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Naddika [18.5K]
2 years ago
13

1. The large wheels on the train have a mass of 0.5 kg, while the small wheels have a mass of 0.15 kg. The train body, and child

, have a total mass of 40 kg. If the large wheel is rotating at 3 m/s, determine the total kinetic energy of the train.
Physics
1 answer:
blsea [12.9K]2 years ago
5 0

Answer: 60.975 Joules

KE = 1/2 mv^2

=> 1/2 * 40.65 * 3

=> 60.975 J

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A coil with an inductance of 2.3 H and a resistance of 14 Ω is suddenly connected to an ideal battery with ε = 100 V. At 0.13 s
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Given Information:

Resistance = R = 14 Ω

Inductance = L = 2.3 H

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time = t = 0.13 s

Required Information:

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(b) thermal energy is appearing in the resistance

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(b) thermal energy is appearing in the resistance ≈ 267 watts

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U = \frac{1}{2} Li^{2}

The rate at which the energy is being stored in the inductor is given by

\frac{dU}{dt} = Li\frac{di}{dt} \: \: \: \: eq. 1

The current through the RL circuit is given by

i = \frac{V}{R} (1-e^{-\frac{t}{ \tau} })

Where τ is the the time constant and is given by

\tau = \frac{L}{R}\\ \tau = \frac{2.3}{14}\\ \tau = 0.16

i = \frac{110}{14} (1-e^{-\frac{t}{ 0.16} })\\i = 7.86(1-e^{-6.25t})\\\frac{di}{dt} = 49.125e^{-6.25t}

Therefore, eq. 1 becomes

\frac{dU}{dt} = (2.3)(7.86(1-e^{-6.25t}))(49.125e^{-6.25t})

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\frac{dU}{dt} = (2.3) (4.37) (21.8)\\\frac{dU}{dt} = 219.11 \: watts

(b) thermal energy is appearing in the resistance

The thermal energy is given by

P = i^{2}R\\P = (7.86(1-e^{-6.25t}))^{2} \cdot 14\\P = (4.37)^{2}\cdot 14\\P = 267.35 \: watts

(c) energy is being delivered by the battery?

The energy delivered by battery is

P = Vi\\P = 110\cdot 4.37\\P = 481 \: watts

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