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4 years ago

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An object travels in a circular path of radius 5.0 meters at a uniform speed of 10. m/s. What is the magnitude of the object's a

cceleration?
2.0 m/s/s
2.5 m/s/s
5.0 m/s/s
20. m/s/s
50. m/s/s

2 answers:

vladimir1956 [14]4 years ago

8 0

I think F= mv²/r
And F=ma
So, ma = mv²/r
a = v²/r
a = 100/5
a = 20 m/s

Genrish500 [490]4 years ago

4 0

Answer:

a = 20 m/s²

Explanation:

The magnitude of the acceleration of an object that moves in a circular path is given by:

$a= \sqrt{(a_{t})^{2} +(a_{n})^{2} }$ Formula (1)

where:

at = α*R : Formula (2) :Tangential acceleration

ac = ω²*R : Formula (3) : Centripetal acceleration

α : angular acceleration (rad/s²)

ω: angular speed (rad/s)

R : is radius where the object is located from the center of the circular path

The tangential velocity of the body is calculated as follows:

v = ω*R Formula (4)

where:

v is the tangential velocity or linear velocity (m /s)

ω is the angular speed (rad/s)

R is radius where the body is located from the center of the circular path

Data

v = 10 m/s : tangential speed of the object (uniform)

R = 10 m

Calculating of ω (angular speed)

We replace data in the formula (4)

v = ω*R

10 = ω*5

ω = 10 / 5

ω = 2 rad/s

Calculating of the Centripetal acceleration (ac)

We replace ω = 2 rad/s in the formula (3)

ac = ω²*R

ac = (2)²*(5)

ac = 20 m/s²

Calculating of the tangential acceleration (at)

Because the magnitude of the tangential speed is uniform , then α=0

We replace α=0 in the formula (2)

at =α*R = 0*5

at = 0

Calculating of the magnitude of the object's acceleration (a)

We replace : at = 0 and ac = 20 m/s² in the formula (1)

$a= \sqrt{(0)^{2} +(20)^{2} }$

a = 20 m/s²

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Answer:

a) El piñón debe tener 20 dientes.

b) La bicicleta avanza aproximadamente 1,759 metros por cada pedaleada completa.

Explanation:

a) El plato es el engranaje más grande que forma parte del sistema de transmisión, acompañando a la cadena y el piñón integrado a la rueda trasera. Asumiendo que no existen pérdidas por fricción seca y que las condiciones de lubricación del sistema de transmisión son óptimas tal que las pérdidas de potencia son despreciables. Además, supongamos que la bicicleta viaja a velocidad constante, entonces tenemos la siguiente identidad mediante las definiciones de trabajo y potencia:

$T_{P}\cdot \omega_{P} = T_{p}\cdot \omega_{p}$ (1)

Donde:

$T_{P}$ - Torque del plato, en newton-metros.

$T_{p}$ - Torque del piñón, en newton-metros.

$\omega_{p}$ - Rapidez angular del piñón, en radianes por segundo.

$\omega_{P}$ - Rapidez angular del plato, en radianes por segundo.

Sabiendo el hecho que tanto el plato y el piñón experimenta la misma velocidad tangencial, podemos simplificar (1) como sigue:

$\frac{T_{P}}{R_{P}} = \frac{T_{p}}{R_{p}}$ (1b)

Puesto que el radio de cada elemento y el número de dientes son, por separado, directamente proporcionales al número de dientes, modificamos (1b) así y tenemos la siguiente identidad, la cual equivale a su vez a la razón de desarrollo:

$\frac{T_{P}}{T_{p}} = \frac{N_{P}}{N_{p}} = \frac{R_{P}}{R_{p}} = \frac{\omega_{p}}{\omega_{P}}$ (1c)

Donde:

$N_{p}$ - Número de dientes del piñón, sin unidad.

$N_{P}$ - Número de dientes del plato, sin unidad.

Si tenemos que $r = 1,4$ y $N_{P} = 28$ , entonces tenemos que el número de dientes del piñón es:

$r = \frac{N_{P}}{N_{p}}$

$N_{p} = \frac{N_{P}}{r}$

$N_{p} = \frac{28}{1,4}$

$N_{p} = 20$

El piñón debe tener 20 dientes.

b) De acuerdo con la relación de desarrollo, por cada revolución realizada por el plato, el piñón realiza 1,4 revoluciones. Entonces, el avance realizado por la rueda trasera ( $s$ ), en metros, es igual al productor de la relación de desarrollo y la circunferencia de la rueda, es decir:

$s = r\cdot 2\pi\cdot R$ (1)

Donde $R$ es el radio de la rueda trasera, en metros.

Si conocemos que $r = 1,4$ y $R = 0,2\,m$ , entonces el avance realizado por la rueda trasera es:

$s = r\cdot 2\pi\cdot R$

$s = (1,4)\cdot (2\pi)\cdot (0,2\,m)$

$s \approx 1,759 \,m$

La bicicleta avanza aproximadamente 1,759 metros por cada pedaleada completa.

3 0

3 years ago