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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). D r. D r. position. D t. D t. Velocity = . = slope!. time. Steeper slope. D r. position. D t. time.

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## Force and Motion

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**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)**Dr Dr position Dt Dt Velocity = = slope! time**Steeper slope**Dr position Dt time • Greater Dr in same Dt • Faster • Higher velocity**Horizontal p-T plot**position time • Dr = 0 • Slope = 0 • Velocity = 0**Downward slope**position Dr Dt time • rdecreases 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 = Dv • A change in velocity with time • Rate of change of a rate of change • Another level of abstraction Dt**Cart Coasting on a Ramp**r v a 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.” F a= 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**F2 F2 m2 F1 F2 m2 • F2, m2 adjusted so a2 = a1 • a1 = F1/m1; a2 = F2/m2 F1 m1 m1 m2 m1 F1 = = • Plot should be a straight line through (0,0) with slope = 1**Drag Races Plot**F2 m2 F1 m1 Sources of Error: • Friction • Mis-matched masses • Sloping tracks**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, = g mg F a = = • All objects fall at the same rate (if gravity is the only force acting)! • Acceleration depends on g, not m m 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 ofv: speeds up • Push in direction oppositev: slows down, stops, or reverses • Push at an angle tov: a and v in different directions final v a v**Vectors and Scalars**• Vector: quantity needing a direction to fully specify (direction + magnitude) • Scalar: directionless quantity**these are identical**Represent as Arrows direction: obvious magnitude: length location is irrelevant**A**A C B B A +B=C Add Vectors Head-to-tail (not in your book)**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 tov: a and v in different directions • Add Dv = aDt to initialv to find final v final v a Dv = aDt v Initial v**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

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