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Transcript
PHYSICS 231 Lecture 12: Keeping momentum Remco Zegers Walk-in hour: Thursday 11:30-13:30 am Helproom PHY 231 1 The 3 most difficult exam problems • The Football player (28% correct) • Can out of the train (40% correct) • x-t and v-t graph & block-pulley (47% correct) PHY 231 2 The football player A football player throws a ball with an initial velocity of 40 m/s and an angle of 40o with respect to the field. At what distance from the player will the ball hit the field? Assume that the player’s length is negligible (i.e. the ball is thrown from a vertical height of 0.0 m). 40 m/s 40o 40sin(40o) 40cos(40o) Horizontal direction (0)t+½at2 X(t)=x(0)+vx d=0+40cos(40o)t+0 d=31t d=31*5.2=161.2 m d Vertical direction Y(t)=Y(0)+vy(0)t+½at2 0=0+40sin(40o)t-½gt2 25.7t-½gt2=0 (25.7-½gt)t=0 so t=0 (start) or t=25.7/(½g)=5.2 PHY 231 3 Can out of the train A train is moving with a speed of 25 km/h to the east. An environment-unfriendly passenger throws a can out of the window. The velocity with which he throws the can relative to the moving train is 25 km/h toward the back of the train the (west) and 10 km/h away from the train toward the south. To an onlooker standing on the ground (south of the track), what is the observed direction of motion of the can? Cancel! velocity of can parallel of the train (-25 km/h) N Train (25 km/h) W E velocity of the can S perpendicular to the train (to the south) (10 km/h) PHY 231 4 X-t and v-t graph Xx tt Xv tt PHY 231 5 Pulley 40 kg A block of mass 40.0 kg sliding on a frictionless table is attached to another block of 10kg 10 kg mass 10.0 kg by a string over a massless pulley (see figure). What is the acceleration of the bigger mass? Use Newton’s second law for each object separately! 40 kg 10 kg T=40a (only hor. direction) -T+10g=10a -T+98.1=10a -40a+98.1=10a 98.1=50a so a=98.1/50=1.96 m/s2 40 kg PHY 231 6 Tail of chapter 5 30o h L=5m If relieved from rest, what is the velocity of the ball at the lowest point? (PE+KE)=constant PErelease=mgh (h=5-5cos(30o)) =6.57m J KErelease=0 PEbottom=0 KEbottom=½mv2 ½mv2=6.57m so v=3.6 m/s PHY 231 7 A running person While running, a person dissipates about 0.60 J of mechanical energy per step per kg of body mass. If a 60 kg person develops a power of 70 Watt during a race, how fast is she running (1 step=1.5 m long) What is the force the person exerts on the road? W=Fx P=W/t=Fv PHY 231 8 Chapter 6 Momentum & Collisions When a bullet hits the wall, its velocity is very much reduced. The wall does not move, although the force on the ball is the same as the force on the wall (Newton’s 3rd law: Fwall-bullet=-Fbullet-wall). Fwall-bullet=mbulletabullet Fbullet-wall=mwallawall Mbullet << Mwall |abullet|>> awall PHY 231 9 Is it only the mass??? Vbullet=100 m/s Vbullet=200 m/s When the bullet gets stopped in the wall, it deaccelerates from its initial velocity to 0. So, its acceleration is vbullet/t, with t some small time (independent of v). Second law: Fwall-bullet=mbulletabullet=mbulletvbullet/t The force also depends on the velocity of the bullet! PHY 231 10 More general…and formal. F=ma Newton’s 2nd law F=mv/t a=v/t F=m(vfinal-vinital)/t Define p=mv p: momentum (kgm/s) F=(pfinal-pinitial)/t F=p/t The net force acting on an object equals the change in momentum (p) in a certain time period (t). Since velocity is a vector, momentum is also a vector, pointing in the same direction as v. PHY 231 11 Impulse F=p/t p=Ft Definition: F2 F1 Force=change in (mv) per time period (t). The change in momentum equals the force acting on the object times how long you apply the force. p=Impulse What if the force is not constant within the time period t? p=Ft=(F1s+F2s+F3s)= = t(F1s+F2s+F3s)/t = tFaverage F3 s s s t p=Faverage t PHY 231 12 Some examples A tennis player receives a shot approaching him (horizontally) with 50m/s and returns the ball in the opposite direction with 40m/s. The mass of the ball is 0.060 kg. A) What is the impulse delivered by the ball to the racket? B) What is the work done by the racket on the ball? PHY 231 13 Child safety A friend claims that it is safe to go on a car trip with your child without a child seat since he can hold onto your 12kg child even if the car makes a frontal collision (lasting 0.05s and causing the vehicle to stop completely) at v=50 km/h (about 30 miles/h). Is he to be trusted? PHY 231 14