5.2 Dynamics and newtons second law

Newton's Second Law

• Newton's second law connects force and motion.

• Formula: $ext{Force}_{ ext{net}} = m imes ext{a}$
  where ( m ) is mass and ( a ) is acceleration.

• In component form:

  • $\sum F<em>x = m \times a</em>x$

  • $\sum F<em>y = m \times a</em>y$

Problem Solving Approach

• Dynamics problems utilize Newton's second law for forces and kinematics.

Types of Dynamic Problems

1. Forces Known: Use forces to find acceleration, then position/velocity via kinematics.

2. Acceleration Known: Use acceleration to find forces acting on an object.

Steps to Solve

1. Prepare: Create a visual overview including:

   • List of known values and requirements of the problem.

   • Force identification diagram.

   • Free body diagram to depict forces.

   • Motion diagram for acceleration direction.

2. Write Equations:

   • Use component form: $\sum F<em>x = m \times a</em>x$, $\sum F<em>y = m \times a</em>y$.

3. Access: Check results for correct units and reasonableness.

Example Problem: Golf Ball

• Given: Mass = 46 grams, initial speed = 3.0 m/s, friction = 0.02 N.

• Determine if the ball travels 10m.

• Steps:

  1. Find acceleration using Newton's: $a_x = \frac{-0.02 \, ext{N}}{0.046 \, ext{kg}} = -0.435 \text{ m/s}^2$.

  2. Kinematic equation: $v<em>{x,final}^2 = v</em>{x,initial}^2 + 2a_x \Delta x$.

  • Solve for ( \Delta x ):

  • $\Delta x = \frac{0 - (3.0)^2}{2 \times (-0.435)} \approx 10.3 \text{ m}$.

• Conclusion: The ball will reach the hole if aimed correctly, as it can travel 10.3 m before stopping.