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2 years ago

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Two ice skaters hold hands and rotate, making one revolution in 2.87 s. Their masses are 59.0 kg and 73.0 kg, and they are separ

ated by 1.10 m. Find the angular momentum of the system about their center of mass. If the skaters pull towards each other and decrease their separation to 0.60 m, what is the new period of rotation about the center of mass?

1 answer:

pychu [463]2 years ago

7 0

Answer:

86.43

25.72

Explanation:

Location of center of mass from 59 Kg

$r_1=\frac {xm_2}{m1+m2}=\frac {1.1*73}{59+73}= 0.608333m$

Location of center of mass from 73 Kg

$r_2=\frac {xm_1}{m1+m2}=\ frac {1.1*59}{59+73}= 0.491667m$

Momentum of inertia

$I=m1r_1^{2}+m2r_2^{2}=59*0.608333^{2}+73*0.491667^{2}=21.8341 +17.64674=39.48083 Kgm^{2}$

Angular moment

$L=I\omega=I(\frac {2\pi}{T})=39.48083(\frac {2*\pi}{2.87 s})=86.43393Js$

(b)

When separation is 0.6 m

Location of centre of mass from 59 Kg

$r_1=\frac {xm_2}{m1+m2}=\frac {0.6*73}{59+73}= 0.331818 m$

Location of centre of mass from 73 Kg

$r_2=\frac {xm_1}{m1+m2}=\ frac {0.6*59}{59+73}= 0.268182 m$

Momentum of intertia

$I=m1r_1^{2}+m2r_2^{2}=59*0.331818^{2}+73*0.268182^{2}=6.496095 + 5.250269=11.74636 Kgm^{2}$

Angular moment

$L=I\omega=I(\frac {2\pi}{T})=11.74636(\frac {2*\pi}{2.87 s})=25.71588 Js$

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Answer:

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Then, moves to

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so, the distance traveled here is

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after this, the ant travels to

$\vec{r}_2 = 14 \ inch \ \hat{i}$

so, the distance traveled here is

$d_2 = |\vec{r}_2 - \vec{r}_1 | = | 14 \ inch \ \hat{i} - 29 \ inch \ \hat{i} |$

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$d_2 = 15 \ inch$

The total distance traveled will be:

$d_1 + d_2 = 13 \ inch + 15 \ inch = 28 \ inch$

The displacement is the final position vector minus the initial position vector:

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Answer: There will be 75258 nuclei left at 6 pm.

Explanation:

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Half life is the amount of time taken by a radioactive material to decay to half of its original value.

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$k=\frac{0.69}{t_{\frac{1}{2}}}=\frac{0.693}{2hours}=0.346hours^{-1}$

b) Expression for rate law for first order kinetics is given by:

$A=A_0e^{-kt}$

where,

k = rate constant

t = time for decomposition = 6 hours ( from 12 noon to 6 pm)

A = activity at time t = ?

$A_0$ = initial activity = 600, 000

$A=600000\times e^{-0.346\times 6}$

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From the question,

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Where ΔEp = change in Potential Energy of the hiker, m = mass of the hiker, g = acceleration due to gravity, h₁ = lowest point in Death valley, h₂ = Elevation of Mt. Whitney.

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Substituting into equation 1

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