Pluto's diameter is approximately 2370 km, and the diameter of its largest satellite Charon is 1250 km. Although the distance varies, they are often about 19700 km apart, center to center. Assuming that both Pluto and Charon have the same composition and hence the same average density, find the location of the center of mass of this system relative to the center of Pluto.
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- kg, 4. (a) The masses of the Earth and the Moon are 5.98 × 1024 kg and 7.35 x 1022 respectively, and their centers are separated by 3.84 × 108 m. Where is the center of mass of this system located? (b) Consider two objects with masses mA = 35 kg and mp = 25 kg. They have velocities (in m/s) đA = 12î – 16j and õB of the center of mass of the system. -20î + 14j. Determine the velocityProblem 3: A particle with mass ma = 3.00 kg is located at ra = (2.50 i + 3.50 j) m, and a second particle of mass m2B = 5.00 kg is located at rB = (1.50 i - 3.00 j) m. Find the location of the center of mass of the system relative to the point (1,1).Find the center of mass of a 120-cm long rod, made of 60 cm of iron (density 8.5 g/cm3) and 60 cm of aluminum (density 2.9 g/cm3). Express the location of the center of mass as measured from the left of the rod, assuming that the iron part of the rod is on the left and the aluminum part is on the right.
- Find the mass and center of mass of the lamina that occupies the region D and has the given density function p: D is the triangular region with vertices (0,0), (2, 1), (0,3); p(x, y) = x +yPluto and its satellite Charon have masses which are more similar to each other than any other knonw pair of orbiting bodies in the Solar system. How far from the center of pluto is the barycenter or center of mass of the Pluto-Charon system? Take the mass of Pluto to be 1.31 × 10^22 kg, and 1.59 × 10^21 kg for Charon (about one eighth that of Pluto). Assume Pluto and its moon Charon are separated by 19,640 km while the radius of Pluto and Charon are 1190 km and that of Charon are 606 km respectively. Treating Pluto and Charon as spherically symmetric objects, how far from Pluto is the barycenter of the Pluto - Charon pair, and is this point inside are outside of Pluto? Hint: Place Pluto at the origin and Charon on the x axis. A. 289 km; inside B. 781 km; inside C. 2130 km; outside D. 5910 km; outsideDuring the filming of a certain movie scene, the director wants a small car (whose mass is m1) traveling due east at speed v1 to collide with a small truck (whose mass is m2) traveling north. The director also wants the collision to be arranged so that just afterward, the interlocked vehicles travel straight toward the camera. If the line between the camera and collision makes an angle of theta with respect to north, at what speed v2 should the trucker drive?
- A system of four particles moves along one dimension. The center of mass of the system is at rest, and the particles do not interact with any objects outside of the system. Find the velocity v4 of particle 4 at t1 = 2.75 s given the details for the motion of particles 1, 2, and 3. particle 1: mj = 1.33 kg, vi (t) = (7.41 m/s) + (0.277 m/s²) × t particle 2: m2 = 3.05 kg, v2 (t) = (8.05 m/s) + (0.567 m/s²) × t particle 3: m3 = 4.25 kg, v3 (t) = (6.33 m/s) + (0.195 m/s²) × t particle 4: m4 = 5.27 kgTwo manned satellites approaching one another at a relative speed of 0.300 m/s intend to dock. The first has a mass of 5.50 ✕ 103 kg, and the second a mass of 7.50 ✕ 103 kg. If the two satellites collide elastically rather than dock, what is their final relative velocity? Adopt the reference frame in which the second satellite is initially at rest and assume that the positive direction is directed from the second satellite towards the first satellite.Problem 14: Suppose a space probe of mass m1 4200 kg expels m, = 3300 kg of its mass at a constant rate with an exhaust speed of Vex = 2.15 x 10° m/s. art (a) What is the increase in speed, of the space probe, in terms of the variables given in the introduction? You may assume the g is negligible at the probe's location. Gra Dec Pote m1 m1 - m2 Av = Vex In Av = ver In + vo Av = ver In + vo mị – m2 m1 m2 Sub Atte (20 mi m2 m2 m1 deta Δυ Av = Ver In Av = Vex Vez In Au = Ver In mi m1 m1 - m2 Submit Hint Feedback I give up! Part (b) Calculate the increase in speed, in meters per second, of the space probe.