4.2 Three point masses lie at the corners of an equilateral triangle whose sides have length 1.00 m. A 5.00 kg mass is located at the origin of the coordinate system, a 10.0 kg mass lies on the positive x-axis, and a 15.0 kg mass is in the first quadrant of the xy-plane. (a) Calculate the coordinates of the center-of-mass (CM) of the system. (b) How far is the CM from the origin, and what angle does it make with respect to the x-axis?

4.2 Three point masses lie at the corners of an equilateral triangle whose sides have length 1.00 m. A 5.00 kg mass is located at the origin of the coordinate system, a 10.0 kg mass lies on the positive x-axis, and a 15.0 kg mass is in the first quadrant of the xy-plane. (a) Calculate the coordinates of the center-of-mass (CM) of the system. (b) How far is the CM from the origin, and what angle does it make with respect to the x-axis?

University Physics Volume 1

18th Edition

ISBN:9781938168277

Author:William Moebs, Samuel J. Ling, Jeff Sanny

Publisher:William Moebs, Samuel J. Ling, Jeff Sanny

Chapter9: Linear Momentum And Collisions

Section: Chapter Questions

Problem 73P: Find the center of mass of a cone of uniform density that has a radius R at the base, height h, and...

See similar textbooks

Similar questions

During 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?
One of the first ion engines on a commercial satellite used Xenon as a propellant and could eject the ionized gas at a rate of 2.98 ✕ 10−6 kg/s with an exhaust speed of 3.04 ✕ 104 m/s. What instantaneous thrust (in N) could the engine provide? (Enter your answer to at least three significant figures. Enter the magnitude.)
The Merlin rocket engines developed by SpaceX can produce 7.12 ✕ 105 N of instantaneous thrust with an exhaust speed of 3.05 ✕ 103 m/s in vacuum. What mass of fuel does the engine burn each second to produce this thrust? (Enter your answer in kg/s.)
A 6 meter rod has a linear density of f(x) = ax + b, if one one end the linear density is 2kg/m and on the other end is 10kg/m, where is the center of mass?
Find the center of mass of a rod of length L whose mass density changes from one end to the other quadratically. That is, if the rod is laid out along the x-axis with one end at the origin and the other end at x = L , the density is given by ρ(x) = ρ0 + (ρ1 − ρ0) (x/L)2 , where ρ0 and ρ1 are constant values.
Find the center of mass of the regular ∟-shaped iron bar with sides 0.40 m and 0.70 m, respectively. (Assume the ∟ shape of the rod is thin.)
A lamina occupies the region inside the circle x^2+y^2=16 but outside the circle x^2+y^2=64 The density at each point is inversely proportional to its distance from the orgin. Where is the center of mass?
Give the location of the centre of mass of a (i) sphere, (ii) cylinder, (iii) ring, and (iv) cube, each of uniform mass density. Does the centre of mass of a body necessarily lie inside the body ?
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.
A barefoot field-goal kicker imparts a speedof 27 m/s to a football initially at rest.If the football has a mass of 0.59 kg and thetime of contact with the ball is 0.034 s, whatis the magnitude of the force exerted by theball on the kicker’s foot?Answer in units of N.
The mass of a particular skateboard plus its rider is ms=78.6kg, and the skateboarder is holding a book with mass mb=3.07kg. Initially at rest, the skateboarder tosses the textbook with a velocity of vb=2.74m/s at an angle θ=24.3∘ above the horizontal, and the book is caught by a friend. Calculate the magnitude, in meters per second, of the velocity of the student. What is the magnitude, in newton seconds, of the momentum, pE, which was transferred to the the Earth during the time the book was being thrown?
A particle of mass 2.4 kg is subject to a force that is always pointed towards the North but whose magnitude changes quadratically with time. Let the y-axis point towards the North. The magnitude of the force is given as F = 6t2, and has units of newtons Determine the change in velocity Δv, in meters per second, of the particle between t=0 and t=1.3s. Determine the change in y coordinate, in meters, of the particle Δ y betweent=o and t=1.3 if the initial velocity= 15.9 m/s and directed North, in the same direction as the force.