Physics - Conservation of Momentum

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Conservation of Momentum

Table of Contents

Introduction

Problems

Answers

Introduction

System

Set of objects that interact with each other.

Isolated System

The only forces present are those between the objects of the system. The sum of all forces will be zero.

Law of Conservation of Momentum

The total momentum of an isolated system of bodies remains constant.

momentum before = momentum after

m₁v₁ + m₂v₂ = m₁v'₁ + m₂v'₂

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Problems

1.	A 1500. kg car moving at 120. km/h hits and attaches to a stationary 200. kg cart. How fast are they moving after the collision?
2.	Sam, 110. kg, is on a bicycle, 10.0 kg, going 8.00 m/s down the concourse when he picks up Rachel, 45.0 kg, walking at 2.00 m/s in the opposite direction. How fast are they moving after the collision?
3.	James, 95.0 kg, is on a bicycle, 10.0 kg, going 7.00 m/s down the concourse when he picks up Lela, 50.0 kg, walking at 1.50 m/s in the same direction. How fast are they moving after the collision?
4.	Laneka, 75.0 kg, is on a bicycle, 10.0 kg, going 40.0 km/h when she throws a bag she was carrying behind her at 10.0 m/s. If she is now moving 45.0 km/h, what was the mass of the bag?

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Answers

1.	A 1500. kg car moving at 120. km/h hits and attaches to a stationary 200. kg cart. How fast are they moving after the collision?
	m_carv_car + m_cartv_cart = m_carv'_car + m_cartv'_cart v'_car = v'_cart = v' m_carv_car + m_cartv_cart = ( m_car + m_cart ) v' m_carv_car + m_cartv_cart 1500. kg x 120. km/h + 200. kg x 0 km/h v' = ----------------------------------- = ---------------------------------------------------------- = 106 km/h ( m_car + m_cart ) ( 1500. kg + 200. kg )

2.	Sam, 110. kg, is on a bicycle, 10.0 kg, going 8.00 m/s down the concourse when he picks up Rachel, 45.0 kg, walking at 2.00 m/s in the opposite direction. How fast are they moving after the collision?
	m_{Sam + bicycle}v_{Sam + bicycle} + m_Rachelv_Rachel = m_{Sam + bicycle}v'_{Sam + bicycle} + m_Rachelv'_Rachel v'_{Sam + bicycle} = v'_Rachel = v' m_{Sam + bicycle}v_{Sam + bicycle} + m_Rachelv_Rachel = ( m_{Sam + bicycle} + m_Rachel ) v' m_{Sam + bicycle}v_{Sam + bicycle} + m_Rachelv_Rachel v' = ------------------------------------------------------------ v_{Sam + bicycle} will be the positive direction. m_{Sam + bicycle} + m_Rachel 120. kg x 8.00 m/s + 45.0 kg x ( -2.00 m/s) v' = ---------------------------------------------------------- = 5.27 m/s 120. kg + 45.0 kg

3.	James, 95.0 kg, is on a bicycle, 10.0 kg, going 7.00 m/s down the concourse when he picks up Lela, 50.0 kg, walking at 1.50 m/s in the same direction. How fast are they moving after the collision?
	m_James_{+ bicycle}v_James_{+ bicycle} + m_Rachelv_Rachel = m_James_{+ bicycle}v'_James_{+ bicycle} + m_Rachelv'_Rachel m_James_{+ bicycle}v_James_{+ bicycle} + m_Rachelv_Rachel = ( m_James_{+ bicycle} + m_Rachel ) v' m_James_{+ bicycle}v_James_{+ bicycle} + m_Rachelv_Rachel v' = ---------------------------------------------------------------- v_James_{+ bicycle} will be the positive direction. m_James_{+ bicycle} + m_Rachel 105.0 kg x 7.00 m/s + 50.0 kg x 1.50 m/s v' = ---------------------------------------------------------- = 5.23 m/s 105.0 kg + 50.0 kg

4.	Laneka, 75.0 kg, is on a bicycle, 10.0 kg, going 40.0 km/h when she throws a bag she was carrying behind her at 10.0 m/s. If she is now moving 45.0 km/h, what was the mass of the bag?
	m_Lanekav + m_bagv = m_Lanekav'_Laneka + m_bagv'_bag v_Laneka = v_bag = v 10.0 m 3600 s 1 km ---------- x ----------- x ----------- = 36.0 km/h s 1 h 1000 m m_bagv - m_bagv'_bag = m_Lanekav'_Laneka - m_Lanekav Factor out m_bag. m_Lanekav'_Laneka - m_Lanekav m_bag = ----------------------------------------- Forward direction is positive. v - v'_bag 75.0 kg x 45.0 km/h - 75.0 kg x 40.0 km/h m_bag = ----------------------------------------------------------- = 4.93 kg 40.0 km/h - ( -36.0 km/h)

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