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maks197457 [2]
3 years ago
13

Applying the Law of Conservation of Momentum

Physics
1 answer:
IgorC [24]3 years ago
6 0

answer

the final velocity is half of train car B's initial velocity

explanation

the conservation of momentum states that the initial and final total momentum are equal

m1v1 + m2v2 for initial momentum

(m1 + m2)v3 for final momentum because both cars stick together so their masses are combined

m1v1 + m2v2 = (m1 + m2)v3

since the mass of both are the same, m1 = m2

m1v1 + m1v2 = (m1 + m1)v3

m1(v1 + v2) = 2m1v3

divide both sides by m1

v1 + v2 = 2v3

since train car A is initially at rest, v1 = 0

v2 = 2v3

v3 = v2 * 1/2

the final velocity is half of train car B's initial velocity

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An infant's toy has a 120 g wooden animal hanging from a spring. If pulled down gently, the animal oscillates up and down with a
Morgarella [4.7K]

Answer:

0.37 m

Explanation:

The angular frequency, ω, of a loaded spring is related to the period, T,  by

\omega = \dfrac{2\pi}{T}

The maximum velocity of the oscillation occurs at the equilibrium point and is given by

v = \omega A

A is the amplitude or maximum displacement from the equilibrium.

v = \dfrac{2\pi A}{T}

From the the question, T = 0.58 and A = 25 cm = 0.25 m. Taking π as 3.142,

v = \dfrac{2\times3.142\times0.25\text{ m}}{0.58\text{ s}} = 2.71 \text{ m/s}

To determine the height we reached, we consider the beginning of the vertical motion as the equilibrium point with velocity, v. Since it is against gravity, acceleration of gravity is negative. At maximum height, the final velocity is 0 m/s. We use the equation

v_f^2 = v_i^2+2ah

v_f is the final velocity, v_i is the initial velocity (same as v above), a is acceleration of gravity and h is the height.

h = \dfrac{v_f^2 - v_i^2}{2a}

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3 0
3 years ago
Tarzan has foolishly gotten himself into another scrape with the animals and must be rescued once again by Jane. The 60.0 kg Jan
Brut [27]

Complete part of Question: What is Jane's (and the vine's) angular speed just before she grabs Tarzan

Answer:

Jane's (and the vine's) angular speed just before she grabs Tarzan, w = 1.267 rad/s

Explanation:

According to the law of energy conservation:

Total change in kinetic energy = Total change in potential energy

Mass of Jane = 60 kg

Mass of the vine = 32 kg

Mass of Tarzan = 72 kg

Height of Tarzan = 5.50 m

Length of the vine = 8.50 m

Jane's change in gravitational potential energy,

U_J = 60 * 9.8 * 5.5\\U_J = 3234 J

Vine's gravitational potential energy,

U_v = Mgh/2\\U_v = 32*9.8*5.5/2\\U_v = 862.4J

Vine's Kinetic energy :

KE_V = 0.5 I w^{2} \\I_V = \frac{ML^2}{3} = \frac{32 * 8.5^2}{3} = 770.67 kg m^2\\ KE_V = 0.5 *770.67 * w^{2}\\KE_V = 385.33 w^{2}

Jane's Kinetic energy:

KE_J = 0.5m(wL)^2\\KE_J = 0.5*60(w * 8.5)^2\\KE_J = 2167.5 w^2

U_J + U_V = KE_J + KE_V

3234 + 862.4 = 2167.5w² + 385.33w²

4096.4 = 2552.83w²

w² = 4096.4/2552.83

w² = 1.605

w = √1.605

w = 1.267 rad/s

5 0
3 years ago
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