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Chapter 6 and 7 momentum = mass x velocity p = mv units: kgm/s or Ns What is the value of the momentum of a 10 kg ball rolling down a bowling alley at a speed of 5 m/s? p = mv p = (10 kg)(5 m/s) p = 50 kgm/s Momentum is a vector, it has a direction The ball bounces off the wall. What is the change in momentum? Dp = pfinal - pinitial = 2p Newton’s 2nd Law: F = ma = mDv/Dt p Impulse-Momentum Theorem FDt = p If this girl throws a 0.2 kg snowball at 20 m/s…at you, and it impacts your skull for 0.05 s, what is the force of the impact? FDt = mDv F = mDv/Dt F = (0.2 kg)(20 m/s)/0.05 s F = 80 N Stopping Distance A 2500 kg car brakes to slow from 25 m/s to 10 m/s in 6 s. What was the force of braking? F = mDv/Dt = (2500 kg)(10 m/s – 25m/s)/6s F = -6250 N How far will it go in that time? Dx = ½(vi + vf)Dt = ½(25m/s + 10m/s) 6s Dx = 105 m Conservation of Momentum The total momentum before equals the total momentum after, if there are no external forces. m1v1i + m2v2i = m1v1f + m2v2f 80 kg Schoettle steps out of his 100 kg boat with a velocity of 2 m/s. What is the boat’s velocity? 0 0 m1v1i + m2v2i = m1v1f + m2v2f v2f = -m1v1f/m2 v2f = -(80 kg)(2 m/s)/100 kg v2f = 1.6 m/s Types of collisions (two things hitting each other) Perfectly Inelastic: the two things stick together m1v1i + m2v2i = (m1 + m2)vf 10 kg v1i = 3 m/s 5 kg What is the velocity after they stick? m1v1i + m2v2i = (m1 + m2)vf m1v1i = (m1 + m2)vf vf = 2 m/s Centripetal Acceleration An object moving in a circle is accelerated toward the center Forces that maintain circular motion Something moving in a circular path has a tendency to want to continue in a tangent path. A force must hold it in its circular path. This is called Centripetal Force. What provides the centripetal force in the picture? What keeps a car on a circular path moving in a circle? Universal Gravitation All matter creates a force of gravity with other matter Mass of two objects m1m 2 Fg G 2 r Force of Gravity G 6.673x10 11 Nm2 kg 2 Distance between two objects m1m 2 Fg G 2 r If I double m1, what happens to the force of gravity? If I triple m2, what happens to the force of gravity? If I double the distance between the masses, what happens to the force of gravity? If I halve the distance between the masses, what happens to the force of gravity? If I triple the distance, what happens to the force? m1m 2 Fg G 2 r Fg = mg m1m 2 mg G 2 r mE g G rE 2 Rotation: the spinning of an object Revolution: the orbital motion