Chapter 3: Force and Motion The First Law of Motion An object at rest will remain at rest and an object in motion will remain in motion (at constant velocity) unless acted upon by an external force. Forces are the “causes” of changes in motion. forces on an object arise from interactions with other objects. The inertia of an object is its resistance to changes in its motion. Mass is a measure of inertia.

Mass as a measure of inertia two interacting objects, initially at rest B vA B vB A A relative changes in motion: vA /vB = mB /mA Units: kilogram = kg (other units: slugs, sometimes “pounds mass”) 1kg ~ 2.2 lb. Force: the influence which causes change in motion change in velocity = change in speed or direction A net force (or unbalanced force) creates changes in motion If the resultant of all forces acting on an object is zero, there is no change in motion: the object is in equilibrium.

The Second Law of Motion The net force acting on an object equals the product of the mass and the acceleration. F = m a (net force) = (mass)(acceleration) Units: 1 Newton = 1N = 1 kg · m/s2 1N ~ 1/4 pound Example 3.1: A 60 g tennis ball approaches a racket at 30 m/s, is in contact with the racket for 5 ms and then rebounds at 30 m/s. What is the average force the racket exerts on the ball?

Example 3.2: A human cannon ball with mass 70 kg is fired from a compressed-air cannon whose barrel is 20m long. He emerges from the cannon at 40 m/s. Find his average acceleration and the force exerted on him during the firing of the cannon. Example 3.3: A horizontal force of 10 N is applied to a 4.0 kg block which is initially at rest on a smooth level surface. Find the speed of the block and its displacement after it has gone for 6.0 s.

Weight: the force exerted by earth (via gravity) on an object In free fall, gravity is the only force acting on the object F = ma = mg = w Weight = (mass)(acceleration of gravity) Example 3.4: A loaded elevator whose total mass is 800 kg is suspended by a cable whose maximum permissible tension is 20,000 N. What is the greatest upward acceleration possible? What is the greatest downward acceleration? (draw free-body diagrams)

The third law of motion: action/reaction When an object exerts a force on a second object, the second object exerts a force on the first of equal magnitude, but opposite direction. For every action there is an equal but opposite reaction. Forces arise from interactions! Forces on an Object Action/Reaction reaction force of table on computer reaction force of table on computer force of computer on table weight of computer

T=FB mB = 30kg (+) B (+) T A mA = 15kg wA -T=FA =mA g-T w

T (+) T-wA=FA wB-T=FB (+) w A B mA = 15kg mB = 30kg

due to surfaces sticking together Friction opposes motion due to surfaces sticking together Kinetic Friction: surfaces are moving relative to each other a.k.a. Sliding Friction Static Friction: surfaces are not moving relative to each other. Static Friction prevents stationary objects from moving until sufficient force has been applied. Friction Applied Force

Coefficient of Friction Frictional forces depend upon how hard the surfaces are being pressed together -> force perpendicular to the surface = normal force the types of surfaces that are in contact -> coefficient of friction Material static: ms kinetic: mk wood on wood 0.5 0.3 wood on stone 0.5 0.4 steel on steel (smooth) 0.15 0.09 rubber tire on dry concrete 1.0 0.7 rubber tire on wet concrete 0.7 0.5 steel on Teflon 0.04 0.04

Example 3.11: A 100 kg wooden crate is at rest on a level stone floor. (a) What is the minimum horizontal force needed to start the crate moving? (b) What is the minimum horizontal force needed to keep the crate in motion at constant horizontal speed? (c) What will happen if a horizontal force of 500 N is applied to the crate? ` Example 3.14:A wooden chute is being built along which wooden crates are to be slid down at constant speed. (a) What angle should the chute make with respect to the horizontal? (b) What force needs to be applied to a 100 kg crate to start it sliding down this chute? FN Ff mg sinq q mg cosq q mg