at the same speed.
So, when the bomb hits the ground, the helicopter will be exactly over it.

8 0

4 years ago

Plz help!!! Will give brainsiest!!!!

Zanzabum

Answer:

2KOH(aq) + H2SO4(aq) ⇒ K2SO4(aq) + 2H2O(l)

Explanation:

The reaction is a neutralization reaction since an acid, aqeous H2SO4 reacts completely with an appropriate amount of alkali, aqueous KOH to produce salt, aqueous K2SO4 and liquid water, H2O only.

2KOH(aq) + H2SO4(aq) ⇒ K2SO4(aq) + 2H2O(l)

Alkali + Acid → Salt + Water.

During this reaction, 2 moles of KOH neutralize 1 mole of H2SO4 to yield 1 mole of K2SO4 and 2 moles of H2O.

7 0

4 years ago

A parallel-plate capacitor has square plates that are 9.00 cmcm on each side and 4.10 mmmm apart. The space between the plates i

Mars2501 [29]

Answer:

U= 1.9*10^-7

Explanation:

given:

L=8 cm

d_1=d_2=2.05_10^-3

K_py=4.3

K_po=3

V_ab=86 V

required

U=??

solution:

the energy stored in the capacitor

U=1/2C_t*V^2_ab (1)

voltage is known but capacitance is not

we can consider the two plates of polystyrene and pyrex glass as a two separate capacitors connected on series so the total capacitance of series capacitor is given by:

1/C_t= 1/C_py+1/C_po (2)

the capacitance of polystyrene

C_po=K_po*A/d

=8.9*10^-11

= 89 pF

the capacitance of pyrex

C_py=K_py*A/d

=128 pF

substitution in 2 yields

1/C_t= 1/128+1/89

C_t= 52.6 pF

substitution in 1 yields

U=1/2C_t*V^2_ab

= 1.9*10^-7

7 0

3 years ago

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