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3 years ago

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An astronaut in space cannot use a scale or balance to weigh objects because there is no gravity. But she does have devices to m

easure distance and time accurately. She knows her own mass is 76.4 kg, but she is unsure of the mass of a large gas canister in the airless rocket. When this canister is approaching her at 3.50 m/s, she pushes against it, which slows it down to 1.30 m/s (but does not reverse it) and gives her a speed of 2.60 m/s. What is the mass of the canister?

1 answer:

Nana76 [90]3 years ago

8 0

Answer:90.3 kg

Explanation:

Given

Mass of astronaut $m=76.4 kg$

Initial velocity of canister $v_1=3.5 m/s$

Final velocity of canister $v_2=1.3 m/s$

Final speed of Astronaut $v_f=2.6 m/s$

let M be the mass of canister

As there is no external force therefore we can conserve momentum

$M\cdot v_1=mv_f+M\cdor v_2$

$M(3.5-1.3)=76.4\times 2.6$

$M=\frac{76.4\times 2.6}{2.2}$

$M=90.29\approx 90.3 kg$

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X = 1.328 m

(This is 1.328 m from the end we designated x=0 m from the start)

So, the centre of mass moves a distance of (1.572 - 1.328) towards the end of the boat we designated x=0 m from the start.

Hence, the boat moves 0.244 m towards the end where the 59 kg person was at the start of the calculations.

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3 years ago

Para fabricar la bicicleta de un niño pequeño se tiene en cuenta que la fuerza que puede desarrollar es menor que la de un adult

Georgia [21]

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