Problem 4. A 1.2-kg spring-activated toy bomb slides on a smooth surface along the x-axis with a speed of 0.50 m/s. At the origin 0, the bomb explodes into two fragments. Fragment 1 has a mass of 0.40 kg and a speed of 0.90 m/s along the negative y-axis. (a) Find the x-component of the velocity of fragment 2. (b) Find the y-component of the velocity of fragment 2. (c) Find the velocity of the center of mass of the system after the explosion. 0.50 m/s 1.2 kg 0 Before After 0.80 kg 0.40 kg 0.90 m/s X

Problem 4. A 1.2-kg spring-activated toy bomb slides on a smooth surface along the x-axis with a speed of 0.50 m/s. At the origin 0, the bomb explodes into two fragments. Fragment 1 has a mass of 0.40 kg and a speed of 0.90 m/s along the negative y-axis. (a) Find the x-component of the velocity of fragment 2. (b) Find the y-component of the velocity of fragment 2. (c) Find the velocity of the center of mass of the system after the explosion. 0.50 m/s 1.2 kg 0 Before After 0.80 kg 0.40 kg 0.90 m/s X

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter11: Collisions

Section: Chapter Questions

Problem 73PQ: Three runaway train cars are moving on a frictionless, horizontal track in a railroad yard as shown...

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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 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.
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.
An bullet of mass m = 8.00 g is fired into a block of mass M = 250 g that is initially at rest at the edge of a table of height h = 1.00 m (Fig. P6.42). The bullet remains in the block, and after the impact the block lands d = 2.00 m from the bottom of the table. Determine the initial speed of the bullet. Figure P6.42
There is a compressed spring between two laboratory carts of masses m1 = 105 g and m2 = 212 g. Initially, the carts are held at rest on a horizontal track (Fig. P10.40A). The carts are released, and the cart of mass m1 has velocity vi=2.035i m/s in the positive x direction (Fig. 10.40B). Assume rolling friction is negligible. a. What is the net external force on the two-cart system? b. Find the velocity of cart 2. FIGURE P10.40 Problems 40 and 41.
Assume the pucks in Figure P11.66 stick together after theircollision at the origin. Puck 2 has four times the mass of puck 1 (m2 = 4m1). Initially, puck 1s speed is three times puck 2s speed (v1i = 3v2i), puck 1s position is r1i=x1ii, and puck 2s position is r2i=y2ij. a. Find an expression for their velocity after the collision in terms of puck 1s initial velocity. b. What is the fraction Kf/Ki that remains in the system?
Sand 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 P8.64
A space probe, initially at rest, undergoes an internal mechanical malfunction and breaks into three pieces. One piece of mass ml = 48.0 kg travels in the positive x-direction at 12.0 m/s, and a second piece of mass m2 = 62.0 kg travels in the xy-plane at an angle of 105 at 15.0 m/s. The third piece has mass m3 = 112 kg. (a) Sketch a diagram of the situation, labeling the different masses and their velocities, (b) Write the general expression for conservation of momentum in the x- and y-directions in terms of m1, m2, m3, v1, v2 and v3 and the sines and cosines of the angles, taking to be the unknown angle, (c) Calculate the final x-components of the momenta of m1 and m2. (d) Calculate the final y-components of the momenta of m1 and m2. (e) Substitute the known momentum components into the general equations of momentum for the x- and y-directions, along with the known mass m3. (f) Solve the two momentum equations for v3 cos and v3 sin , respectively, and use the identity cos2 + sin2 = 1 to obtain v3. (g) Divide the equation for v3 sin by that for v3 cos to obtain tan , then obtain the angle by taking the inverse tangent of both sides, (h) In general, would three such pieces necessarily have to move in the same plane? Why?
(a) Figure P9.36 shows three points in the operation of the ballistic pendulum discussed in Example 9.6 (and shown in Fig. 9.10b). The projectile approaches the pendulum in Figure P9.36a. Figure P9.36b shows the situation just after the projectile is captured in the pendulum. In Figure P9.36c, the pendulum arm has swung upward and come to rest momentarily at a height A above its initial position. Prove that the ratio of the kinetic energy of the projectilependulum system immediately after the collision to the kinetic energy immediately before is m1|/(m1 + m2). (b) What is the ratio of the momentum of the system immediately after the collision to the momentum immediately before? (c) A student believes that such a large decrease in mechanical energy must be accompanied by at least a small decrease in momentum. How would you convince this student of the truth? Figure P9.36 Problem. 36 and 43. (a) A metal ball moves toward the pendulum. (b) The ball is captured by the pendulum. (c) The ballpendulum combination swings up through a height h before coming to rest.
A 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?
A 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?
What exhaust speed is required to accelerate a rocket in deep space from 800 m/s to 1000 m/s in 5.0 s if the total rocket mass is 1200 kg and the rocket only has 50 kg of fuel left?
Three runaway train cars are moving on a frictionless, horizontal track in a railroad yard as shown in Figure P11.73. The first car, with mass m1 = 1.50 103 kg, is moving to the right with speed v1 = 10.0 m /s; the second car, with mass m2 = 2.50 103 kg, is moving to the left with speed v2 = 5.00 m/s, and the third car, with mass m3 = 1.20 103 kg, is moving to the left with speed v3 = 8.00 m /s. The three railroad cars collide at the same instant and couple, forming a train of three cars. a. What is the final velocity of the train cars immediately after the collision? b. Would the answer to part (a) change if the three cars did not collide at the same instant? Explain. FIGURE P11.73