Forces and Newton’s Laws (Dynamics)

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.

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 Strong strong – holds quarks and nucleus together

Newton’s 1st Law Example “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

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

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

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.

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

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?

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.

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?

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.

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.

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

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

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

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

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

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?

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

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.

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

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.

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