Classical Mechanics
# Momentum

**Details**

- The train is \(l = 200\) m long, and has an empty weight of \(m_0 = 500\) kg.
- \(v_0=45\) m/s
- \(\alpha_m = 20\) kg/s

**Details**

- The train is \(l = 200\) m long, and has an empty weight of \(m_0 = 500\) kg.
- \(v_0=45\) m/s
- \(\alpha_m = 20\) kg/s

After the balls are released, and the first ball touches the ground, each ball bounces off its neighboring ball. If \(v_{n}\) is the speed of the \(nth\) ball right after it bounces of its adjacent ball. What is the ratio of the speed of the \(20th\) ball right after it bounces to the \(5th\) ball right after it bounces.

Simply put what is \[\large{\frac { { v }_{ 20 } }{ { v }_{ 5 } }} \]

**Details and assumptions**

All the collisions that take place are elastic collisions.

Assume \({ M }_{ 1 }\gg { M }_{ 2 }\gg { M }_{ 3 }\gg ........{ M }_{ n }\).

**Assumptions and Details**

- The collision with the ground is perfectly elastic.
- The ball does not slip while it contacts the ground.
- The radius of the ball is \(\SI{3}{\centi\meter}.\)

A 100 m rope of line density \(\lambda=0.1\) kg/m is suspended vertically so that the bottom of the rope is just touching a scale. It is then released and falls onto the scale, which perceives a time dependent weight.

What is the reading on the scale in **Newtons** at the moment half the rope lies on the scale?

**Assumptions and Details**

- \(g=9.8\) m/s\(^{2}\).

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