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skelet666 [1.2K]
3 years ago
6

Problem 5 please! I need an equation to solve

Physics
2 answers:
Maru [420]3 years ago
3 0
N(t) = N(0) x [1/2]^(t/th)
N(t) = 12.5
N(0) = 100
t = 10
th = half life ... your answer
ziro4ka [17]3 years ago
3 0
You could try the equation (12.5/100) = (1/2)^x .
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A) First, we're going to use the work-energy theorem that states total work (W) done on an object is equal to the change in its kinetic energy (\Delta K):

W=\Delta K = K_{f}-K_{i} (1)

So, all we must do is to find the change on kinetic energy. Because we're working with rotational body, we should use the equation K=\frac{I\omega^{2}}{2} for the kinetic energy so:

\Delta K=\frac{I(\omega_{f})^{2}}{2}-\frac{I(\omega_{i})^{2}}{2} (2)

with \omega_{i} the initial angular velocity, \omega_{f} the final angular velocity (is zero because the wheel stops) and I the moment of inertia that for a thin hoop is I=MR^{2}, using those on (2)

\Delta K=0-\frac{MR^{2}(\omega_{i})^{2}}{2} (3)

By (3) on (1):

W= \frac{MR^{2}(\omega_{i})^{2}}{2} = \frac{(32.0)(1.2)^{2}(29.32)^{2}}{2}

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B) Average power is work done divided by the time interval:

P=\frac{W}{\Delta t}=\frac{19806.62}{15.0}

P=1320.44\,W

NOTE: We use the relation 1rpm*\frac{2\pi}{60s}=\frac{rad}{s} to convert 280 rev/min(rpm) to 29.32 rad/s

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