A rod of length 30.0 cm has linear density (mass per length) given by                                        λ = 50.0 + 20.0xwhere x is the distance from one end, measured in meters, and λ is in grams/meter. (a) What is the mass of the rod? (b) How far from the x = 0 end is its center of mass?

Explorers in the jungle find an ancient monument in the shape of a large isosceles triangle as shown. The monument is made from tens of thou- sands of small stone blocks of density = 800 kg/m3 . The monument is 15.7 m high and 64.8 m wide at its base and is everywhere 3.60 m thick from front to back. Before the monument was built many years ago, all the stone blocks lay on the ground. (a) Choosing a coordinate system with x = 0 at the center of the pyramid, y = 0 at the base of the pyramid, and z = 0 at the face of the pyramid shown in the diagram, determine the coordinates of the center of mass of the pyramid in the x, y, and z directions. (b) How much work did laborers do on the blocks to put them in position while building the entire monument? Note: The gravitational potential energy of an object–Earth system is given by Ug = MgyCM, where M is the total mass of the object and yCM is the elevation of its center of mass above the chosen reference level.

A 4,600 kg open train car is rolling on frictionless rails at 21.1 m/s when it starts pouring rain. A while later the car's speed is 19.5 m/s. What mass of water has collected in the car? Provide your answer in appropriate units of meters (m), seconds (s), kilograms (kg), radians (rad) or combinations thereof, such as m/s or m/s^2. Use at least three significant figures in your answer, do not use scientific notation. Using more significant figures will not be considered incorrect; using fewer may lead to errors due to rounding.

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A water molecule consists of an oxygen atomwith two hydrogen atoms bound to it. Theangle between the two bonds is 106◦.  If each bond is 0.093 nm long, how far fromthe oxygen atom is the center of mass of themolecule? Take the mass of an oxygen atomto be 16 times the mass of a hydrogen atom.Answer in units of nm

To keep the calculations fairly simple, but still reasonable, we shall model a human leg that is 92.0 cm long (measured from the hip joint) by assuming that the upper leg and the lower leg (which includes the foot) have equal lengths and that each of them is uniform. For a 70.0 kg person, the mass of the upper leg is 8.60 kg, while that of the lower leg (including the foot) is 5.25 kg. Find the location of the center of mass of this leg, relative to the hip joint, if it is (a) fully extended, and (b) bent at the knee to form a right angle with the upper leg.

Pluto 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; outside

Saved Help Required information of 2 Particle A has a mass of 5.40 g and particle B has a mass of 1.80 g. Particle A is located at the origin and particle B is at the point (x, y) = (25.0 cm, 1.70 cm). What is the x-component of the CM? ook cm Hint rint rences 10 11 of 21 rch...pdf 2 Edje PreLab Arch..pdf

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The answer I have is 0 kg m/s, not 24 kg m/s. I was just not sure how to calculate to get 0 kh m/s. Can you recheck the problem to see if it was done correctly? Thanks.