A thin stick is placed along the x-axis so that one of its ends is at x = 0.00 m and the other one at x2 = 1.55 m. The stick has a non-uniform mass density A(x) = ax + b, where a = 0.609 kg/m² and b = 0.342 kg/m. What is the x-coordinate of the center of mass of the stick? Xcm =

A thin stick is placed along the x-axis so that one of its ends is at x = 0.00 m and the other one at x2 = 1.55 m. The stick has a non-uniform mass density A(x) = ax + b, where a = 0.609 kg/m² and b = 0.342 kg/m. What is the x-coordinate of the center of mass of the stick? Xcm =

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Description: How do I find this question correctly with steps? A thin stick is placed along the x-axis so that one of its ends is at x1 = 0.00 m and the other one at x2 = 1.55 m. The stickhas a non-uniform mass density À(x) = ax + b, where a = 0.609 kg/m² and b =

University Physics Volume 1

18th Edition

ISBN:9781938168277

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

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

Chapter12: Static Equilibrium And Elasticity

Section: Chapter Questions

Problem 37P: To get up on the roof, a person (mass 70.0 kg) places 6.00-m aluminum ladder (mass 10.0 kg) against...

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To get up on the roof, a person (mass 70.0 kg) places 6.00-m aluminum ladder (mass 10.0 kg) against the house on a concrete pad with the base of ladder 2.00 m from the house. The ladder rests against a plastic rain gutter, which we can assume to frictionless. The center of ladder is 2.00 m from the bottom. The person is standing 3.00 m from the bottom. Find the normal reaction and friction forces on the ladder at its base.
Two metersticks are connected at their ends as shown in Figure P10.18. The center of mass of each individual meterstick is at its midpoint, and the mass of each meterstick is m. a. Where is the center of mass of the two-stick system as depicted in the figure, with the origin located at the intersection of the sticks? b. Can the two-stick system be balanced on the end of your finger so that it remains lying flat in front of you in the orientation shown? Why or why not? FIGURE P10.18 (a) The center of mass of the stick on the x axis would be at (0.5 m, 0), and the center of mass of the stick on the stick on the y axis be at (0, 0.5 m), assuming the sticks are uniform. We can then use Equation 10.3 to find the x and y coordinates of the center of mass. xCM=1Mj=1nmjxj=12m[m(0.50m)]=0.25myCM=1Mj=1nmjyj=12m[m(0.50m)]=0.25m The location of the center of mass is (0.25m,0.25m) (b) No. The location of the center of mass is not located on the object, so your finger would not be in contact with the object. In a different orientation, balancing by applying a force at the center of mass might be possible, but not in the orientation shown.
Two small-sized objects are placed on a uniform9.00/rmkg plastic beam 3.00 long,rmm . Assume that m1= 8.20kg and kg =7.45kg Find the location of the center of mass of this system by setting x = 0 at the right end of the beam.
PART 1: A 5.00 kg particle has the xy coordinates (1.20 m, 2.00 m), and a 6.00 kg particle has the xy coordi-nates (0.300 m, 0.750 m). Both lie on a horizontal plane. At what (a) x and (b) y coordinates must you placea 4.00 kg particle such that the center of mass of the three-particle system has the coordinates (0.500 m, 0.900 m)? PART 2: A rope is used to pull a 3.5 kg block at constant speed 6 m along a horizontal oor. The force onthe block from the rope is 7 N and directed = 20 above the horizontal. What are (a) the work done by therope's force, (b) the increase in thermal energy of the block- oor system. PART 3: Draw a labelled gure to explain the idea of turning point in terms of energy.
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Three masses at m1 = 1 kg, r1 = 1i + 2j m2 = 2 kg, r2 = -2i +3j m3 = 3 kg, r3 = 0i + 3j. The system's center of mass is at rcm = xi + yj. Find both x and y.
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Which one of the following is the y-coordinate of the centre of mass from three homogeneous solid spheres of masses 1 kg, 2 kg and 4 kg that are arranged with their centres at (2i + j + k) meters, (3i – 2 j + 2k) meters and (4i – j – 2k) meters respectively where i, j, and k are unit vectors in the x, y and z directions
"A three particle system with with masses: m1 = 2.0 Kg, m2 = 4.0 Kg and m3 = 8.0 Kg. The position co-ordinates for particle 1 are (3,3), for particle 2 are (2,1) and for particle 3 are (1,2). What will be the x coordinate of the system s center of mass?" a 1.57 b 1.28 c 2.22 d The data is not enough to calculate the center of mass
John’s mass is 87.7 kg, and Barbara’s is 59.9 kg. He is standing on the x axis at xJ = +10.3 m, while she is standing on the x axis at xB = +2.10 m. They switch positions. How far and in which direction does their center of mass move as a result of the switch?
A 1.29 kg particle has the xy coordinates (-1.25 m, 0.116 m), and a 5.32 kg particle has the xy coordinates (0.300 m, -0.345 m). Both lie on a horizontal plane. At what (a) x and (b) y coordinates must you place a 2.97 kg particle such that the center of mass of the three-particle system has the coordinates (-0.308 m, -0.473 m)?
In the figure, three uniform thin rods, each of length L = 25.0 cm, form an inverted U. The vertical rods each have a mass of 19.0 g; the horizontal rod has a mass of 57.0 g. What are (a) the x coordinate and (b) the y coordinate of the system's center of mass?