Physic 3 Lecture 5 Main points of today s lecture: Addition i of velocities i v = v + vt v is the velocity in the "stationary" frame v is the velocity in the " moving"frame v t is the velocity of the " moving"frame Newton s st law: Newton s nd law: F = ma
example A small can is hanging from the ceiling. A rifle is aimed directly at the can, as the figure illustrates. At the instant the gun if fired, the can is released. Ignore air resistance and show that the bullet will always strike the can, regardless of the initial speed of the bullet. Assume that the bullet strikes the can before the can reaches the ground. Δ xbullet = v0 cosθt =Δxline _ of _ sight Δy Δ ybullet = v0 sinθt gt gravity Δy can Δ y = Δ y +Δy bullet line _ of _ sight gravity Δ ycan = gt Δ ycan = Δygravity θ Therefore bullet will hit the can.
Reading Quiz. The acceleration vector of a particle in projectile motion A. points along the path of the particle. B. is directed horizontally. C. vanishes ih at tthe particle s til highest hih point. it D. is directed down at all times. E. is zero. Slide 3-9
Concept problem A battleship simultaneously fires two shells at enemy ships. If the shells follow the parabolic trajectories shown, which ship gets hit first? a) A b) both at the same time c). B d) need more information initial vertical velocity for A exceeds the initial vertical velocity for B: Proof: v = v gh = 0 y,top 0 v0 = gh; ha > hb v0y,a > v0y,b v Δ ytot = 0 = vy0t tot gt tot t tot = g y0 comparing the two trajectories: v0y,a > v0y,b ttot,a > ttot,b
example A motorcycle daredevil is attempting to jump across as many buses as possible (see the drawing). The takeoff ramp makes an angle of 8.0 above the horizontal, and the landing ramp is identical to the takeoff ramp. Thebuses are parked side by side, and each bus is.74 m wide. The cyclist leaves the ramp with a speed of 33.5 m/s. What is the maximum number of buses over which the cyclist can jump? 33.5 m/s.74m v 0 33.5 m/s a) vy = vy0 gt θ 8 ( ) o b) Δy y y0 = vy + vyo c) Δ y = v d) v y 0 Which equation to use? v y y0 t gt = gδy t vy0 = 33.5sin(8 ) = 0.35m / s Δ y= vy0t gt = 0 vy0t = gt vy0 t = =.s g Δ x = vx0t = 33.5cos(8 )(.s) = 67.5m Δx 67.5m Nbuses = = = 4.5 4buses w.74m bus
t Exercise: what you sometime have to do if initial and final heights are different A ball is thrown downwards d from a 00 m high h building with an initial iti speed of 40 m/s. How much later does it hit the ground? a) s g = 98m/s 9.8m/s downwards b) 4.5 s v = v0 gt c) 8.5 s d) s Δy y y0 = ( v + vo )t Δ y = vt 0 gt Δy = v0t gt gt v t 0 +Δ y = 0 v v = g Δy y Ui Using quadratic formula 0 t = = v ± v gδy 0 0 g ( )( ) + t= s 40m / s 600m / s 9.8m / s 00m / s 9.8m / s Δy v 0-00 m -40 m/s check by plugging in: (9.8)() ( 40)() 00 = 9.60+80-00 0
relative velocity problems Lbl Label each object tby a letter ltt that thtreminds id you of what htiti is (for example p for paper, g for ground, t for truck). Look for phases such as "the velocity of the paper relative to truck" and write the velocity as: v paper = v _ relative _ to _ truck pt Take the three velocities and assemble them into an equation such as; v pg = v tg + v pt S l f th l it t N t th t th l iti d t b Solve for the velocity you want. Note that these velocities need not be parallel. You may need to solve two equations, one in the x direction and another in the y direction.
exercise Chuck looks ahead and sees Grandpa Harper. He throws him a newspaper over the top of the hood to him. The truck is moving 40 km/hr due West. Relative to the truck, the newspaper also moves West with a velocity of 40 km/hr. What is the velocity of the newspaper relative to Grandpa Harper? a) 0 km/hr v paper _ relative _ to _ ground b) 80 km/hr due west c) 80 km/hr due east = vtruck + vpaper _ relative _ to _ truck d) don t know v = 40+ 40 paper _ relative _ to _ ground = 80 km/hr West v truck v paper relative to truck 40 km/hr West 40 km/hr West v paper relative to ground?
Example north y Af ferry boat tis traveling in a direction 35. 35 o north of east with a speed of 5. m/s relative to the water. A passenger is walking with a velocity of.7 m/s due east relative to the boat. What is the velocity (magnitude and direction) of the passenger with respect to the water? v pb =.7 m/s v = v + v pw pb bw x bw,x ( ) east v = 5.cos(35. ) = 4.9m / s vbw,y = 5.sin(35. ) =.94m / s x y mag θ v pb.7 0.7 0 v bw 4.9.94 5. 35. v pw 69 6.9 94.94 75 7.5 3 vpw = 6.9 +.94 = 7.5m / s θ 35. o ( 94 ) θ = tan.94 3 north of east v pb =.7 m/s 6.9 =
Reading Quiz. A net force is A. the sum of the magnitudes of all the forces acting on an object. B. the difference between two forces that are acting on an object. C. the vector sum of all the forces acting on an object. D. the force with the largest magnitude acting on an object. Slide 4-7
Newton s First Law If there is no net force, the velocity of a mass remains constant (neither the magnitude nor the direction of the velocity changes). Objects at rest feel no net force. Objects in motion with a constant velocity feel no net force. movie