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 = 3.55 m. The stick has a non-uniform mass density A(x) = ax + b, where a = -0.301 kg/m² and b= 0.782 kg/m. What is the x-coordinate of the center of mass of the stick? Xan m

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 = 3.55 m. The stick has a non-uniform mass density A(x) = ax + b, where a = -0.301 kg/m² and b= 0.782 kg/m. What is the x-coordinate of the center of mass of the stick? Xan m

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter10: Rotational Motion

Section: Chapter Questions

Problem 29P

See similar textbooks

Related questions

Q: In the figure, a 5.13 g bullet is fired into a 0.298 kg block attached to the end of a 0.985 m…

Q: A sodium atom (Z = 11) contains 11 protons in its nucleus. Strictly speaking, the Bohr model does…

A: Given Data: Ionization energy (E) = 5.1 eV. To Determine: (a). The value of Zeffective.(b). The…

Q: The landing gear on a commercial aircraft experiences an impulse load upon landing. Assuming six…

A: A) Calculate the time taken before the landing gear reaches the given load cycles. t=Load cycles…

Q: TEXT ANSWER Calculate the total resistance of the circuit shown below. Show your work. 42 Q2 55 Ω…

Q: Find the force constant of this tendon in N/m. Express your answer in newtons per meter.

Q: An object is 24 cm in front of a diverging lens that has a focal length of -14 cm. How far in front…

Q: Two pots are identical except that the flat bottom of one is aluminum, whereas that of the other is…

A: The boiling temperature of water in the pot is 100.0 °C. The aluminum botto is hitting at the…

Q: The moon's diameter is 3.48 x 106m, and its mean distance from the earth is 3.85 x 108 m. The moon…

A: Given DataMoon's diameter - 3.48 * 106 mDistance from earth = 3.85 * 108 mCalculation :

Q: Red light of wavelength 633 nm from a helium- neon laser passes through a slit 0.390 mm wide. The…

A: Solution: Given: λ = wavelength of light = 633 nm = 633 x 10-9 m D = distance between slit and…

Q: The body in the figure is pivoted at O. Three forces act on it in the directions shown: FA = 12.0 N…

Q: More than one analyzer can be used in a setup like that in the drawing, each analyzer following the…

A: Write the given values with the suitable variables. θ=24°I=I0100 Here, θ is the angle between the…

Q: A steel rod (p = 7860 kg/m3) has a length of 2.54 m. It is bolted at both ends between immobile…

A: When a steel rod looses energy as heat it means there is a thermal expansion taking place on the…

Q: Q11. Determine the reactions at supports A and B if the beam is of constant cross section and…

Q: Q/ answer by true or false: 1. The polarization in dielectric material can generate accumulation of…

A: THE ANSWER OF THE FIRST QUESTION IS YES Explanation Yes, the polarization of a dielectric material…

Q: While riding his bicycle, Jans does 7.5 E7 J of work and gives off 4.3 E7 J of heat. What is the…

A: Work done by Jan (W) = 7.5×107 J Heat released (Q)= 4.3×107 J We want to find change in internal…

Q: Suppose that a simple pendulum consists of a small 76 g bob at the end of a cord of negligible mass.…

A: Note - As per bartleby guidelines i can answer only one question, kindly post remaining part…

Q: 10. A toy gun fires a 9.41-g projectile disc by using a compressed spring (k = 1.72 x 10³ N/m) and a…

Q: Our refrigerated microcentrifuge has a rotor that has a 5.6 cm radius. If a protocol asks for a…

Q: - The equation = A sin(kx-ot + 2 is the same as

A: The expression A sin(kx-wt+pi/2) can be simplified using trigonometric identities. We know that…

Q: What is the electric field intensity in the region r greater than or equal to 2R?

A: The electric field intensity, E, and potential are related as E=-dVdr

Q: FIND THE RESULTANT VECTOR OF THE FOLLOWING VECTORS USING COMPLEX NUMBERS LOCATION 30° 3.m 5m 7m 50°…

Q: In the figure here, a solid brass ball of mass 0.252 g will roll smoothly along a loop-the-loop…

A: a) At the top of the loop, the centripetal force equals the weight of the ball. FC=Wmv2R=mgv2=Rg

Q: A steel bucket contains 4 liters of water at 12℃. An electric immersion heater rated at 1400 watts…

Q: Two waves are travelling through outer space. Wave 1 has a frequency of 300 MHz and wave 2 has a…

A: We have given, frequency of wave 1 f1 = 300 MHz = 300×106Hz…

Q: The minimum uncertainty Ay in the position y of a particle is equal to its de Broglie wavelength.…

A: The de Broglie wavelength of a particle with momentum p is given by: λ = h/p where h is the Planck's…

Q: The figure depicts a simplistic optical fiber: a plastic core (n₁ = 1.58) is surrounded by a plastic…

Q: Explain briefly the importance of wind energy for electricity generation in Ireland, highlighting…

A: Wind energy is one of the most important sources of electricity in Ireland, and its importance has…

Q: Consider the circuit of (Figure 1). For related problemsolving tips and strategies, you may want to…

Q: A spring-mass system has a natural period T= 0.29 s. What will be the new period of this system if…

A: Period (T) = 0.29 s Spring constant ' k ' is increased by 65℅ .

Q: FIND THE RESULTANT VECTOR OF THE FOLLOWING VECTORS USING COMPLEX NUMBERS 2 FORCES 8N K 30 JON L 30⁰…

Q: In the Bohr model of hydrogen, the electron moves in a circular orbit around the nucleus. Determine…

A: angular speed of electron in first and fourth orbit

Q: A DC chopper has a resistive load of R 10 2 and an input voltage of Vs = 220 V. When the chopper…

A: Resistive load = 10 ohminput voltaeg = 20 VVoltage drop = 2 VDuty cycle = 50 %

Q: Kause's law is derived from the differential formula 7-E = ? P. E.

Q: The batteries shown in the circuit in the figure have 10.0 V 30.0 Ω negligibly small internal…

Q: The bicycle and rider shown in (Figure 1) have a mass of 45 kg with center of mass located at G. The…

A: Combined mass of bicycle and rider: m = 45 kg Coefficient of kinetic friction at the rear tyre: μB…

Q: A very long line charge having a charge density A is surrounded by a conducting cylindrical shell…

Q: 1000 kg satellite orbits the earth with a speed of 9997 m/sm/s. What is the radius of the orbit?…

Q: 5. A finite line charge with length 0.02 m and uniform charge per unit length ₁ = 0.05 C/m is…

Q: An object with a mass 16.95 g is submerged in water, then its mass is 11 g. What is the volume and…

Q: A hollow ball (1 = 23 MR2) with a mass of 0.934 kg is released from rest and slides down a hillside…

A: Solution: Given: I = MI of hollow ball = (2/3) mr2 m = mass of hollow ball = 0.934 kg θ = angle of…

Q: Monochromatic light strikes a diffraction grating at normal incidence before illuminating screen…

Q: Light from a point source of 50 candlepower, which radiates uniformly in all directions, falls on a…

A: To calculate the fraction of the total flux from the source that is incident on the lens, we need to…

Q: Most galaxies, including our own Milky Way, have supermassive black holes at their centers.…

Q: 7.) An 87-g box is attached to a spring with a force constant of 82 N/m. The spring is compressed 11…

A: The mass of the box: m=87 g=0.087 kg The force constant of the spring: k=82 N/m The initial…

Q: Akyat Manaog. Ball A having a mass of 1.00 kg is released from rest on a frictionless inclined at a…

A: Mass of ball A, mA=1kg Height from whcih ball A was released, H=0.5m Mass of ball B, mB=3kg Speed of…

Q: Ball 1 (m = 65g) is rolling at 4.5 m/s [N35°W] on a frictionless surface when it collides with ball…

Q: A group of particles is traveling in a magnetic field of unknown magnitude and direction. You…

Q: A. Determine the extra distance traveled by the wave leaving the bottom of the lower slit as…

A: Path difference: ∆=dsinθ

Q: = Cylindrical shell of inner radius R ₁ 1.35R and outer radius R 2 = 3.69R is filled uniformly with…

A: R1= 1.35 R R2 = 3.69 R r = 7.2 R Q = 7.6 q

Q: A 65.0-kg file cabinet of is sliding down a rough ramp for a distance of 5.00 m as shown. The…

A: Mass of cabinet, m = 65 kg Friction force, f = 75 N Distance traveled, d = 5 m

Concept explainers

Center of Gravity of a system

The centre of gravity is a property that is based on the geometry of a rigid body or any particle. It is described as an equilibrium point or a hypothetical location where the total weight of the body is concentrated.

Question

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= 3.55 m. The stick has a
non-uniform mass density A(x) = ax + b, where a = -0.301 kg/m² and b= 0.782 kg/m. What is the x-coordinate of the center
of mass of the stick?
Xan
E

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1: Given data

VIEW

Step 2: Calculation

VIEW

Solution

VIEW

Step by step

Solved in 3 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.

Similar questions

A thin rod of length 2.65 m and mass 13.7 kg is rotated at anangular speed of 3.89 rad/s around an axis perpendicular to therod and through its center of mass. Find the magnitude of therods angular momentum.
Consider the disk in Problem 71. The disks outer rim hasradius R = 4.20 m, and F1 = 10.5 N. Find the magnitude ofeach torque exerted around the center of the disk. FIGURE P12.71 Problems 71-75
A crane of mass m1 = 3 000 kg supports a load of mass m2 = 10 000 kg as shown in Figure P10.36. The crane is pivoted with a frictionless pin at A and rests against a smooth support at B. Find the reaction forces at (a) point A and (b) point B. Figure P10.36
A 68 kg man is in the prone position while during pushups. His feet and hands are 95 cm and 42 cm away respectively from his center of mass. What is the normal force exerted by on each (a) hand and (b) foot?
Why is the following situation impossible? A uniform beam of mass mb = 3.00 kg and length ℓ = 1.00 m supports blocks with masses m1 = 5.00 kg and m2 = 15.0 kg at two positions as shown. The beam rests on two triangular blocks, with point P a distance d = 0.300 m to the right of the center of gravity of the beam. The position of the object of mass m2 is adjusted along the length of the beam until the normal force on the beam at O is zero.
A uniform solid cylindrical log begins rolling without slipping down a ramp that rises 28.0° abovethe horizontal. After it has rolled 4.20 m along the ramp, what is the magnitude of the linearacceleration of its center of mass?A) 4.60 m/s2 B) 3.07 m/s2 C) 9.80 m/s2 D) 3.29 m/s2 E) 2.30 m/s2
The wheels of a wagon can be approximated as the combination of a thin outer hoop of radius ?h=0.580 mrh=0.580 m and mass 4.32 kg,4.32 kg, and two thin crossed rods of mass 7.80 kg7.80 kg each. Imagine replacing the wagon wheels with uniform disks that are ?d=4.62 cmtd=4.62 cm thick, made out of a material with a density of 6910 kg/m3.6910 kg/m3. If the new wheel is to have the same moment of inertia about its center as the old wheel about its center, what should the radius of the disk be?
A 5.40 kg particle with velocity v→=(4.09m/s)î-(3.06m/s)ĵ is at x = 9.82 m, y = 9.03 m. It is pulled by a 2.10 N force in the negative x-direction. About the origin, what are (a) the particle's angular momentum, (b) the torque acting on the particle, and (c) the rate at which the angular momentum is changing?
A hollow spherical shell with mass 1.50 kg rolls without slipping down a slope that makes an angle of 37.0 degree with the horizontal. a) Find the magnitude of the acceleration of the center of mass of the spherical shell. Take the free-fall acceleration to be g = 9.80 m/s^2. b) Find the magnitude of the frictional force acting on the spherical shell. Take the free-fall acceleration to be g = 9.80 m/s^2.
A uniform cube with mass 0.700 kg and volume 0.0270 m^3 is sitting on the floor. A uniform sphere with radius 0.300 m and mass 0.900 kg sits on top of the cube. How far is the center of mass of the two-object system above the floor? Express your answer with the appropriate units.
A uniform solid sphere of mass 6.0 kg and radius 10 cm is rolling without slipping along a horizontal surface with a speed of4.9m/s (this is the speed of the center of mass) when it starts up a ramp that makes an angle of 30° with the horizontal. a)What is the maximum distance it can go up the ramp, measured along the surface of the ramp? b)While the ball is moving up the ramp, find i)the acceleration (magnitude and direction) of its center of mass and ii)the friction force (magnitude and direction) acting on it due to the surface of the ramp. Moment of inertia of a solid sphere is ???=?????. Directions must be given as either up the ramp or down the ramp.
A person carries a plank of wood 1.9 m long with one hand pushing down on it at one end with a force F1 and the other hand holding it up at 49 cm from the end of the plank with force F2. If the plank has a mass of 18 kg and its center of gravity is at the middle of the plank, what are the magnitudes of the forces F1 and F2? (The distance of 49 cm is measured from the location of F1.)