Force and Motion PHYS 1090 Unit 2

Force and Motion Fundamentals: position, mass and time Velocity = rate of change of position

Motion Graphs (one dimension) position time tt rr = slope! Velocity = rr tt

Steeper slope position time tt rr Greater  r in same  t Faster Higher velocity

Horizontal p-T plot position time  r = 0 Slope = 0 Velocity = 0

Downward slope position time tt rr r decreases as t increases Backward motion Negative velocity

Curved p-T plot position time Slope is not constant Velocity changes What motion would have a p-T plot like this?

Acceleration Rate of change of velocity A change in velocity with time Rate of change of a rate of change Another level of abstraction a = vv tt

Cart Coasting on a Ramp v a r t

Newton’s First Law Exemplified by ball-on-tray activity

Newton’s First Law “An object at rest will remain at rest, and an object in motion will continue in motion in a straight line and at a constant speed unless acted on by an outside force.” Specifies not only speed, but also direction of motion Force changes an object’s motion

Force Any influence changing an object’s velocity (speed or direction) Examples: –Gravity –Friction –Contact support –Any push or pull

Newton’s Second Law “The acceleration of an object is directly proportional to the net force applied to it, and inversely proportional to the object’s mass.” a =a = F m F = net force = sum of all external forces on the object

Rail Carts For the same mass, a greater force gives a greater acceleration The greater the cart’s mass, the slower the acceleration from the same force The greater the cart’s mass, the greater the force needed to achieve the same acceleration

Drag Races Plot F2F2 F1F1 m2m2 m1m1 F 2, m 2 adjusted so a 2 = a 1 a 1 = F 1 /m 1 ; a 2 = F 2 /m 2 F1F1 m1m1 F2F2 m2m2 = m2m2 m1m1 F2F2 F1F1 = Plot should be a straight line through (0,0) with slope = 1

Drag Races Plot F2F2 F1F1 m2m2 m1m1 Friction Mis-matched masses Sloping tracks Sources of Error:

Force of Gravity Newton’s second law: the more massive something is, the more force is needed to accelerate it F = ma Gravity: the more massive something is, the harder gravity pulls on it F = mg

Acceleration by Gravity Newton’s second law: a = F/m Gravity: F = mg So, a = F m mg m = = g All objects fall at the same rate (if gravity is the only force acting)! Acceleration depends on g, not m

Vectors Position, velocity, acceleration, force all have direction Newton’s second law: a = F/m a and F have direction; m does not a and F are always in the same direction

Stick Ball Push in direction of v: speeds up Push in direction opposite v: slows down, stops, or reverses Push at an angle to v: a and v in different directions v a final v

Vectors and Scalars Vector: quantity needing a direction to fully specify (direction + magnitude) Scalar: directionless quantity

Represent as Arrows direction: obvious magnitude: length location is irrelevant these are identical

Add Vectors A C B A + B = C Head-to-tail (not in your book) A B

How to Add Vectors Place following vector’s tail at preceding vector’s head Resultant starts where the first vector starts and ends where the last vector ends

Oblique Force Push at an angle to v: a and v in different directions Add  v = a  t to initial v to find final v v a final v Initial v  v = a  t

Uniform Circular Motion Speed is constant, direction changes This still means velocity changes with time The object accelerates Acceleration requires a nonzero net force Acceleration and force are toward the center of the circular path