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The total linear momentum of a system can be zero, even if all the objects in the system are moving. True or false?
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- 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?Two 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.A hockey puck of mass 150 g is sliding due east on a frictionless table with a speed of 10 m/s. Suddenly, a constant force of magnitude 5 N and direction due north is applied to the puck for 1.5 s. Find the north and east components of the momentum at the end of the 1.3-s interval.
- 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.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?From what might be a possible scene in the comic book The X-Men, the Juggernaut (mJ) is charging into Colossus (mC) and the two collide. The initial speed of the Juggernaut is vJi and the initial speed of Colossus is vCi. After the collision, the final speed of the Juggernaut is vJf and the final speed of Colossus is vCf as they each bounce off of the other, heading in opposite directions. a. What is the impulse experienced by the Juggernaut? b. What is the impulse experienced by Colossus? c. In your own words, explain how these impulses must compare with each other and how they are related to the average force each superhero experiences during the collision.
- This is a symbolic version of Problem 23. 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?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 projectile of mass 2.0 kg is fired in the air at an angle of 40.0 to the horizon at a speed of 50.0 m/s. At the highest point in its flight, the projectile breaks into three parts of mass 1.0 kg, 0.7 kg, and 0.3 kg. The 1.0-kg part falls straight down after breakup with an initial speed of 10.0 m/s, the 0.7-kg part moves in the original forward direction, and the 0.3-kg part goes straight up. Launch a. Find the speeds of the 0.3-kg and 0.7-kg pieces immediately after the break-up. b. How high from the break-up point does the 0.3-kg piece go before coming to rest? c. Where does the 0.7-kg piece land relative to where it was fired from?
- A massive asteroid collides with a spacecraft in circular orbit around the Earth, landing in the vehicle's storage tank. This collision is the product of (a) The only thing that is conserved is momentum. (b) Only the kinetic energy of the system is conserved. (c) kinetic and momentum energy are also conserved. (d) There is no conservation of momentum or kinetic energy.A rocket has an initial mass m, = 2.8X10°kg of which 2.1X10°kg was fuel. The fuel was burned with a constant rate and the exhaust speed u is 2400 m/s. The rocket starts from rest and moves vertically under uniform gravity g = 9.8 m/s2. The speed of the rocket at burnout is 1955 m/s. Assume that the thrust is such that the rocket takes off immediately. a) Calculate the burnout time to of the rocket.If the resultant of all the external forces acting on a system of particles is zero, then from an inertial frame,one can surely say that : A linear momentum of the system does not change in time kinetic energy of the system does not change in time C angular momentum of the system does not change in time potential energy of the system does not change in time