(a) Show that the CM of a uniform thin rod oflength / and mass M is at its center. (b)Determine the CM of the rod assuming itslinear mass density A (its mass per unitlength) varies linearly from A = at the leftend to double that value, A = 2A0, at the rightyend.dm λdxX0хdx

(a)Consider lambda be the uniform mass density of the rod.From the definition of center of mass.

Answered: (a) Show that the CM of a uniform thin…

Classical Dynamics of Particles and Systems

5th Edition

ISBN:9780534408961

Author:Stephen T. Thornton, Jerry B. Marion

Publisher:Stephen T. Thornton, Jerry B. Marion

Chapter9: Dynamics Of A System Of Particles

Section: Chapter Questions

Problem 9.47P

See similar textbooks

Similar questions

If 1 of the Earth’s mass were transferred to the Moon, how far would the center of mass of the Earth-Moon-population system move? The mass of the Earth is 5.971024kg and that of the Moon is 7.341022kg . The radius of the Moon’s orbit is about 3.84105m .
In an elastic collision of two particles with masses m1 and m2, the initial velocities are u1 and u2 = u1. If the initial kinetic energies of the two particles are equal, find the conditions on u1/u2 and m1/m2 such that m1 is at rest after the collision. Examine both cases for the sign of .
A 2-kg object moving to the right with a speed of 4 m/s makes a head-on, elastic collision with a 1-kg object that is initially at rest. The velocity of the 1-kg object after the collision is (a) greater than 4 m/s, (b) less than 4 m/s, (c) equal to 4 m/s, (d) zero, or (e) impossible to say based on the information provided.
A rod 2 meters long has a linear density of p(x) = 8 - 3x. How far, in meters, is the center of mass of the rod if measured from the left?
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.
A bullet, having a mass of 0.04 kg moving with a velocity of 450 m/s penetrates a distance of 0.08 m into a wooden block firmly attached to the earth. Assuming a constant accelerating force, compute the following: a) the acceleration of the bullet, b) the accelerating force, c) the time of acceleration, and d) the impulse of the collision.
Calculate the location of the center of mass of a thin uniform meter stick of mass 70.0 g, on which at attached two masses, 1.20 kg at 0.00 cm position, and 2.30 kg at the 100 cm position.
The centre of mass of a non-uniform rod of length 4 m whose mass per unit length is K = 3x kg/m, where xis in m. The distance of centre of mass from its one end which is at origin will be
Determine the center of mass of a uniform cone of height h and radius R, with its axis pointing along z. (Hints: What is the CM in x and y? Let λ by the mass density per unit volume, and find the mass of the thin disk shown in the drawing. How is r/z related to R/h?)
Three steel spheres of equal mass are suspended from the ceiling bystrings of the same length that are spaced at a distanceslightly larger than the diameter of the spheres. After pulling it andReleasing it, sphere A hits sphere B, which then hits sphere C.If the coefficient of restitution between the spheres is denoted by e and by v0 thevelocity of A just before it hits B, determine, (a) the velocitiesof A and B immediately after the first collision, b) the velocities ofB and C immediately after the second crash. c) If now it is assumedthat n spheres are suspended from the ceiling and that the first is pulled and released asdescribed above, determine the velocity of the last sphere aftertakes the first hit. d.Use the result of part c to find the velocity of the last sphere.when n = 6 and e = 0.95.
Two balls moving in opposite directions have velocities v1ix= 14ˍm/s and v2ix = -8.4ˍm/s . If their masses are m1 = 3.3ˍkg and m2 = 6.9ˍkg, respectively, and if their collision is perfectly elastic, then predict the velocity of each ball following the collision.
Mass A, traveling at 1.5 m/s, collides with mass B, which is at rest, as shown. After the collision, mass B moves in a direction of 30 degrees relative to horizontally, after the collision, mass A will travel at what speed? and move in the direction at what angle to the horizontal ?. Given that mass A is equal to mass B and the coefficient of elasticity is 0.60.

SEE MORE QUESTIONS

Recommended textbooks for you

Classical Dynamics of Particles and Systems

Physics

ISBN:

9780534408961

Author:

Stephen T. Thornton, Jerry B. Marion

Publisher:

Cengage Learning

University Physics Volume 1

Physics

ISBN:

9781938168277

Author:

William Moebs, Samuel J. Ling, Jeff Sanny

Publisher:

OpenStax - Rice University

Principles of Physics: A Calculus-Based Text

Physics

ISBN:

9781133104261

Author:

Raymond A. Serway, John W. Jewett

Publisher:

Cengage Learning

Classical Dynamics of Particles and Systems

Physics

ISBN:

9780534408961

Author:

Stephen T. Thornton, Jerry B. Marion

Publisher:

Cengage Learning

University Physics Volume 1

Physics

ISBN:

9781938168277

Author:

William Moebs, Samuel J. Ling, Jeff Sanny

Publisher:

OpenStax - Rice University

Principles of Physics: A Calculus-Based Text

Physics

ISBN:

9781133104261

Author:

Raymond A. Serway, John W. Jewett

Publisher:

Cengage Learning

SEE MORE TEXTBOOKS

(a) Show that the CM of a uniform thin rod of length / and mass M is at its center. (b) Determine the CM of the rod assuming its linear mass density A (its mass per unit length) varies linearly from A = at the left end to double that value, A = 2A0, at the right y end. dm λdx X 0 х dx