* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Wed 9/16
Laplace–Runge–Lenz vector wikipedia , lookup
Classical mechanics wikipedia , lookup
Quantum vacuum thruster wikipedia , lookup
Theoretical and experimental justification for the Schrödinger equation wikipedia , lookup
Coriolis force wikipedia , lookup
Photon polarization wikipedia , lookup
Equations of motion wikipedia , lookup
Hooke's law wikipedia , lookup
Angular momentum operator wikipedia , lookup
Mass versus weight wikipedia , lookup
Newton's theorem of revolving orbits wikipedia , lookup
Fictitious force wikipedia , lookup
Nuclear force wikipedia , lookup
Electromagnetism wikipedia , lookup
Relativistic mechanics wikipedia , lookup
Centrifugal force wikipedia , lookup
Relativistic angular momentum wikipedia , lookup
Centripetal force wikipedia , lookup
Section 2.4 – 2.6 Momentum Principle & the Universal Speed limit Predictions of Motion under the influence of Forces Meet Gravitation – constant force Meet Springs – changing force Q 2.2 a An object is moving in the +x direction. Which of the following statements about the net force acting on the object could be true? a) b) c) d) e) f) g) The net force is in the +x direction The net force is in the –x direction The net force is zero A and B B and C A and C A, B and C Q 2.2 b Three carts are moving on three tracks. Which cart(s) experience a net force to the left? A. B. C. D. E. F. Green Cart which moves to the left at constant speed. Red Cart which moves to the left, gradually speeding up. Blue Cart which moves to the left, gradually slowing down. Both Green and Red carts Both Blue and Red carts Both Green and Blue carts Question A car is moving at 3 m/s in the positive x direction. Which of these describes that fact: a) V = <-3,0,0> m/s b) V = 3 m/s x^ ^ c) V = 3 m/s -x d) V = <0,3,0> m/s Question A car experiences a force in the -x^ direction. Which of these is a possible change in momentum it would experience: a) Dp = <-10,0,0> kg m/s b) Dp = 10 kg m/s x^ c) Dp = 10 kg m/s -x^ d) Dp = <0,-10,0> kg m/s e) Answers (b) and (d) f) Answers (a) and (c) Question A ball has a momentum in the y^ direction at one moment. At the next moment has a motion in the –y^ direction. What direction does the force on it point? ^ a) Dp = 10 kg m/s y ^ b) Dp = -10 kg m/s y c) Dp = 10 kg m/s x^ ^ d) Dp = -10 kg m/s x e) Not enough information to tell. Q 2.3 d: You practice on paper like homework Inside a spaceship in outer space there is a small steel ball. At a particular instant, the ball has momentum < -8, 3, 0 > kg· m/s and is pulled by a string, which exerts a force < 20, -10, 0 > N on the ball. What is the ball’s (vector) momentum 2 seconds later? A. B. C. D. E. < -28, 23, 0 > kg· m/s < 12, -7, 0 > kg· m/s 36.2 kg· m/s < 32, -17, 0 > kg· m/s < 40, -20, 0 > kg· m/s Students collide • • • • • • • • • • The initial momentum of the one-student system is nonzero. The initial momentum of the two-student system is zero. We're interested in the force exerted on one student, so we apply the Momentum Principle to a system consisting of one student. We can estimate Δt from the compression distance in the collision. The final momentum of the one-student system is nonzero. The net force on the two-student system is zero because the interatomic force exerted by student 1 on student 2 is equal in magnitude but opposite in direction to the force exerted by student 2 on student 1. A good estimate of the initial speed of one of the running students is 0.1 m/s. The Momentum Principle can't be applied in this analysis because we have no way of estimating Δt. The final momentum of the two-student system is nonzero. The Momentum Principle when applied to the two-student system is simply 0 = 0 and doesn't give us any information. Updating Position in Computer Simulations Position Update (ch 1) robject new robjectold vobjectave Dt vobjectave pobjectave mobject Dt Momentum Update (ch 2) pobjectnew pobjectold Fnet object ave Dt Note: If Dt is small enough, old speed is close enough to average, old force is close enough to average to approximate in simulation. A “while loop” while t<tmax t t Dt pobject pobject Fnet objectDt p object robject robject Dt mobject 1-D Motion fan cart (1-D). Suppose you have a fan cart whose mass is 400 gram and it’s on a huge, 8m long track. Initially you set the cart moving down the track in the x-direction at location <0.5,0,0>m with velocity <1.2,0,0>m/s. The force due to the fan is <0.2,0,0>N; comparatively, friction is negligible. What are the momentum and position of the cart 3 seconds later? Calculate this in a series of 1 second intervals. Gravitational force • Constant force over small regions. Works well for an integrated solution. Magnitude: FEarth mg 9.8 m/s2 Mass Direction: toward earth (sign and component depend on your choice of coordinate systems) Smoothly-Varying Force: Spring Fsp k s s k s sLˆ Example: With the spring over here, I hang 4.9 N (0.5 kg) weight from it, and it stretches by ______m. So, what’s it’s stiffness? Example: A spring is 0.14 m long when it is relaxed. When a force of magnitude 325 N is applied, the spring becomes 0.22 m long. (a) What is the stiffness of this spring? (b) Next, this spring is compressed so that its length is 0.08 m. What magnitude of force is required to do this? Q 2.5 c A spring is 12 cm (0.12 m) long when relaxed. Its stiffness is 30 N/m. You push on the spring, compressing it so its length is now 10 cm (0.10 m). What is the magnitude of the force the spring now exerts on your hand? a) 0.6 N b) 3N c) 3.6 N d) 30 N