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Isaac Newton (1643 – 1727) Defining his 3 Laws Newton at age 46 Scalar vs. Vector • Speed is scalar – (how fast something is going) • Velocity is a vector so its direction matters! – (speed and direction) • Acceleration is also a vector it has magnitude and direction Speed and Direction Speed is important (100 km/hr) But . . . Direction can be even more important!!! Uniform circular motion How Many Accelerators Does Your Car Have? Newton’s First Law of Motion • Every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it Forces are Balanced a = 0 m/s2 Object at rest Object in Motion V = 0 m/s V ≠ 0 m/s Stay in motion same Stay at rest speed and direction in straight line Car in motion makes a left hand turn Acceleration in a car Car starts from rest Moving car brakes to stop Newton’s Second Law of Motion • The relationship between an object’s mass (m), its acceleration (a), and the applied force (F) is F = ma In terms of acceleration: a = F/m Forces are Unbalanced There is an acceleration a = F/m The acceleration The acceleration depends directly depends inversely upon the upon the “net force” object’s mass Aristotle vs. Newton • Aristotle force maintains motion (s) (F=ms) Common sense • Newton force causes change in velocity • (F=ma) looks at all forces involved Baseball and Tennis Ball A. Drop in a vacuum from height of ~ 30 feet B. Drop from the roof of DeLaRoche Which hits the ground 1st? Baseball - mass 142 to 149 g -circumference 22.9 to 23.5 cm Tennis ball - mass 57.7 to 58.5 g -circumference 19.95 to 20.95 cm Drop a baseball and tennis ball (in vacuum) • _____________________ • Baseball 2.5 times mass of tennis ball – Earth pulls 2.5 times as hard on baseball But • Baseball’s greater mass makes it 2.5 times as hard to accelerate • ___________________________________ Drop a baseball and tennis ball (off DeLaRoche) • ________________ lands first • must take into account air resistance • when air resistance = gravity terminal velocity • ______________ reaches terminal velocity quicker than ______________ • ___________ falls longer before air resistance balances gravity – more time to fall more time to accelerate Terminal Velocity [Don’t try to memorize] Vt is the terminal velocity m is the mass of the falling object g is gravitational acceleration at the Earth's surface Cd is the drag coefficient ρ is the density of the fluid the object is falling through A is the object's cross-sectional area Momentum • Momentum – “mass in motion” • All objects have mass so if moving object has momentum • Newton’s statement of his second law involved the rate of change of “motion” (=momentum) • can be restated in terms of momentum ρ=m•v Stopping Momentum • Any object with momentum is hard to stop • Must apply a force against its motion over time • The greater the momentum the greater the force or longer the time period to stop the object Impulse = Force • Time = Change in Momentum Can be derived from Newton’s 2nd law F = ma a = Δ v/t F = m(Δ v/t) Ft = Δmv To minimize the affect of the force on an object time must be increased [Ft = Δmv] To maximize the affect of the force on an object time must be decreased [Ft = Δmv] Combinations of Force and Time required to produce 100 units of Impulse Force Time Impulse 100 1 100 50 2 100 25 4 100 10 10 100 4 25 100 2 50 100 1 100 100 0.1 1000 100 Real Life Examples Hitting the “Long Ball” Hitting the “Long Ball” • You want the ball to have the largest possible velocity when it leaves the bat • What does the impulse-momentum equation say about this? • You want the largest possible momentum for the ball as it leaves the bat. Ball has essentially zero momentum when you hit it (i.e., zero velocity) Hitting the “Long Ball” • You want the largest possible change in momentum for the ball • The change in momentum of the ball equals the impulse that you apply (with the bat) to the ball • To get the largest possible change in momentum, apply the largest possible impulse to the ball Hitting the “Long Ball” • Impulse depends directly on force applied and time the force is applied. (Impulse = (force)(time) • To get the largest possible impulse you should either: apply the largest possible force apply the force for the longest possible time or both Hitting the “Long Ball” • You want to apply maximum force by hitting the ball hard. If you hit the ball with twice the force, you will impart twice the impulse to the ball • Impulse = change in momentum - this will double the ball's change in momentum • Momentum equals mass times velocity - doubling the ball's momentum will double its velocity • However, if you try to apply too much force your coordination and timing will suffer, and your swing will not be accurate - you may even miss the ball! Hitting the “Long Ball” • You can also increase the impulse on the ball by increasing the time that the bat exerts its force on the ball - "following through" • If you hit the ball for twice as much time, you will impart twice the impulse to the ball, which means twice the change in momentum for the ball. So, following through is important Golf – Tennis - Soccer • To get largest possible velocity for the ball: want the largest possible momentum for the ball • To get the largest possible momentum for the ball: want to apply the largest possible impulse to the ball • To apply the largest possible impulse to the ball: want to apply the largest possible force apply a force for the longest possible time or both Newton’s Third Law of Motion • For every action there is an equal and opposite reaction Balanced Forces The forces on the person are balanced Gravity pulls The floor pushes downward on the upward on the person person Conservation of Momentum • Product of mass x velocity • In isolated system momentum must remain constant • Adult pushing child away on ice • Angular momentum and a spinning ice skater [Don’t try to memorize following slides!!] Is the force the car exerts on the truck? A. greater than the force the truck exerts on the car B. less than the force the truck exerts on the car C. equal to the force the truck exerts on the car mass-car (m1) = 1500kg mass-truck (m2) = 20,000kg Velocity-car (u1) = 8m/s, Velocity-truck (u2) = 5 m/s solution for final velocity can be derived from conservation of momentum ρ 0 = ρf ρ1 + ρ2 = (m1 + m2)*V (m1u1) – (m2u2) = (m1 + m2)*V V = (m1u1 – m2u2)/(m1 + m2) V= [(1500 kg)(8 m/s) – (20,000 kg)(5 m/s)]/)1500 kg + 20,000 kg) V = -4.09 m/s We can find the forces acting on the driver in each vehicle by noting that the change in velocity of the car or truck is the same as the change in velocity of the driver Let's assume the crash takes place over a time period of about 0.2 s. The acceleration of the truck is a2 = vf - v0/tcrash = (V - u2)/ tcrash = (-4.09 m/s – (-5) m/s)/0.2 s = +4.6 m/s2 The car driver experiences an acceleration of (V - u1)/tcrash = (-4.09 m/s - 8 m/s)/0.2 s = -60.5 m/s2 The magnitude of the forces are equal since, Ftruck = (20,000 kg)(4.6 m/s2) = 92,000 Nt and Fcar = (1500 kg) (60.5 m/s2) = 91,000 Nt with the difference being round off error Since the accelerations of the car and truck are opposite signed, the directions of the forces on both are in opposite directions just as Newton's Third Law demands If the truck driver and car driver are about the same mass, then the force on the car driver is about 13 times as great as the force on the truck driver! F = ma if mass = 70 kg = 154 lbs Ftruck driver = 70kg * 4.6 m/s2 = 322 Nt Fcar driver = 70kg * 60.5 m/s2 = 4235 Nt

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posted: | 8/8/2011 |

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