Essential University Physics (3rd Edition)
3rd Edition
ISBN: 9780134202709
Author: Richard Wolfson
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Textbook Question
Chapter 9, Problem 91P
A thin rod extends from x = 0 to x = L. It carries a nonuniform mass per unit length μ = Mxa/L1+a, where M is a constant with units of mass, and a is a non-negative dimensionless constant. Find expressions for (a) the rod’s mass and (b) the location of its center of mass. (c) Are your results what you expect when a = 0?
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
The height varies from h to zero according to this function: y(x) = h ( – 1)´ . The constants h
and e replace 1.00 m and 3.00 m. There is also a thickness t and a density p. You need two
integrals, the total mass and the center of mass. Possibly surprisingly, you don't actually need the
numbers t, h, and p.
Ax
y(x)
X
The column at x has a mass Am = (density * volume) = y(x) p t Ax. You add all the Am values to get
%3D
the total mass M. The sum becomes an integral:
М — pt
y(x) dx
For the center of mass, you add each column's x Am, and divide by M:
pt
Xc
х у(x) dx
Calculate xc. The only quantity you'll need is e = 5 m.
A rod of length 24.00 cm has linear density (mass per length) given by 50.0 + 19.0x where x is the distance from one end, and Ï is measured in grams/meter. What is its mass? How far from the x end is its center of mass? Need Help? Read
Needs Complete typed solution with 100 % accuracy.
A rod of length 3 meters with density 8(x) = 1.1 + 1.1x4grams/meter is positioned along the positive x-axis, with its left end at the
origin. Find the total mass and the center of mass of the rod.
Round your answers to four decimal places.
The total mass of the rod is i
The center of mass of the rod is i
grams.
meters.
Chapter 9 Solutions
Essential University Physics (3rd Edition)
Ch. 9.1 - Prob. 9.1GICh. 9.2 - A 500-g fireworks rocket is moving with velocity...Ch. 9.2 - Two skaters toss a basketball back and forth on...Ch. 9.3 - Which of the following systems has (1) zero...Ch. 9.4 - Which of the following qualifies as a collision?...Ch. 9.5 - Which of the following collisions qualify as...Ch. 9.6 - One ball is at rest on a level floor. A second...Ch. 9 - Roughly where is your center of mass when youre...Ch. 9 - Prob. 2FTDCh. 9 - Prob. 3FTD
Ch. 9 - The momentum of a system of pool balls is the same...Ch. 9 - An hourglass is inverted and placed on a scale....Ch. 9 - Why are cars designed so that their front ends...Ch. 9 - Give three everyday examples of inelastic...Ch. 9 - Is it possible to have an inelastic collision in...Ch. 9 - Prob. 9FTDCh. 9 - Why dont we need to consider external forces...Ch. 9 - How is it possible to have a collision between...Ch. 9 - A pitched baseball moves no faster than the...Ch. 9 - Two identical satellites are going in opposite...Ch. 9 - Prob. 14ECh. 9 - Two particles of equal mass m are at the vertices...Ch. 9 - Rework Example 9.1 with the origin at the center...Ch. 9 - Prob. 17ECh. 9 - Prob. 18ECh. 9 - A popcorn kernel at rest in a hot pan bursts into...Ch. 9 - A 60-kg skater, at rest on frictionless ice,...Ch. 9 - A plutonium-239 nucleus at rest decays into a...Ch. 9 - A toboggan of mass 8.6 kg is moving horizontally...Ch. 9 - A 150-g trick baseball is thrown at 60 km/h. It...Ch. 9 - An object with kinetic energy K explodes into two...Ch. 9 - Two 140-kg satellites collide at an altitude where...Ch. 9 - High-speed photos of a 220-g flea jumping...Ch. 9 - Youre working in mission control for an...Ch. 9 - In a railroad switchyard, a 56-ton freight car is...Ch. 9 - In a totally inelastic collision between two equal...Ch. 9 - Prob. 30ECh. 9 - Two identical trucks have mass 5500 kg when empty,...Ch. 9 - An alpha particle (4He) strikes a stationary gold...Ch. 9 - Playing in the street, a child accidentally tosses...Ch. 9 - A block of mass m undergoes a one-dimensional...Ch. 9 - A proton moving at 6.9 Mm/s collides elastically...Ch. 9 - A head-on, elastic collision between two particles...Ch. 9 - Find the center of mass of a pentagon with five...Ch. 9 - Wildlife biologists fire 20-g rubber bullets to...Ch. 9 - Consider a system of three equal-mass particles...Ch. 9 - Youre with 19 other people on a boat at rest in...Ch. 9 - A hemispherical bowl is at rest on a frictionless...Ch. 9 - Physicians perform needle biopsies to sample...Ch. 9 - Find the center of mass of the uniform, solid cone...Ch. 9 - A firecracker, initially at rest, explodes into...Ch. 9 - An 11,000-kg freight car rests against a spring...Ch. 9 - On an icy road, a 1200-kg car moving at 50 km/h...Ch. 9 - A 1250-kg car is moving with velocity...Ch. 9 - Masses m and 3m approach at the same speed v and...Ch. 9 - A 238U nucleus is moving in the x-direction at 5.0...Ch. 9 - A cylindrical concrete silo is 4.0 m in diameter...Ch. 9 - A 42-g firecracker is at rest at the origin when...Ch. 9 - A 60-kg astronaut floating in space simultaneously...Ch. 9 - Assuming equal-mass pieces in Exercise 24, find...Ch. 9 - A 62-kg sprinter stands on the left end of a...Ch. 9 - Youre a production engineer in a cookie factory,...Ch. 9 - Mass m, moving at speed 2v, approaches mass 4m,...Ch. 9 - Verify explicitly that kinetic energy is conserved...Ch. 9 - While standing on frictionless ice, you (mass 65.0...Ch. 9 - Youre an accident investigator at a scene where a...Ch. 9 - A fireworks rocket is launched vertically upward...Ch. 9 - Two objects moving in opposite directions with the...Ch. 9 - Explosive bolts separate a 950-kg communications...Ch. 9 - Youre working in quality control for a model...Ch. 9 - Youre investigating an accident in which a 1040-kg...Ch. 9 - A 400-mg popcorn kernel is skittering across a...Ch. 9 - Two identical objects with the same initial speed...Ch. 9 - A proton (mass 1 u) moving at 6.90 Mm/s collides...Ch. 9 - Two objects, one initially at rest, undergo a...Ch. 9 - Blocks B and C have masses 2m and m, respectively,...Ch. 9 - Derive Equation 9.15b.Ch. 9 - An object collides elastically with an equal-mass...Ch. 9 - A proton (mass 1 u) collides elastically with a...Ch. 9 - Two identical billiard balls are initially at rest...Ch. 9 - Find an expression for the impulse imparted by a...Ch. 9 - A 32-u oxygen molecule (O2) moving in the...Ch. 9 - A 114-g Frisbee is lodged on a tree branch 7.65 m...Ch. 9 - You set a small ball of mass m atop a large ball...Ch. 9 - A car moving at speed v undergoes a...Ch. 9 - A 200-g block is released from rest at a height of...Ch. 9 - A 14-kg projectile is launched at 380 m/s at a 55...Ch. 9 - During a crash test, a car moving at 50 km/h...Ch. 9 - Use numerical or graphical techniques to estimate...Ch. 9 - A block of mass m1 undergoes a one-dimensional...Ch. 9 - Two objects of unequal mass, one initially at...Ch. 9 - Prob. 86PCh. 9 - Prob. 87PCh. 9 - In a ballistic pendulum demonstration gone bad, a...Ch. 9 - An 80-kg astronaut has become detached from the...Ch. 9 - Prob. 90PCh. 9 - A thin rod extends from x = 0 to x = L. It carries...Ch. 9 - Model rocket motors are specified by giving the...Ch. 9 - A block of mass M is moving at speed r0 on a...Ch. 9 - Youre interested in the intersection of physics...Ch. 9 - Youre interested in the intersection of physics...Ch. 9 - Youre interested in the intersection of physics...Ch. 9 - Youre interested in the intersection of physics...
Additional Science Textbook Solutions
Find more solutions based on key concepts
9. A cannon tilted upward at 30º fires a cannonball with a speed of 100 m/s. At that instant, what is the compo...
College Physics: A Strategic Approach (3rd Edition)
3. What is free-fall, and why does it make you weightless? Briefly describe why astronauts are weightless in th...
The Cosmic Perspective
Q22.11 Lightning is a flow of electrons. The lightning current runs through the copper cables since copper is a...
University Physics with Modern Physics (14th Edition)
62. Why is there so little wind on the surface of Venus?
Conceptual Physical Science (6th Edition)
33. * What is the evidence that a large proportion of the mass of the universe is in the form of dark matter? E...
College Physics
The pV-diagram of the Carnot cycle.
Sears And Zemansky's University Physics With Modern Physics
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 small box of mass m₁ is sitting on a board of mass m₂ and length L (Figure 1). The board rests on a frictionless horizontal surface. The coefficient of static friction between the board and the box is μg. The coefficient of kinetic friction between the board and the box is, as usual, less than μg. Throughout the problem, use g for the magnitude of the free-fall acceleration. In the hints, use f for the magnitude of the friction force between the board and the box. igure m₁ m₂ L F 1 of 1 Find Fmin, the constant force with the least magnitude that must be applied to the board in order to pull the board out from under the the box (which will then fall off of the opposite end of Express your answer in terms of some or all of the variables μs, m₁, m2, g, and L. Do not include f in your answer. ► View Available Hint(s) Π| ΑΣΦ Fmin = Submit Provide Feedback ? board). Activate Windows Go to Settings to activate Wiarrow_forwardIn the attached Word file, a shape is on an x-y axis, beginning at x = 0. The bottom of the shape is 25 cm long and it reaches a height of 20 cm. The shape weights 450 g. The curved part of the shape is a parabola, i.e., it has the form y = ax2, where a is a constant to be determined. a) Determine the constant from the information given. b) If shape has a uniform density and a uniform width in the z-direction, find the x-component of the center-of-mass.arrow_forwardDo Chapter 12, Problem 5. This is an integration problem, to calculate the center of mass (center of gravity) for a continuous distribution. Specifically, we need the horizontal component of the center of mass. The height varies from h to zero according to this function: y(x)=h(xℓ−1)2y(x)=h(xℓ−1)2 . The constants h and ℓ replace 1.00 m and 3.00 m. There is also a thickness t and a density ρ. You need two integrals, the total mass and the center of mass. Possibly surprisingly, you don't actually need the numbers t, h, and ρ.arrow_forward
- A rod of length 23.50 cm has a linear density (mass per length) given by λ = 50 +22.5x where x is the distance from one end and λ is measured g/m. a) What is the mass of the rod? (in grams) b) How far from the x=0 end is the center of mass of the rod? (in m)arrow_forwardA 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?arrow_forwardPoint A (1, 2, 3 cm) is subjected to forces shown in the diagram below. Determine magnitude of force F if (a) magnitude of moment about point A = 3 kN-cm (b) y-component of the moment about point A = 20 kN-cm counterclockwise. We are using a 3x3 matrix method to solve this.arrow_forward
- A puck of mass m, = 80.0 g and radius r, = 4.00 cm glides across an air table at a speed of v = 1.50 m/s as shown in Figure Pl1.26a. It makes a glancing collision with a second puck of radius r, = 6.00 cm and mass m, = 120 g (initially at rest) such that their rims just touch. Because their rims are coated with instant-acting glue, the pucks stick together and rotate after the collision (Fig. Pl1.26b). (a) What is the angu- lar momentum of the system relative to the center of mass? (b) What is the angular speed about the center of mass? a Figure P11.26arrow_forwardTo 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.arrow_forwardA block of mass m = 2.00 kg is sitting stationary on a table. A horizontal force of magnitude F= 5.00 N is applied to the block, as shown. The coefficient of static friction is us = 0.700, and the coefficient of kinetic friction is PK = 0.500. What is the %3D magnitude of the force of friction between the block and the table, in units of newtons? Enter the numerical answer without units. Your answer must be within 1% of the exact answer to receive credit. ls = 0.7 HK = 0.5 m = 2.0 kg F = 5.0 N block at restarrow_forward
- A two dimensional force system is given. The objective is to find the resultant force of the system by using vector operations. There are three forces present in the system. A. Find the vector form for each of the three forces: F1=10, Theta 1=45: F2=40x Theta 2=135; F3=30, Theta 3=270 B.Find the vector form of the resultant force C.Find the magnitude of the resultant force D. Find the angle of the force referred from the x-axis and describe its directionarrow_forwardConsider a tube and a roller shown in (Figure 1). The tube E has a mass of 105 kg and the roller D has a mass of 130 kg. The force acts parallel to the plane, and the coefficients of static friction at the contacting surfaces are HA=0.3, μB = 0.25, and c = 0.4. The roller and tube each have a radius of 150 mm. Figure 1 of 1 30° E Part A Determine the minimum force P needed to push the tube E up the incline. Express your answer to three significant figures and include the appropriate units. μA P = 489 N Submit Previous Answers Request Answer X Incorrect; Try Again; 3 attempts remaining Provide Feedbackarrow_forwardThree electrical charges isolated from the rest of the universe are located at the vertices of an equilateral triangle. Charge 3 attracts charge 1 with a force of modulus F1(3) = 4.3 N and repels charge 2 with a force of modulus F2(3) = 6.7 N. What is the modulus of the sum of the reaction forces on the charge 3 in Newtons? a. 10,95 b. 8,45 c. 9,60 d. None of the other alternatives are correct. e. 12,39 f. 2,21 g. 15,17 h. 0,86arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- College PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage LearningUniversity Physics (14th Edition)PhysicsISBN:9780133969290Author:Hugh D. Young, Roger A. FreedmanPublisher:PEARSONIntroduction To Quantum MechanicsPhysicsISBN:9781107189638Author:Griffiths, David J., Schroeter, Darrell F.Publisher:Cambridge University Press
- Physics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningLecture- Tutorials for Introductory AstronomyPhysicsISBN:9780321820464Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina BrissendenPublisher:Addison-WesleyCollege Physics: A Strategic Approach (4th Editio...PhysicsISBN:9780134609034Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart FieldPublisher:PEARSON
College Physics
Physics
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Cengage Learning
University Physics (14th Edition)
Physics
ISBN:9780133969290
Author:Hugh D. Young, Roger A. Freedman
Publisher:PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:9781107189638
Author:Griffiths, David J., Schroeter, Darrell F.
Publisher:Cambridge University Press
Physics for Scientists and Engineers
Physics
ISBN:9781337553278
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:9780321820464
Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:Addison-Wesley
College Physics: A Strategic Approach (4th Editio...
Physics
ISBN:9780134609034
Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:PEARSON
Momentum | Forces & Motion | Physics | FuseSchool; Author: FuseSchool - Global Education;https://www.youtube.com/watch?v=DxKelGugDa8;License: Standard YouTube License, CC-BY