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kipiarov [429]
3 years ago
15

A particle moves along a circular path over a horizontal xy coordinate system, at constant speed. At time t1 = 4.50 s, it is at

point (5.80 m, 5.60 m) with velocity (3.50 m/s) j and acceleration in the positive x direction. At time t2 = 11.7 s, it has velocity (–3.50 m/s) i and acceleration in the positive y direction. What are the (a) x and (b) y coordinates of the center of the circular path? Assume at both times that the particle is on the same orbit.

Physics
1 answer:
Reptile [31]3 years ago
6 0

Answer:

a) x=11.15m

b) y= 5.6m

Explanation:

This is the given data:

t1=4.5s                          t2=11.7s

V1=3.5 (j)m/s                 V2=-3.5 (i)m/s

a1 = a(i)                          a2 = a(j)

r1 = 5.8(i)+5.6(j) m

From this data we conclude that the orbit is as the one shown in the picture.

So, the position of the center will be rc = r1 + R(i) = (5.8+R)(i) + 5.6(j)

Calculating the distance traveled by the particle:

S = V*Δt = 3.5 * (11.7-4.5) = 25.2m

Since S = θ * R  and from the picture we know that θ = 3π/2

R = 5.35m

Now we calculate the center of the orbit as:

rc = r1 + R(i) = (5.8+5.35)(i)  +  5.6(j) = [11.15(i) + 5.6(j)] m

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En una librería un libro de 0.6 kg colocado inicialmente en un estante a 40 cm del suelo fue movido a otro estante con una altur
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Considerando la definición de energía potencial:

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  • el cambio en la energía potencial del libro es 5,2974 J.
<h3 /><h3>Definición de energía potencial</h3>

La energía potencial es la energía que mide la capacidad que tiene un sistema para realizar un trabajo en función de su posición. En otras palabras, esta es la energía que tiene un cuerpo situado a una determinada altura sobre el suelo.

La energía potencial gravitatoria es la energía asociada con la fuerza gravitatoria. Esta dependerá de la altura relativa de un objeto a algún punto de referencia, la masa, y la fuerza de la gravedad.

Entonces para un objeto con masa m, en la altura h, la expresión aplicada a la energía gravitacional del objeto es:

Ep= m×g×h

Donde

  • Ep es la energía potencial en julios (J).
  • m es la masa en kilogramos (kg).
  • h es la altura en metros (m).
  • g es la aceleración de caída en m/s² (aproximadamente 9,81 m/s²).

<h3>Energía potencial en cada lugar</h3>

En primer lugar, se sabe inicialmente del libro:

  • m= 0,6 kg
  • g= 9,81 m/s²
  • h= 40 cm= 0,4 m (siendo 1 cm= 0,01 m)

Entonces, reemplazando en la definición de energía potencial:

Ep1= 0,6 kg× 9,81 m/s²× 0,4 m

Resolviendo:

<u><em>Ep1= 2,3544 J</em></u>

Por otro lado, se sabe los siguientes datos del libro luego de ser movido:

  • m= 0,6 kg
  • g= 9,81 m/s²
  • h= 1,30 m

Entonces, reemplazando en la definición de energía potencial:

Ep2= 0,6 kg× 9,81 m/s²× 1,30 m

Resolviendo:

<u><em>Ep2= 7,6518 J</em></u>

En resumen, la energía potencial del libro inicialmente es 2,3544 J y luego de ser movido a otro estante es 7,6518 J.

<h3>Cambio de energía potencial</h3>

El cambio en la energía potencial del libro será la diferencia entre la energía potencial luego de ser movido y la energía potencial inicial del libro:

ΔEp= Ep2 - Ep1

ΔEp= 7,6518 J - 2,3544 J

<u><em>ΔEp= 5,2974 J</em></u>

Finalmente, el cambio en la energía potencial del libro es 5,2974 J.

Aprende más sobre energía potencial:

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