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Sauron [17]
3 years ago
7

Please help with a step by step method ​

Physics
1 answer:
Elan Coil [88]3 years ago
3 0

Answer:

Explanation:

This is a First Law of thermodynamics problem. We have to remember that the total energy available to a system is constant throughout the whole problem and that energy cannot be created or destroyed. So we need to find the total energy available right at the start. Well it just so happens that we are told that the total energy is 1000J and that it is all potential energy when the sphere is at rest and is 25 m off the ground. If the object isn't moving, all the energy is potential until it starts moving and the energy begins to convert from potential to kinetic a little bit at a time. The thing that we don't know is the mass of the shpere. Begin with the fact that the PE = 1000 (I'm going to se 2 sig fig's since there's only 1 in 1000). If

PE = 1000 and PE = mgh, then

1000 = m(9.8)(25) so

m = 4.1 kg

We also need the height at which this sphere has a PE of 600. Again, if

PE = 600 and PE = mgh, then

600 = (4.1)(9.8)h so

h = 15 Filling in the total energy equation now, using the fact that the total energy available to the system is 1000J:

TE = PE + KE and

1000 = (4.1)(9.8)(15) + \frac{1}{2}(4.1)v^2 and we are looking for v.

1000 = 6.0 × 10² + 2.1v² so

v=\sqrt{\frac{1000-6.0*10^2}{2.1} } and

v=\sqrt{\frac{4.0*10^2}{2.1} } gives us

v = 14 m/s

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Read 2 more answers
When a condenser discharges electricity, the instantaneous rate of change of the voltage is proportional to the voltage in the c
e-lub [12.9K]

Answer:

460.52 s

Explanation:

Since the instantaneous rate of change of the voltage is proportional to the voltage in the condenser, we have that

dV/dt ∝ V

dV/dt = kV

separating the variables, we have

dV/V = kdt

integrating both sides, we have

∫dV/V = ∫kdt

㏑(V/V₀) = kt

V/V₀ = e^{kt}

Since the instantaneous rate of change of the voltage is -0.01 of the voltage dV/dt = -0.01V

Since dV/dt = kV

-0.01V = kV

k = -0.01

So, V/V₀ = e^{-0.01t}

V = V₀e^{-0.01t}

Given that the voltage decreases by 90 %, we have that the remaining voltage (100 % - 90%)V₀ = 10%V₀ = 0.1V₀

So, V = 0.1V₀

Thus

V = V₀e^{-0.01t}

0.1V₀ = V₀e^{-0.01t}

0.1V₀/V₀ = e^{-0.01t}

0.1 = e^{-0.01t}

to find the time, t it takes the voltage to decrease by 90%, we taking natural logarithm of both sides, we have

㏑(0.01) = -0.01t

So, t = ㏑(0.01)/-0.01

t = -4.6052/-0.01

t = 460.52 s

3 0
3 years ago
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