Isaac Newton: 1600’s, England Force: A push or pull between pairs of objects Mass is a measure of resistance to acceleration

Mass (inertia) vs weight How do astronauts know which chocolate milk carton is empty? Mass m: a measure of _________________________ Weight W =

Newton’s second law The acceleration of an object is _________________ to the total force on it, and __________________________ to the mass: a = F = Unit of force: In terms of a 1 kg mass… 1 Newton = 1 kg *1 m/s 2 (1 Newton = lb)

Newton’s second law Normal force N: perpendicular to surface Friction force f: parallel

Newton’s second law Mary has a mass of 40 kg (weight = 392 N), and stands on a scale in the elevator. The elevator accelerates downward at 2 m/s 2. What is the scale reading? (draw FBD)

Forces are vectors! Always draw a free-body diagram Free-body diagrams 1. Draw the object of interest alone (you can combine several objects as a “single object” if they have the same a). 2. Draw forces on the object exerted by other, external things 3. Label each force with a different symbol 4. Choose a positive direction (usually in the direction of a) for each component 5. Draw the vector a on the diagram, but not on the object (it’s not a force) 6. For the FBD you can write  F x = ma x and  F y = ma y (m is the mass of the object in the diagram)

Newton’s second law

Kinetic and static friction

Static friction Static friction exactly cancels sideways force, until….

Static friction The 70 kg block is at rest. The static coefficient of friction is 0.6. What is the acceleration if you push with: a) 200 N b) 400 N c) 600 N

P1. A monkey starts to slide down a rope. As it speeds up, it tightens its grip, until it slides at a constant velocity down the rope. Which of these choices is true as it slides at constant speed? a) The gravitational force is equal (in magnitude) to the frictional force. b) The gravitational force is greater equal (in magnitude) than the frictional force. c) The gravitational force is less than the frictional force (in magnitude).

P1. A monkey starts to slide down a rope. As it speeds up, it tightens its grip, until it slides at a constant velocity down the rope. Which of these choices is true as it starts to speed up? a) The gravitational force is equal (in magnitude) to the frictional force. b) The gravitational force is greater equal (in magnitude) than the frictional force. c) The gravitational force is less than the frictional force (in magnitude).

Ping-pong ball cannon A 2-gram (0.002 kg) ping-pong ball is pushed 3 meters along an evacuated tube by a constant force of 40 N from air behind it. What is the final velocity?

Forces on object in equilibrium Find the weight of the hanging mass, given 100 N tension in the right rope. P2 Knowing that the T on the right rope is 100 N find T 2. a) 0 to 40 N b) 40 to 80 N c) 80 to 120 N d) 120 to 160 N e) more than N

Forces on object in equilibrium Find the tensions if the weight (W) of the boy is known. P3 Write two equations that you could solve to find T 1 and T 2. a) I did my best and checked with a classmate b) I did my best alone T2T2 T2T2

Lecture 5, Second law and friction Basic concepts: ◦ mass as resistance to acceleration ◦ weight vs. mass ◦ breaking static friction Basic problems, skills: ◦ F = ma in one dimension ◦ friction from normal force ◦ free body diagrams Advanced concepts: ◦ effect of initial v y ◦ F = ma for both x and y directions ◦ Normal force often does not equal the weight Advanced problems, skills: ◦ Normal force from free body diagram ◦ Using symbols instead of numbers in setting up problems and doing algebra ◦ Equilibrium with ropes and cables at angles ◦ Solving 2 equations simultaneously for two unknowns