☰ Chapter 4: Linear Kinetics

• Explain Newton's three laws of motion
• Apply Newton's second law of motion to determine the acceleration of an object if the forces acting on the object are known
• Apply Newton's second law of motion to determine the net force acting on an object if the acceleration of the object is known
• Define impulse
• Define momentum
• Explain the relationship between impulse and momentum
• Describe the relationship between mass and weight

Isaac Newton (1642-1727)

Newton's Laws of Motion

Conservation of Momentum
L=mv

Money experiment (\(penny mass = 2.5 g \), \( nickel = 5.0 g \))

Elastic collisions: \( m_a u_a + m_b u_b = m_a v_a + m_b v_b\)

Elestic versus inelastic collisions
Newton's cradle

Coefficient of Restitution

\( e = {\sqrt{{bounce height} \over {drop height}}} \)

\( e = {{v_2 - v_1} \over {u_1-u_2}} \)

Partly elastic collisions: \(m_a u_a + m_b u_b = m_a v_a + m_b [e(u_a - u_b) + v_a] \)

Force affects motion

Measuring Ground Reaction Forces

Ground Reaction Forces in Running

F=ma

Buildup of velocity in the shot put (Download Video)

When Force is Changing: Impulse = \( F_{avg} Δ t \)
How do we calculate impulse?

Soccer Kick Example (video)

Long Jump Example

\(Average force = 658 N\)

\(Average force = 658 N\) \(Impulse = 658 N (0.0133 s) = 8.75 Ns\) \(8.75 Ns = 0.42 kg (Δv)\) \(Δv = {8.75 \over 0.42} {m \over s} = 20.8 {m \over s} \)

Summary of Newton's Laws
First law: Inertia (resistance to a change in motion)
Second law: F=ma
Third law: Action-reaction

\( F = G({m_1 m_2}) \over {r^2} \)

\( G = 6.67300 \times 10^{-11} {m \over {{kg} (s^2) }} \)

\( Mass \: of \: earth = 5.9742 \times 10^{24} kg \)

\( Radius \: of \: earth = 6378.1 km \)

\( {G({m_{earth}}) \over {r_{earth}^2}} = ? \)

\( F=ma \) or \( W=mg \)

How much does an astronaut weigh?

NASA / Neil A. Armstrong [Public domain]

What is astronaut's weight on Moon? G is universal constant = \( {6.7 \times 10^{-11}} {Nm^2 \over {kg^2}} \) Mass of Moon = \( 7.35 \times 10^{22} kg \) Radius of Moon = \( 1.74 \times 10^6 m \) Mass of Astronaut = \( 150 kg \) (including space suit) Weight on Moon = ?

NASA / Neil A. Armstrong [Public domain]

What is astronaut's weight on Moon? G is universal constant = \( {6.7 \times 10^{-11}} {Nm^2 \over {kg^2}} \) Mass of Moon = \( 7.35 \times 10^{22} kg \) Radius of Moon = \( 1.74 \times 10^6 m \) Mass of Astronaut = \( 150 kg \) (including space suit) Weight on Moon = 244 N

1. Can a body be moving if no external forces are acting upon it?
2. Can a body change its direction of motion if no external forces act on it?
3. Can a body be moving with constant velocity if external forces are acting on it?
4. If you pull on a tug of war rope with a force of 50 lb, how much force does the rope exert on you?