Assume the pucks in Figure P11.66 stick together after their collision at the origin. Puck 2 has four times the mass of puck 1 (m2 = 4m1). Initially, puck 1’s speed is three times puck 2’s speed (v1i = 3v2i), puck 1’s position is
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Physics for Scientists and Engineers: Foundations and Connections
- Initially, ball 1 rests on an incline of height h, and ball 2 rests on an incline of height h/2 as shown in Figure P11.40. They are released from rest simultaneously and collide elastically in the trough of the track. If m2 = 4 m1, m1 = 0.045 kg, and h = 0.65 m, what is the velocity of each ball after the collision?arrow_forwardInitially, ball 1 rests on an incline of height h, and ball 2 rests on an incline of height h/2 as shown in Figure P11.40. They are released from rest simultaneously and collide in the trough of the track. If m2 = 4 m1 and the collision is elastic, find an expression for the velocity of each ball immediately after the collision. FIGURE P11.40 Problems 40 and 41.arrow_forwardA small block of mass m1 = 0.500 kg is released from rest at the top of a frictionless, curve-shaped wedge of mass m2 = 3.00 kg, which sits on a frictionless, horizontal surface as shown in Figure P8.55a. When the block leaves the wedge, its velocity is measured to be 4.00 m/s to the right as shown in Figure P8.55b. (a) What is the velocity of the wedge after the block reaches the horizontal surface? (b) What is the height h of the wedge?arrow_forward
- A mother pushes her son in a stroller at a constant speed of 1.52 m/s. The boy tosses a 56.7-g tennis ball straight up at 1.75 m/s and catches it. The boys father sits on a bench and watches. a. According to the mother, what are the balls initial and final momenta? b. According to the father, what are the balls initial and final momenta? c. According to the mother, is the balls momentum ever zero? If so, when? If not, why not? d. According to the father, is the balls momentum ever zero? If so, when? If not, why not?arrow_forwardSand from a stationary hopper falls onto a moving conveyor belt at the rate of 5.00 kg/s as shown in Figure P8.64. The conveyor belt is supported by frictionless rollers and moves at a constant speed of v = 0.750 m/s under the action of a constant horizontal external force Fext supplied by the motor that drives the belt. Find (a) the sands rate of change of momentum in the horizontal direction, (b) the force of friction exerted by the belt on the sand, (c) the external force Fext, (d) the work done by Fext in 1 s, and (e) the kinetic energy acquired by the falling sand each second due to the change in its horizontal motion. (f) Why are the answers to parts (d) and (e) different? Figure P8.64arrow_forwardTwo bumper cars at the county fair are sliding toward one another (Fig. P11.54). Initially, bumper car 1 is traveling to the east at 5.62 m/s, and bumper car 2 is traveling 60.0 south of west at 10.00 m/s. They collide and stick together, as the driver of one car reaches out and grabs hold of the other driver. The two bumper cars move off together after the collision, and friction is negligible between the cars and the ground. a. If the masses of bumper cars 1 and 2 are 596 kg and 625 kg respectively, what is the velocity of the bumper cars immediately after the collision? b. What is the kinetic energy lost in the collision? c. Compare your answers to part (b) from this and Problem 54. Is one answer larger than the other? Discuss and explain any differences you find.arrow_forward
- Problems 44 and 45 are paired. C A model rocket is shot straight up. As it reaches the highest point in its trajectory, it explodes in midair into three pieces with velocities indicated by the arrows in Figure P10.44, as viewed from directly above the explosion. Rank the mass of each piece in order from smallest to largest and justify your answer. FIGURE P10.44 Problems 44 and 45.arrow_forwardTwo metersticks are connected at their ends as shown in Figure P10.18. The center of mass of each individual meterstick is at its midpoint, and the mass of each meterstick is m. a. Where is the center of mass of the two-stick system as depicted in the figure, with the origin located at the intersection of the sticks? b. Can the two-stick system be balanced on the end of your finger so that it remains lying flat in front of you in the orientation shown? Why or why not? FIGURE P10.18 (a) The center of mass of the stick on the x axis would be at (0.5 m, 0), and the center of mass of the stick on the stick on the y axis be at (0, 0.5 m), assuming the sticks are uniform. We can then use Equation 10.3 to find the x and y coordinates of the center of mass. xCM=1Mj=1nmjxj=12m[m(0.50m)]=0.25myCM=1Mj=1nmjyj=12m[m(0.50m)]=0.25m The location of the center of mass is (0.25m,0.25m) (b) No. The location of the center of mass is not located on the object, so your finger would not be in contact with the object. In a different orientation, balancing by applying a force at the center of mass might be possible, but not in the orientation shown.arrow_forwardTwo skateboarders, with masses m1 = 75.0 kg and m2 = 65.0 kg, simultaneously leave the opposite sides of a frictionless half-pipe at height h = 4.00 m as shown in Figure P11.49. Assume the skateboarders undergo a completely elastic head-on collision on the horizontal segment of the half-pipe. Treating the skateboarders as particles and assuming they dont fall off their skateboards, what is the height reached by each skateboarder after the collision? FIGURE P11.49arrow_forward
- A rocket has total mass Mi = 360 kg, including Mfuel = 330 kg of fuel and oxidizer. In interstellar space, it starts from rest at the position x = 0, turns on its engine at time t = 0, and puts out exhaust with relative speed ve = 1 500 m/s at the constant rate k = 2.50 kg/s. The fuel will last for a burn time of Tb = Mfuel/k = 330 kg/(2.5 kg/s) = 132 s. (a) Show that during the burn the velocity of the rocket as a function of time is given by v(t)=veln(1ktMi) (b) Make a graph of the velocity of the rocket as a function of time for times running from 0 to 132 s. (c) Show that the acceleration of the rocket is a(t)=kveMikt (d) Graph the acceleration as a function of time. (c) Show that the position of the rocket is x(t)=ve(Mikt)ln(1ktMi)+vet (f) Graph the position during the burn as a function of time.arrow_forwardA girl of mass mg is standing on a plank of mass mp. Both are originally at rest on a frozen lake that constitutes a frictionless, flat surface. The girl begins to walk along the plank at a constant velocity vgp to the right relative to the plank. (The subscript gp denotes the girl relative to plank.) (a) What is the velocity vpi of the plank relative to the surface of the ice? (b) What is the girls velocity vgi relative to the ice surface?arrow_forwardA water molecule consists of an oxygen atom with two hydrogen atoms bound to it (Fig. P8.36). The angle between the two bonds is 106. If the bonds are 0.100 nm long, where is the center of mass of the molecule? Figure P8.36arrow_forward
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