Principles of Physics: A Calculus-Based Text
Principles of Physics: A Calculus-Based Text
5th Edition
ISBN: 9781133104261
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
bartleby

Concept explainers

bartleby

Videos

Textbook Question
Book Icon
Chapter 10, Problem 72P

Review. A block of mass m1 = 2.00 kg and a block of mass m2 = 6.00 kg are connected by a massless string over a pulley in the shape of a solid disk having radius R = 0.250 m and mass M = 10.0 kg. The fixed, wedge-shaped ramp makes an angle of θ = 30.0° as shown in Figure P10.72. The coefficient of kinetic friction is 0.360 for both blocks. (a) Draw force diagrams of both blocks and of the pulley. Determine (b) the acceleration of the two blocks and (c) the tensions in the string on both sides of the pulley.

Chapter 10, Problem 72P, Review. A block of mass m1 = 2.00 kg and a block of mass m2 = 6.00 kg are connected by a massless

Figure P10.72

(a)

Expert Solution
Check Mark
To determine

Sketch the force diagrams of both blocks and pulley.

Answer to Problem 72P

The free body diagram of the block of mass m1 is shown below.

Principles of Physics: A Calculus-Based Text, Chapter 10, Problem 72P , additional homework tip  1

The free body diagram of the block of mass m2 is shown below.

Principles of Physics: A Calculus-Based Text, Chapter 10, Problem 72P , additional homework tip  2

The free body diagram of the pulley is shown below.

Principles of Physics: A Calculus-Based Text, Chapter 10, Problem 72P , additional homework tip  3

Explanation of Solution

Consider the figure of given system

Principles of Physics: A Calculus-Based Text, Chapter 10, Problem 72P , additional homework tip  4

In physics and engineering free body diagrams are used for visualizing the forces, movements, and reaction forces acting on a body. The direction of the forces are also shown in free body diagram using straight arrows.

The free body diagram of the block of mass m1 is shown below

Principles of Physics: A Calculus-Based Text, Chapter 10, Problem 72P , additional homework tip  5

The mass m1 is resting on the plane, a normal force n1 acting in upward direction, just opposite to normal force, the gravitational force due to the weight of the block m1g is acting downwards. fk1 is the kinetic friction force, and T1 is the tension of the string connected between mass m1, and the pulley.

The free body diagram of the block of mass m2 is shown below

Principles of Physics: A Calculus-Based Text, Chapter 10, Problem 72P , additional homework tip  6

The mass m1 is resting on the inclined plane, a normal force n2 acting in direction perpendicular to the surface of the block, the gravitational force due to the weight of the block m2g is acting downwards. fk2 is the kinetic friction force, and T2 is the tension of the string connected between mass m2, and the pulley, both are in same direction.

The free body diagram of the pulley is shown below.

Principles of Physics: A Calculus-Based Text, Chapter 10, Problem 72P , additional homework tip  7

Mg is the weight of the pulley, and n3 is the normal force on pulley.

(b)

Expert Solution
Check Mark
To determine

The acceleration of two blocks.

Answer to Problem 72P

The acceleration of two blocks is 0.309m/s2_.

Explanation of Solution

Consider the free body diagram of mass m1.

Write the expression for the total force acting on mass m1 in vertical direction.

  Fy=may        (I)

Here, m is the mass, and ay is the acceleration along y direction.

The net force acting in vertical direction will be zero, since the normal force and m1g are opposite to each other.

Rewrite equation (I).

  Fy=mayn1m1g=0n1=m1g        (II)

Write the expression for kinetic friction force on m1.

  fk1=μkn1        (III)

Here, μk is the coefficient of kinetic friction.

Write the expression for the force acting in x direction.

  Fx=max        (IV)

Here, ax is the acceleration along x direction.

Rewrite equation (IV) including the components of forces in horizontal direction.

  fk1+T1=m1a        (V)

Write the expression for the total torque.

  τ=Iα        (VI)

Here, I is the moment of inertia, α is the angular acceleration.

Substitute, T1R+T2R for τ, 12MR2 for I, and aR for α in equation (VI).

  T1R+T2R=12MR2(aR)T1+T2=12Ma        (VII)

Similarly the net force acting on x direction in mass m2 is also zero.

  n2m2gcosθ=0n2=m2gcosθ        (VIII)

Write the expression for the kinetic force of friction acting on mass m2.

  fk2=μkn2        (IX)

Write the expression for the forces acting on y direction.

  fk2T2+m2gsinθ=m2a        (X)

Add equation (V), (VII), and (X)

fk1+T1+(T1+T2)fk2T2+m2gsinθ=m2a+12Ma+m1afk1fk2+m2gsinθ=m2a+12Ma+m1a        (XI)

Substitute, equation (IX) and (III) in (XI), m1g for n1, m2gcosθ for n2 to obtain an expression for acceleration.

  (μkm1g)(μkm2gcosθ)+m2gsinθ=(m2+12M+m1)aa=m2(sinθμkcosθ)μkm1m2+12M+m1g        (XII)

Conclusion:

Substitute, 6.00kg for m2, 30.0° for θ, 0.360 for μk, 2.00kg for m1, 9.80m/s2 for g, 10.0kg for M in equation (XII).

  a=6.00kg(sin30.0°0.360×cos30.0°)0.360×2.00kg6.00kg+12(10.0kg)+2.00kg(9.80m/s2)=0.309m/s2

Therefore, the acceleration of two blocks is 0.309m/s2_.

(c)

Expert Solution
Check Mark
To determine

The tension in the string on both sides of the pulley.

Answer to Problem 72P

The tension in the string on both sides of the pulley is T1=7.67N_, and T2=9.22N_.

Explanation of Solution

Use equation (V) and (VII) to obtain the answer.

Conclusion:

Substitute, 2.00kg for m1, 0.309m/s2 for a, and 7.06N for fk1 in equation (V) to find T1.

  (7.06N)+T1=(2.00kg)(0.309m/s2)T1=(2.00kg)(0.309m/s2)+7.06N=7.67N

Substitute, 10.0kg for M, 0.309m/s2 for a, 7.67N for T1 in equation (VII) to find T2.

  7.67N+T2=12(10.0kg)(0.309m/s2)T2=7.67N+12(10.0kg)(0.309m/s2)=9.22N

Therefore, the tension in the string on both sides of the pulley is T1=7.67N_, and T2=9.22N_.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
A wheel of radius 0.269 m, which we can model as a thin disk, is mounted on a frictionless horizontal axis. The mass of the wheel is 2.44 kg. A massless cord wrapped around the wheel is attached to a block of 4.16 kg that slides on a horizontal frictionless surface. If a horizontal force P with a magnitude of 10.1 N is applied to the block as shown below. If the wheel and block start at rest, and the block is moved through a displacement of 2.60 m what is the final angular velocity of the wheel in rad/s, assuming the cord does not slip. P
A block of mass m, = 1.65 kg and a block of mass m, = 6.20 kg are connected by a massless string over a pulley in the shape of a solid disk having radius R = 0.250 m and mass M = 10.0 kg. The fixed, wedge-shaped ramp makes an angle of e = 30.0° as shown in the figure. The coefficient of kinetic friction is 0.360 for both blocks. Use g=9.8 m/s². М, R (b) Determine the acceleration of the two blocks. (Enter the magnitude of the acceleration.) m/s2 (c) Determine the tensions in the string on both sides of the pulley. left of the pulley right of the pulley N
A block of mass m, = 1.95 kg and a block of mass m, = 5.70 kg are connected by a massless string over a pulley in the shape of a solid disk having radius R = 0.250 m and mass M = 10.0 kg. The fixed, wedge- shaped ramp makes an angle of e = 30.0° as shown in the figure. The coefficient of kinetic friction is 0.360 for both blocks. Use g=9.8 m/s2. М, R (b) Determine the acceleration of the two blocks. (Enter the magnitude of the acceleration.) m/s2 (c) Determine the tensions in the string on both sides of the pulley. left of the pulley N right of the pulley N

Chapter 10 Solutions

Principles of Physics: A Calculus-Based Text

Ch. 10 - Prob. 2OQCh. 10 - Prob. 3OQCh. 10 - Prob. 4OQCh. 10 - Assume a single 300-N force is exerted on a...Ch. 10 - Consider an object on a rotating disk a distance r...Ch. 10 - Answer yes or no to the following questions. (a)...Ch. 10 - Figure OQ10.8 shows a system of four particles...Ch. 10 - As shown in Figure OQ10.9, a cord is wrapped onto...Ch. 10 - Prob. 10OQCh. 10 - Prob. 11OQCh. 10 - A constant net torque is exerted on an object....Ch. 10 - Let us name three perpendicular directions as...Ch. 10 - A rod 7.0 m long is pivoted at a point 2.0 m from...Ch. 10 - Prob. 15OQCh. 10 - A 20.0-kg horizontal plank 4.00 m long rests on...Ch. 10 - (a) What is the angular speed of the second hand...Ch. 10 - Prob. 2CQCh. 10 - Prob. 3CQCh. 10 - Which of the entries in Table 10.2 applies to...Ch. 10 - Prob. 5CQCh. 10 - Prob. 6CQCh. 10 - Prob. 7CQCh. 10 - Prob. 8CQCh. 10 - Three objects of uniform densitya solid sphere, a...Ch. 10 - Prob. 10CQCh. 10 - If the torque acting on a particle about an axis...Ch. 10 - Prob. 12CQCh. 10 - Stars originate as large bodies of slowly rotating...Ch. 10 - Prob. 14CQCh. 10 - Prob. 15CQCh. 10 - Prob. 16CQCh. 10 - Prob. 17CQCh. 10 - During a certain time interval, the angular...Ch. 10 - A bar on a hinge starts from rest and rotates with...Ch. 10 - Prob. 3PCh. 10 - Prob. 4PCh. 10 - The tub of a washer goes into its spin cycle,...Ch. 10 - Why is the following situation impossible?...Ch. 10 - An electric motor rotating a workshop grinding...Ch. 10 - Prob. 8PCh. 10 - Prob. 9PCh. 10 - A wheel 2.00 m in diameter lies in a vertical...Ch. 10 - A disk 8.00 cm in radius rotates at a constant...Ch. 10 - Make an order-of-magnitude estimate of the number...Ch. 10 - A car traveling on a flat (unbanked), circular...Ch. 10 - Prob. 14PCh. 10 - A digital audio compact disc carries data, each...Ch. 10 - Figure P10.16 shows the drive train of a bicycle...Ch. 10 - Big Ben, the Parliament tower clock in London, has...Ch. 10 - Rigid rods of negligible mass lying along the y...Ch. 10 - A war-wolf, or trebuchet, is a device used during...Ch. 10 - Prob. 20PCh. 10 - Review. Consider the system shown in Figure P10.21...Ch. 10 - The fishing pole in Figure P10.22 makes an angle...Ch. 10 - Find the net torque on the wheel in Figure P10.23...Ch. 10 - Prob. 24PCh. 10 - Prob. 25PCh. 10 - Prob. 26PCh. 10 - A force of F=(2.00i+3.00j) N is applied to an...Ch. 10 - A uniform beam resting on two pivots has a length...Ch. 10 - Prob. 29PCh. 10 - Prob. 30PCh. 10 - Figure P10.31 shows a claw hammer being used to...Ch. 10 - Prob. 32PCh. 10 - A 15.0-m uniform ladder weighing 500 N rests...Ch. 10 - A uniform ladder of length L and mass m1 rests...Ch. 10 - BIO The arm in Figure P10.35 weighs 41.5 N. The...Ch. 10 - A crane of mass m1 = 3 000 kg supports a load of...Ch. 10 - An electric motor turns a flywheel through a drive...Ch. 10 - Prob. 38PCh. 10 - Prob. 39PCh. 10 - In Figure P10.40, the hanging object has a mass of...Ch. 10 - A potters wheela thick stone disk of radius 0.500...Ch. 10 - A model airplane with mass 0.750 kg is tethered to...Ch. 10 - Consider two objects with m1 m2 connected by a...Ch. 10 - Review. An object with a mass of m = 5.10 kg is...Ch. 10 - A playground merry-go-round of radius R = 2.00 m...Ch. 10 - The position vector of a particle of mass 2.00 kg...Ch. 10 - Prob. 48PCh. 10 - Big Ben (Fig. P10.17), the Parliament tower clock...Ch. 10 - A disk with moment of inertia I1 rotates about a...Ch. 10 - Prob. 51PCh. 10 - A space station is constructed in the shape of a...Ch. 10 - Prob. 53PCh. 10 - Why is the following situation impossible? A space...Ch. 10 - The puck in Figure 10.25 has a mass of 0.120 kg....Ch. 10 - A student sits on a freely rotating stool holding...Ch. 10 - Prob. 57PCh. 10 - Prob. 58PCh. 10 - A cylinder of mass 10.0 kg rolls without slipping...Ch. 10 - A uniform solid disk and a uniform hoop are placed...Ch. 10 - A metal can containing condensed mushroom soup has...Ch. 10 - A tennis ball is a hollow sphere with a thin wall....Ch. 10 - Prob. 63PCh. 10 - Review. A mixing beater consists of three thin...Ch. 10 - A long, uniform rod of length L and mass M is...Ch. 10 - The hour hand and the minute hand of Big Ben, the...Ch. 10 - Two astronauts (Fig. P10.67), each having a mass...Ch. 10 - Two astronauts (Fig. P10.67), each having a mass...Ch. 10 - Prob. 69PCh. 10 - Prob. 70PCh. 10 - The reel shown in Figure P10.71 has radius R and...Ch. 10 - Review. A block of mass m1 = 2.00 kg and a block...Ch. 10 - A stepladder of negligible weight is constructed...Ch. 10 - A stepladder of negligible weight is constructed...Ch. 10 - A wad of sticky clay with mass m and velocity vi...Ch. 10 - Prob. 76PCh. 10 - Prob. 77PCh. 10 - Review. A string is wound around a uniform disk of...Ch. 10 - Prob. 79PCh. 10 - Prob. 80PCh. 10 - A projectile of mass m moves to the right with a...Ch. 10 - Figure P10.82 shows a vertical force applied...Ch. 10 - A solid sphere of mass m and radius r rolls...Ch. 10 - Prob. 84PCh. 10 - BIO When a gymnast performing on the rings...
Knowledge Booster
Background pattern image
Physics
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
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Physics for Scientists and Engineers with Modern ...
Physics
ISBN:9781337553292
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Text book image
Principles of Physics: A Calculus-Based Text
Physics
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Text book image
Physics for Scientists and Engineers
Physics
ISBN:9781337553278
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Text book image
Physics for Scientists and Engineers: Foundations...
Physics
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Cengage Learning
What is Torque? | Physics | Extraclass.com; Author: Extraclass Official;https://www.youtube.com/watch?v=zXxrAJld9mo;License: Standard YouTube License, CC-BY