Understanding Dynamics: Forces & Newton's Laws

1. Forces and Newton’s Laws (Dynamics)

2. Dynamics • Dynamics – study of the effects of forces on matter. • Isaac Newton (1642 – 1727) studied the ways in which forces interact and their influence on motion.

3. Types of Forces • Contact Force – Acts on an object by touching it. • Long Range (field) Forces – Exerted without contact. • Forces in Nature Weak Gravity – mass pulls on other mass Electromagnetic - + pulls - Nuclear - weak - found in radioactive decay Strongstrong – holdsquarks and nucleus together

4. Newton’s 1st Law • “An object at rest will remain at rest and an object in motion will remain in motion until acted on by an outside force.” • Also known as the law of INERTIA • Inertia is the property of an object that causes it to resist changing motion. • The greater the mass, the more inertia an object has. • Ex. Riding in a car. Example

5. FBD (Free Body Diagram) • A diagram that represents all of the forces acting on an object or a system. FN = Normal force always ┴ to the surface. = in magnitude to weight on horizontal surfaces Fw = W = mg

6. Net Force (Fnet) • The net force acting on the object is the sum of all the forces. • Forces are vectors, treat them as such

7. Equilibrium • If the sum of the forces in the y – direction (ΣFy = 0) and the sum of the forces in the x – direction (ΣFx = 0) equal zero, the system is in equilibrium. The motion of the object is not changing. (at rest or constant velocity) • A change in velocity or acceleration is due to a net force Fnet ≠ 0.

8. Newton’s 2nd Law • The acceleration of an object is directly proportional to the Fnet on an object and inversely proportional to the mass of the object. • Fnet = ma • If m a , if F a • Unit of force is a Newton (N) • Force to accelerate 1kg, 1m/s2

9. 2nd Law Practice • Draw an FBD of you sitting in your chair. • If your mass is 100kg, what is your W (Fw or Fg)? What is the FN?

10. More Practice • Draw an FBD of a skydiver before they open their chute and are being accelerated by gravity. • Draw an FBD for after the chute is open and they are falling at a constant rate.

11. One More • A 5 kg block is being accelerated at 2m/s2 across a flat horizontal surface.(assume there is no friction) Draw an FBD of this system. • What is ΣFy and ΣFx? Is the object in equilibrium?

12. Friction Forces • Static Friction - Friction acting on an object that is not moving. • Responds to the applied force and is proportional to the FN of the object. • Kinetic Friction - Friction acting when two surfaces slide past each other. • Proportional to the FN and independent of speed, velocity, or acceleration of the object.

13. Causes of Friction • When two surfaces are in contact, the highpoints of the surface bond together. • To move the object the bonds must break (static friction ----> kinetic friction) • As the surfaces slide past each other, these valleys and peaks interact.

14. Calculating Friction • Ff = µFN • µ (mu) is the coefficient of friction. This coefficient changes based on the surfaces that are interacting. • The front page of your reference tables contain a chart listing coefficients of friction between many surfaces. • µ is different for static surfaces compared to kinetic surfaces

15. Sample Problems • You push a 10.0kg rubber block across a dry concrete floor at a constant velocity of 1m/s. How much pushing force is exerted on the box? (Start with an FBD) FN Ff Fp Fg

16. Because it is at a constant speed it is in equilibrium therefore Fp = Ff • Ff = µFN • FN = mg = (10.0kg) x (9.8m/s2) = 98N • µ = 0.68 • Ff = µFN = (0.68) x (98N) = 66.64N

17. One More Sample • What would the acceleration of the object be if the pulling force from the last question was doubled? FN Ff Fp Fg

18. y - direction FN + Fg = 0 • x - direction Fp + Ff = Fnet = ma Ff = µFN = µmg ma = Fnet = Fp - µmg = 133.2N - 66.6N Fnet = 66.6N = ma 66.6N = 10.0kg a a = 6.7m/s2

19. Practice • A sled of mass 50.0kg is pulled along flat, snow covered ground. The static coefficient friction is .30 and the kinetic friction coefficient is .10. • What does the sled weigh? • What is force is needed to start the sled moving? • What force is needed to keep the sled moving at a constant velocity? • Once moving, what total force must be applied to cause the sled to accelerate 3.0m/s2?

20. Periodic Motion • When an object is pulled away from its equilibrium position and a forces tries to restore that object to its equilibrium position. • Also called simple harmonic motion • Examples: Mass on a spring, pendulum

21. Pendulums • A simple pendulum consists of a bob attached to a fixed point by a string or rod of length (l). • Period (T) - the time it takes to complete one cycle of motion. • Amplitude - maximum distance the object moves from equilibrium.

22. Resonance • Applying a force at regular intervals to a vibrating or oscillating object will increase the amplitude of the object. This is called mechanical resonance. • Examples: • #1 • #2

25. Newton’s 3rd Law • “For every action, there is an equal and opposite reaction.” • These are interaction pairs. • Ex. A ball hits a bat. The ball exerts a force on the bat. The bat exerts a forces on the ball equal in magnitude and opposite in direction. • Outcome: The ball changed direction and accelerates. The bat is slowed down by the ball. • We are now looking at a system instead of an object.

26. A ball falls toward Earth. It accelerates toward Earth. The Earth also accelerates toward the ball. • Rockets • Land Speed Record