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They say you can't go anywhere without forces, and they are right. See if you understand the bread and butter of Newtonian mechanics.

In the figure above, a block on a frictionless slope is hanging on a cord. The mass of the block is \(m= 4.0 \text{ kg}, \) and the slope makes a \( \theta=30 ^\circ \) angle with the horizontal. If the cord is cut, what is the magnitude of the acceleration of the block?

The gravitational acceleration is \( g= 10 \text{ m/s}^2. \)

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A \( 900 \text{-kg} \) rocket sled is to be accelerated from rest to \( 1700 \text{ km/h} \) at a constant rate in \( 1.8 \) seconds in outer space. What is the approximate magnitude of the required net force?

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In the movie *Spiderman 2*, there's a famous minute long scene where Spiderman stops a train. If the initial speed of a five car out of control subway train was around the top speed of the NYC subway (27 m/s), and Spiderman stopped the train in exactly one minute, then what is the magnitude of the force in **Newtons** that Spiderman exerted on the train as he stopped it?

**Details and assumptions**

- A standard New York City subway car full of terrified passengers has a mass of roughly 40,000 kg.
- You may assume the acceleration was constant and any other forces are negligible.

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In the above diagram, two objects with their respective masses \(5\) kg and \(3\) kg are hung on a pulley with no friction. Find the magnitude of acceleration \((\text{in m/s}^2 )\) of the left object with mass \(5\) kg.

Gravitational acceleration is \(g = 10\) m/s\(^{2}\).

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