In the instant of the figure, two particles move in an xy plane. Particle P₁ has mass 7.40 kg and speed v₁ = 1.91 m/s, and it is at distance d₁ = 9.52 m from point O (the figure is not drawn to scale). Particle P₂ has mass 2.73 kg and speed v2 = 2.37 m/s, and it is at distance d₂ = 8.89 m from point O. What is the magnitude of the net angular momentum of the two particles about O? P₁O Number i Units ས། ྋ P2
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- As shown in Figure P8.20, a bullet of mass m and speed v passes completely through a pendulum bob of mass M. The bullet emerges with a speed of v/2. The pendulum bob is suspended by a stiff rod (not a string) of length , and negligible mass. What is the minimum value of v such that the pendulum bob will barely swing through a complete vertical circle? Figure P8.20Three 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 P11.73From 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.
- The coefficient of friction between the block of mass m1 = 3.00 kg and ilie surface in Figure P8.22 is k = 0.400. The system starts from rest. What is the speed of the ball of mass m2 = 5.00 kg when it has fallen a distance h = 1.50 m?The drawing shows a top view of a frictionless horizontal surface, where there are two springs with particles of mass m1 and m2 attached to them. Each spring has a spring constant of 250 N/m. The particles are pulled to the right and then released from the positions shown in the drawing. How much time passes before the particles are side by side for the first time at x = 0 m if (a) m1 = m2 = 6.0 kg and (b) m1 = 6.0 kg and m2 = 54 kg?The figure shows a two-ended “rocket” that is initially stationary on a frictionless floor, with its center at the origin of an x axis. The rocket consists of a central block C (of mass M = 5.70 kg) and blocks L and R (each of mass m = 1.30 kg) on the left and right sides. Small explosions can shoot either of the side blocks away from block C and along the x axis. Here is the sequence: (1) At time t = 0, block L is shot to the left with a speed of 3.00 m/s relative to the velocity that the explosion gives the rest of the rocket. (2) Next, at time t = 0.80 s, block R is shot to the right with a speed of 3.00 m/s relative to the velocity that block C then has (after the second explosion). At t = 2.70 s, what are (a) the velocity of block C (including sign) and (b) the position of its center?
- The figure below shows four objects at the corners of a rectangle, connected by rods of negligible mass. The center of the rectangle lies at the origin of an xy-coordinate system. The width of the rectangle (along the x-axis) is 4.00 m, and the height (along the y-axis) is 6.00 m. Starting at the top left and going clockwise, the masses of the objects are: m1 = 2.90 kg, m2 = 1.90 kg, m3 = 4.10 kg, m4 = 2.50 kg. a) What is the moment of inertia (in kg · m2) of the system about the x-axis? ____ kg · m2 (b) What is the moment of inertia (in kg · m2) of the system about the y-axis? _____kg · m2 (c) What is the moment of inertia (in kg · m2) of the system about an axis through O and perpendicular to the page (that is, the z-axis)? _____kg · m2Three asteroids coated with cosmic slime are moving in the same plane when they collide and stick together. Initially, asteroid A has a mass of 2*107 kg and is moving to the right at a speed of 150 m/s, asteroid B has a mass of 3*107 kg and is moving at 50 m/s towards the lower left at an angle of 60 degrees with respect to asteroid A, while asteroid C has a mass of 5*107 kg and is moving with an unknown speed and angle. After the collision, the resulting single asteroid is moving toward the right at a speed of 50 m/s. Determine the speed and angle of asteroid C prior to the collision.In the figure, a 20 kg bullet with velocity v passes through a 0.5 kg pendulum and exits with velocity v / 2. The pendulum is 2.5 m long and is suspended from a rope of negligible mass. What is the minimum velocity of the projectile for the pendulum to move in a complete vertical circle? (g = 10 m / s ^ 2)
- As the drawing illustrates, two disks with masses m1 and m2 are moving horizontally to the right at a speed of v0. They are on an airhockey table, which supports them with an essentially frictionless cushion of air. They move as a unit, with a compressed spring between them, which has a negligible mass. Then the spring is released and allowed to push the disks outward. Consider the situation where disk 1 comes to a momentary halt shortly after the spring is released. Assuming that m1 = 1.2 kg, m2 = 2.3 kg, and v0 = +4.1 m/s, find the velocity of disk 2 at that moment.Three masses are positioned along the x-axis. Their masses and positions are m 1 = m with x 1 = 1.0 m, m 2 = 2 m with x 2 = 2.0 m, and m 3 = 8.0 m with x 3 = 3.0 m. What is the x-coordinate of the center of mass of this system, to the nearest tenth? a. 4.7 m b. Not enough information c. 0.7 m d. 2.6 m e. 2.0 mA 10 kg projectile was launched at the horizontal ground at a velocity of 20 m/s, 10 degrees with respect to the horizontal. The projectile hit a 30 kg box on top of a table at 0.177 seconds. If the box developed a speed of 5.140 m/s after impact, what is the speed of the projectile after the collision? Please include FBD.