# 1. Objects of masses 1 = 4.00 and 2 = 9.00 are connected by a light string that passes over a...

## Question:

1. Objects of masses 1 = 4.00 and 2 = 9.00 are connected by a light string that passes over a friction-less pulley. The object 1 is held at rest on the floor, and object 2 rests on a fixed incline of {eq}\theta {/eq} = 40.0{eq}^{\circ} {/eq} . The objects are released from rest, and object 2 slides 1.00 m down the incline in 4.00 s.

Determine (a) the acceleration of each object,

(b) the tension in the string, and

(c) the coefficient of kinetic friction between object 2 and the incline.

2. In a Broadway performance, an 80.0-kg actor swings from a 3.75-m-long cable that is horizontal when he starts. At the bottom of his arc, he picks up his 55.0-kg costar in an inelastic collision. What maximum height do they reach after their upward swing?

## Newton's second law of dynamics; Movement on an incline; Conservation of momentum and mechanical energy

**Newton's second law of dynamics**: A force acting upon an object will always cause the change of the object's velocity (either in direction or in magnitude) or, in other words, it will cause an acceleration directed in the direction and the sense of the force.

Expression:{eq}\overrightarrow {F} = M * \overrightarrow{a} {/eq}

**Movement on an incline**: An incline (or ramp) is one of the mechanics' "simple machines". It 'saves' force at the cost of displacement - one can rise an object at a height h, using a force F < G (the object's weight) but (s)he will have to travel a longer distance.

**Law of conservation of linear momentum**: In an isolated system (i.e. having the total mass constant and not being acted upon by any external forces), the total momentum is conserved (it is constant in time)

{eq}\Delta \left(\sum{\overrightarrow{p}} \right ) = 0
{/eq} |

**Law of conservation of mechanical energy**: In an isolated system, the total amount of energy remains constant in time.

{eq}\Delta E_p = - \Delta E_k {/eq} |

## Answer and Explanation:

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#### Assumptions

**For question 1**:

- As all the given measures are in the I.S. and no units are given for the two masses, we will assume they are measured...

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Chapter 49 / Lesson 1In this lesson, you'll learn about linear momentum, impulse, and energy conservation. These are all important components of collisions, which can be large, small, and everything in between!