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A mango is dropped and falls freely from rest. What are its position and velocity after

marissa [1.9K]

Answer:

$1s^{2}$

Explanation:

5 0

3 years ago

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A mass weighing 24 pounds, attached to the end of a spring, stretches it 4 inches. Initially, the mass is released from rest fro

svetoff [14.1K]

Answer:

The equation of motion is $x(t)=-$ $\frac{1}{3} cos4\sqrt{6t}$

Explanation:

Lets calculate

The weight attached to the spring is 24 pounds

Acceleration due to gravity is $32ft/s^2$

Assume x , is spring stretched length is ,4 inches

Converting the length inches into feet $x=\frac{4}{12} =\frac{1}{3}feet$

The weight (W=mg) is balanced by restoring force ks at equilibrium position

mg=kx

$W=kx$ ⇒ $k=\frac{W}{x}$

The spring constant , $k=\frac{24}{1/3}$

= 72

If the mass is displaced from its equilibrium position by an amount x, then the differential equation is

$m\frac{d^2x}{dt} +kx=0$

$\frac{3}{4} \frac{d^2x}{dt} +72x=0$

$\frac{d^2x}{dt} +96x=0$

Auxiliary equation is, $m^2+96=0$

$m=\sqrt{-96}$

= $\frac{+}{} i4\sqrt{6}$

Thus , the solution is $x(t)=c_1cos4\sqrt{6t}+c_2sin4\sqrt{6t}$

$x'(t)=-4\sqrt{6c_1} sin4\sqrt{6t}+c_2$ $4\sqrt{6}$ $cos4\sqrt{6t}$

The mass is released from the rest x'(0) = 0

$=-4\sqrt{6c_1} sin4\sqrt{6(0)}+c_2$ $4\sqrt{6}$ $cos4\sqrt{6(0)}$ =0

$c_2$ $4\sqrt{6} =0$

$c_2=0$

Therefore , $x(t)=c_1$ $cos 4\sqrt{6t}$

Since , the mass is released from the rest from 4 inches

$x(0)= -4$ inches

$c_1 cos 4\sqrt{6(0)} =-\frac{4}{12}$ feet

$c_1=-\frac{1}{3}$ feet

Therefore , the equation of motion is $-\frac{1}{3} cos4\sqrt{6t}$

7 0

3 years ago

The Earth's gravity keeps us from flying out to space. How can you explain that we have a stronger gravitational attraction to t

julia-pushkina [17]

It's the fourth choice.

This is because, since we are closer to the Earth, the Earth will have a stronger gravitational pull on us since again, we are closer.
That also explains tides, but that's just getting off topic. Hope I helped.

6 0

3 years ago

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Why is earth the only planet on which water exists in a liquid state

Gennadij [26K]

This is due to earths location in the solar system. Earth is in the habitat zone or the Goldie locks zone, in this zone it's not too hot or not too cold for water to exist. Other planets in different star systems have liquid oceans due to them being in the habitat zone.

7 0

3 years ago

Porque es un bioelemento el zinc?

Simora [160]

Answer: EL ZINC ES EL ELEMENTO PURO PORQUE NO HA REACCIONADO CON NINGÚN OTRO METAL O NO METAL. EL SULFURO DE ZINC ES UN COMPUESTO PORQUE HA REACCIONADO CON EL AZUFRE PARA HACER EL COMPUESTO.

english:

ZINC IS THE PURE ELEMENT BECAUSE IT HAS NOT REACTED WITH ANY OF OTHER METAL OR NONMETAL. ZINC SULPHIDE IS A COMPOUND BECAUSE IT HAS REACTED WITH SULPHUR TO MAKE COMPOUND.

5 0

3 years ago