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Mass and Acceleration Mass Matter has substance. • Solids, liquids or gases • Subatomic particles • Planets and stars We feel the weight of different objects. We will see that weight is not mass, but mass can have weight. Mass measures the amount of matter in an object. Mass Units Mass is measured in kilograms. • 1 kg = 1000 g • 1 atomic mass unit (about the mass of one hydrogen atom) = 1.66 x 10-27 kg Mass is a scalar. • Mass times a vector gives another vector • For instance, momentum: p mv Force and Acceleration With force there is acceleration. The amount of acceleration depends on the mass. F a m The direction of the force and acceleration are the same. F ma Force Units Force is mass times acceleration. The dimensions of force are M(L/T2). In SI units a newton (N) = 1 kg m / s2. Law of Action 2 The change in motion is proportional to the force and the change is made in the same direction as the force. A force gives rise to action by acceleration. Force = mass x acceleration (Newton’s second law). Initial velocity Final velocity: changed by the force Rocket: has mass Force: becomes acceleration Accelerating a Mass A loaded 747 jet has a mass of 3.6 x 106 kg and four engines. The distance and final velocity are used to get the acceleration. 2 v v0 x v v0 x v 2a It takes 1700 m at constant thrust (force) to reach a takeoff speed of 86 m/s (310 km/h). What is the force per engine? 0 a 0 v2 2a The acceleration and mass give the force. mv2 F ma 2x F = (7.8 x 106 N)/4 = 2.0 x 106 N. Vector Force A 1000 kg satellite in space is moving at 5 km/s when a rocket fires with a thrust of 5 x 103 N at 60° to the direction of motion. The rocket fires for 1 minute. Where does it move after firing? x The force and acceleration are vectors. Pick x in the direction of initial motion. F F F a (cos )iˆ (sin ) ˆj m m m The new velocity is Ft Ft v at v0 ( cos v0 )iˆ ( sin ) ˆj m m vx = 5.1 km/s, vy = 0.26 km/s. next