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Newton’s Laws of Motion

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Newton’s Laws of Motion

AP Physics B Chapter 4 Notes

- Aristotle vs. Galileo
- Natural State of Motion
Galileo Thought Experiment

A force is a push or pull. An object at rest needs a force to get it moving; a moving object needs a force to change its velocity.

The magnitude of a force can be measured using a spring scale.

- Unit is the NEWTON (N)—has direction
- Physical contact (Tension, Friction, Applied Force)
- NO physical contact, called FIELD FORCES ( gravitational, electric, etc)
- DYNAMICSconnects force and motion

- Law of Inertia—why?
- Inertial reference frames vs. noninertial.

Every object continues in its state of rest, or of uniform velocity in a straight line, as long as no net force acts on it.

- Mass is the measure of inertia of an object—”A property of matter” (kg)
- Weight is the force exerted on the object by gravity (N)
- Mass is constant for a given object, weight can change with g

- First law says a net force causes velocity to change…but Δv = a
- What is the relationship between F and a?
Common sense tells us…

The acceleration of an object is directly proportional to the net force acting on it, and is inversely proportional to its mass. The direction of the acceleration is in the direction of the net force acting on the object.

- Example 4-2 pg. 76: Estimate the force needed to accelerate a) a 1000 kg car at 0.5g; b) a 200 g apple at the same rate.
- P11 pg. 98: A race car covers 402m in 6.4s from rest. Assuming constant a, how many g’s does the driver experience? If total mass is 485kg what horizontal force does the road exert on the tires?

- Hammer on a nail and F=ma tells you the nail is accelerated.
- What happens to the hammer?
- Newton knew it was not a one-sided exchange…

- Forces come in pairs (or pears?)
- Objects interacting receive equal treatment
Action and reaction forces act on differentobjects!

Whenever one object exerts a force on a second object, the second exerts an equal force in the opposite direction on the first.

- Example 4-5 pg. 80: How can the man move the sled when it must be pulling back on him with equal force?

Subscript notation: First letter is what the force is acting on and the second letter is the source of the force.

- A bug splats on the windshield of your car: a) Which experienced a greater force of impact? b) Which experienced greater acceleration? c) Which of Newton’s laws explains this?
- How does a rocket propel itself in outer space where there is no atmosphere?
- When you climb up a rope, the first thing you do is pull down on the rope. How do you manage to go up the rope by doing that?

- Weight is the force exerted on an object by gravity:
- An object at rest has no net force acting on it (Newton’s first) so ΣF = ma = 0 (Newton’s second)
- So what is going on with an object at rest on a table?

- Gravity is acting on the bust of our 16th president, yet it is at rest, so there must be another opposing force acting on it.
- This is called the normal force (FN), and is exactly large enough to balance FG
- FN acts perpendicular (or normal) to the supporting surface

Caution: Weight and normal force are not action-reaction pairs

- FBD shows all forces acting on each object in a given system
- Each force is represented by an arrow: direction and magnitude!
- Only show forces acting on one object…several drawings may be needed

FN

T

T

m1g

m2g

- Example 4-12 pg. 87: Two boxes, A and B, are connected by a lightweight cord and are resting on smooth (frictionless) surface. The boxes have masses of 12 kg and 10 kg. A horizontal force FP of 40 N is applied to the 10 kg box. Find a) the acceleration of each box, and b) the tension in the cord connecting the boxes.
- Example 4-13 pg. 88: An elevator (mE = 1150 kg ) and a counterweight (mC = 1000 kg ) are suspended over a pulley by a massless cable. Calculate a) the acceleration of the elevator and b) the tension in the cable.
- P 14 pg. 98: A 75 kg thief wants to escape from a third-story jail window. His makeshift rope of bed sheets can only support 58 kg. How might the thief escape (quantify the answer)?

- On a microscopic level, surfaces are rough—interaction of these surfaces leads to friction
- The interaction is complex but is simple to model:
Ffr = μFN

with μ equal to the coefficient of friction—a measure of the stickiness of the two surfaces

- When an object is sliding, it is kinetic friction
- Static friction occurs before an object is moved
- Coefficients for static friction are higher than for kinetic friction (see Table 4-2, pg. 90)

- Example 4-19 pg. 92: A 10 kg box is pulled along a horizontal surface by a force of 40 N applied at a 30º angle. The coefficient of kinetic friction is 0.3. Calculate the acceleration.
- Example 4-20 pg. 93: Two boxes are connected by a cord running over a pulley. Box A ( m = 5 kg) is on a table with μk = 0.20. Box B (m = 2 kg) hangs freely over the edge of the table. Find the acceleration of the system.

- When an object is on an incline, set a new reference frame with x-axis parallel to the incline and y-axis perpendicular to the incline
- Draw the FBD as you normally would, but note that the only forces acting on the object are gravity, normal, friction and any applied force

Break FG into x- and y-components

- Example 4-21 pg. 94: A skier has just begun descending a 30º slope. Assuming the coefficient of kinetic friction is 0.10, calculate a) her acceleration and b) her speed after 4 s.
- P. 51 pg. 102: A child slides down a slide with a 28º incline, and at the bottom her speed is precisely half what it would have been if the slide had been frictionless. Calculate the coefficient of kinetic friction between the slide and the child.