Now let's apply the center-of-mass equations to a simple one-dimensional system. Suppose a 2.0 kg cat and a 3.0 kg dog are moving toward each other along the x axis, heading for a fight. At a particular instant, the cat is 1.0 m to the right of the origin and is moving in the + direction with speed 3.0 m/s, and the dog is 2.0 m to the right of the origin, moving in the - direction with speed 1.0 m/s. Find the position and velocity of the center of mass of the two-pet system, and also find the total momentum of the system. Find the velocity of the center of mass at the instant described in Part A. Express your answer in meters per second. ΜΕ ΑΣΦ Vcm,z=1 ? m/s Figure Veat.x Vdogx Xcat-1.0m xdog-2.0 m 1 of 1 Submit Previous Answers Request Answer × Incorrect; Try Again; 2 attempts remaining ▼Part C - Practice Problem: Find the total momentum of the system at the instant described in Part A. Express your answer in kilogram-meters per second. Η ΜΕ ΑΣΦ ?

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?

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 Small pickup truck that has a caliper shell slowly coasts toward a red light with negligible friction. Two dogs in the back of the truck are moving and making various inelastic collisions with each other and the walls. What is the effect of the dogs on the motion of the center of mass of the system (truck plus entire load)? What is their effect on the motion of the truck?

(a) Does the center of mass of a rocket in free space accelerate? Explain. (b) Can the speed of a rocket exceed the exhaust speed of the fuel? Explain.

If a rainstorm drops 1 cm of rain over an area of 10km2 in the period of 1 hour, what is the momentum of the rain that falls in one second? Assume the terminal velocity of a raindrop is 10 m/s.

You hold a slingshot at arms length, pull the light elastic band back to your chin, and release it to launch a pebble horizontally with speed 200 cm/s. With the same procedure, you fire a bean with speed 600 cm/s. What is the ratio of the mass of the bean to the mass of the pebble? (a) 19 (b) 13 (c) 1 (d) 3(e) 9

Check Your Understanding Suppose we included the sun in the system. Approximately where would the center of mass of the Earth-moon-sun system be located? (Feel free to actually calculate it.)

Check Your Understanding The changes of momentum for Philae and for Comet 67/P were equal (in magnitude). Were the impulses experienced by Philae and the comet equal? How about the forces? How about the changes of kinetic energies?

Find the center of mass of a rectangular material of length a and width b made up of a material of nonuniform density. The density is such that when the rectangle is placed in the xy-plane, the density is given by (x,y)=0xy .