Mass and Motion

Mass and Force Mass is substance. 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 Force is measured in N. 1 N = 1 kg m/s2 Dimension M(L/T2) Pounds measure weight (a force) not mass. © R. Rathe, NIST

Second Law: Law of Acceleration The change in motion is proportional to the net force and the change is made in the same direction as the net force. Net force gives rise to acceleration. Force = mass x acceleration (Newton’s second law). Final velocity: changed by the force Rocket: has mass Initial velocity Force: becomes acceleration

Force and Acceleration With force there is acceleration. The amount of acceleration depends on the mass. Mass is a scalar. Mass times a vector gives another vector. The direction of the force and acceleration are the same.

Vector Force A 1000 kg satellite in space is moving at 5.0 km/s when a rocket fires with a thrust of 5.0 x 103 N at 60° to the direction of motion. The rocket fires for 1 minute. Where does it move after firing? Identify the quantities in the problem: Mass, m = 1000 kg Initial velocity, v0 = 5 x 103 m/s Force, F = 5 x 103 N at 60° Time, t = 1 min = 60 s Force and velocity are vectors Pick x in the direction of initial motion: vx = v0 . Fx = F cosq Fy = F sinq F = 5000 N q = 60 x

Change in Velocity A 1000 kg satellite in space is moving at 5.0 km/s when a rocket fires with a thrust of 5.0 x 103 N at 60° to the direction of motion. The rocket fires for 1 minute. Where does it move after firing? The force gives acceleration. ax = Fx /m = (F/m) cosq ay = Fy /m = (F/m) sinq The change in velocity is due to this acceleration. vx = v0 + ax Dt = v0 + (F t / m) cosq vy = ay Dt = (F t / m) sinq The final velocity is vx = 5200 m/s = 5.2 km/s vy = 260 m/s = 0.26 km/s. v v0