A bar of length L= 2 m has linear density (mass per length) given by 1= 10+ 3x where x is thedistance from one end, measured in meters, and A is in grams/meter. You must carefully showyour work to get credit.(a) What is the mass of the bar?(b) How far from the x =0 end is its center of mass?

Answered: A bar of length L= 2 m has linear…

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 9.26P

See similar textbooks

Similar questions

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?
Under what conditions, is linear momentum conserved? Check all that apply. There are no frictional forces The work done is positive The net torque is minimal The action of the force is instaneous The net force vanishes
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?
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
A nucleus that captures a stray neutron must bring the neutronto a stop within the diameter of the nucleus by means of thestrong force. That force, which “glues” the nucleus together, is approximatelyzero outside the nucleus. Suppose that a stray neutronwith an initial speed of 1.4 * 107 m/s is just barely captured by anucleus with diameter d = 1.0 * 10-14 m. Assuming the strongforce on the neutron is constant, find the magnitude of that force.The neutron’s mass is 1.67 * 10-27 kg.
One astronaut is 75kg, and another who is 3.4 m away in the x-direction is 85kg. How far from the first astronaut is their mutual center of mass? Do not actually solve the problem numerically or algebraically, just pick the one equation and define the relevant knowns and single unknown.
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 59-kg woman and a 71-kg man sit on a seesaw, 3.5 m long. Where is their center of mass?
A gymnast jumps straight up, with her center of mass moving at 3.99 m/s as she leaves the ground. How high above this point is her center of mass at the following times? (Ignore the effects of air resistance, and assume the initial height of her center of mass is at y = 0.) t (s) y (m) 0.100 0.200 0.300 0.500
A cardboard sheet is cut in the shape of a triangle, with vertices at (0,0), (20,0), and (3,4) units. The thickness of the sheet is uniform. What is the x-coordinate of its center of mass?
A uniform density sheet of metal is cut into the shape of an isosceles triangle, which is oriented with the base at the bottom and a corner at the top. It has a base B = 13 cm, height H = 19 cm, and area mass density σ. e) Set up an integral to calculate the vertical center of mass of the triangle, assuming it will have the form C ∫ f(y) where C has all the constants in it and f(y) is a function of y. What is f(y)? f)Integrate to find an equation for the location of the center of mass in the vertical direction. Use the coordinate system specified in the previous parts, with the origin at the top and positive downward. g) Find the numeric value for the distance between the top of the triangle and the center of mass in cm.
The forearm of length Larm=35.4 cm shown in the figure is positioned at an angle θ with respect to the upper arm, and a 5.30-kg ball is held in the hand. The total mass ?totalmtotal of the forearm and hand is 3.00 kg, and their center of mass is located at LCM=14.6 cm from the elbow. The biceps muscle attaches to the forearm at a distanceLbiceps=3.5 cm from the elbow. What is the magnitude of the force Fbiceps that the biceps muscle exerts on the forearm for ?=49∘? What is the magnitude of the force Fjoint that the forearm exerts on the elbow joint for ?=49∘?

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

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

SEE MORE TEXTBOOKS

A bar of length L= 2 m has linear density (mass per length) given by 1= 10+ 3x where x is the distance from one end, measured in meters, and A is in grams/meter. You must carefully show your work to get credit. (a) What is the mass of the bar? (b) How far from the x = 0 end is its center of mass?