Classical Dynamics of Particles and Systems
5th Edition
ISBN: 9780534408961
Author: Stephen T. Thornton, Jerry B. Marion
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Concept explainers
Textbook Question
Chapter 2, Problem 2.51P
Let us make the (unrealistic) assumption that a boat of mass m gliding with initial velocity v0 in water is slowed by a viscous retarding force of magnitude bv2, where b is a constant, (a) Find and sketch v(t). How long does it take the boat to reach a speed of v0/l000? (b) Find x(t). How far does the boat travel in this time? Let m = 200 kg, v0 = 2 m/s, and b = 0.2 Nm-2s2.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
A contestant in a winter sporting event pushes an mm kg block of ice across a frozen lake by applying a force FF at an angle θθ below the horizontal as shown. Assume that the coefficient of static friction for ice on ice is 0.0300, and the coefficient of kinetic friction for the same is 0.0100. Let to the right be the positive x direction and up be the positive y direction for your equations.
Obtain a numeric value, in newtons, for the magnitude of the maximum applied force, F, consistent with static friction when the force makes an angle 32° below the horizontal and the mass of the block is 63 kg.
Obtain a numeric value for the acceleration, a, in meters per squared seconds, when the mass of the block is 63 kg and the angle of the rope is 32° below the horizontal.
An ideal massless rope passes over a massless, frictionless pulley. Block A with mass mA=9.8 kg, and block B with mass mB=4.3 kg, are suspended from opposite ends of the rope. Consider the motion of the blocks after they are released from rest. Let a be the magnitude of their acceleration, and let FT be the tension in the rope. Let upward be the positive y direction for block B, and let downward be the positive y direction for block A.
1. Write an expression for the net force on block A consistent with the positive direction as given in the problem statement.
2. Write an expression for the net force on block B consistent with the positive direction as given in the problem statement.
3. Enter an expression for the acceleration of either block.
4. What is the numerical value, in newtons, of the tension in the rope?
What is the numerical value, in newtons, of the tension in the rope?
Chapter 2 Solutions
Classical Dynamics of Particles and Systems
Ch. 2 - Prob. 2.1PCh. 2 - Prob. 2.2PCh. 2 - If a projectile is fired from the origin of the...Ch. 2 - A clown is juggling four balls simultaneously....Ch. 2 - A jet fighter pilot knows he is able to withstand...Ch. 2 -
In the blizzard of ’88, a rancher was forced to...Ch. 2 - Prob. 2.7PCh. 2 - A projectile is fired with a velocity 0 such that...Ch. 2 - Consider a projectile fired vertically in a...Ch. 2 - Prob. 2.11P
Ch. 2 - A particle is projected vertically upward in a...Ch. 2 -
A particle moves in a medium under the influence...Ch. 2 - A projectile is fired with initial speed 0 at an...Ch. 2 -
A particle of mass m slides down an inclined...Ch. 2 - A particle is projected with an initial velocity 0...Ch. 2 - A strong softball player smacks the ball at a...Ch. 2 - Prob. 2.19PCh. 2 - A gun fires a projectile of mass 10 kg of the type...Ch. 2 - Prob. 2.21PCh. 2 - Prob. 2.22PCh. 2 - A skier weighing 90 kg starts from rest down a...Ch. 2 - A block of mass m = 1.62 kg slides down a...Ch. 2 - A child slides a block of mass 2 kg along a slick...Ch. 2 - A rope having a total mass of 0.4 kg and total...Ch. 2 - A superball of mass M and a marble of mass m are...Ch. 2 - An automobile driver traveling down an 8% grade...Ch. 2 - A student drops a water-filled balloon from the...Ch. 2 - Prob. 2.31PCh. 2 - Two blocks of unequal mass are connected by a...Ch. 2 - A particle is released from rest (y = 0) and falls...Ch. 2 - Perform the numerical calculations of Example 2.7...Ch. 2 - Prob. 2.36PCh. 2 - A particle of mass m has speed υ = α/x, where x is...Ch. 2 - The speed of a particle of mass m varies with the...Ch. 2 - A boat with initial speed υ0 is launched on a...Ch. 2 - A train moves along the tracks at a constant speed...Ch. 2 - Prob. 2.42PCh. 2 - Prob. 2.45PCh. 2 - Prob. 2.46PCh. 2 - Consider a particle moving in the region x > 0...Ch. 2 - Prob. 2.48PCh. 2 - Prob. 2.49PCh. 2 - According to special relativity, a particle of...Ch. 2 - Let us make the (unrealistic) assumption that a...Ch. 2 - A particle of mass m moving in one dimension has...Ch. 2 - A potato of mass 0.5 kg moves under Earth’s...Ch. 2 - Prob. 2.55P
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
- To understand kinetic and static friction. A block of mass m lies on a horizontal table. The coefficient of static friction between the block and the table is μs. The coefficient of kinetic friction is μk, with μk<μs. Suppose you push horizontally with precisely enough force to make the block start to move, and you continue to apply the same amount of force even after it starts moving. Find the acceleration aaa of the block after it begins to move. Express your answer in terms of some or all of the variables μs, μk, and m, as well as the free-fall acceleration g.arrow_forwardBlock 1, of mass m1, is connected over an ideal (massless and frictionless) pulley to block 2, of mass m2, as shown. Assume that the blocks accelerate as shown with an acceleration of magnitude a and that the coefficient of kinetic friction between block 2 and the plane is μ. Find the ratio of the masses m1/m2. Express your answer in terms of some or all of the variables a, μ, and θ, as well as the magnitude of the free-fall acceleration g.arrow_forwardA mug of root beer is sliding across a horizontal table with a constant velocity of 5.0[m/s], and is experiencing a friction force. If the mug has a total mass of 2.60[kg] and μk = 0.250, find the force due to friction. Express your answer in N.arrow_forward
- A person of mass, m, is riding an elevator while standing on a bathroom scale. The person looks at the bathroom scale and it reads 59 % of their weight. What is the acceleration of the elevator? Consider UP to by (+) and express your answer in m/s/s to 2 significant figures.arrow_forwardA contestant in a winter sporting event pulls an m kg block of ice across a frozen lake by applying a force F at an angle θ above the horizontal as shown. Assume that the coefficient of static friction for ice on ice is 0.0300, and the coefficient of kinetic friction for the same is 0.0100. Let to the right be the positive x direction and up be the positive y direction for your equations. Obtain a numeric value, in newtons, for the magnitude of the maximum applied force, F, consistent with static friction when the force makes an angle 22° above the horizontal and the mass of the block is 34 kg. Obtain a numeric value for the acceleration, a, in meters per squared seconds, when the mass of the block is 34 kg and the angle of the rope is 22° above the horizontal.arrow_forwardA student stands in an elevator that is continuously accelerating upward with acceleration a. Her backpack is sitting on the floor next to the wall. The width of the elevator car is L. The student gives her backpack a quick kick at t = 0, imparting to it speed v and making it slide across the elevator floor. At time t, the backpack hits the opposite wall. Find the coefficient of kinetic friction mk between the backpack and the elevator floor.arrow_forward
- A rocket travels through the atmosphere and experiences a linear drag force given by -ku, where k is a positive constant. Assume that all other external forces are negligible (e.g. ignore gravity). Let m; be the initial mass of the rocket plus fuel and m, is the final mass of the rocket after all the fuel has burned, and u is the speed of the exhaust fuel relative to the rocket. a) Write down the differential equation of motion (i.e. Newton's 2nd Law). b) The rocket burns fuel at a constant rate a = -dm/dt. Assuming that the rocket begins from rest, what is the final speed of the rocket in terms of m;, mf, a, u, and k.arrow_forwardPlease Asaparrow_forwardcormula for the drag force is F = dv° (found to be valid for a large regime of datalere : s the drag force, d is a constant (involving the area of the object, density of the fluid, etc.), and v is the relative speed between the object and the fluid. la) Rewrite the drag force equation in the form: 1b) In a plot of log F (y- log F = (...) log v + log (...) variable) vs log v (x- variable), what do you expect to be the slope value? |lb) In a plot of log F (y- variable) vs log v (x- variable), what do you expect to be the y-intercept?arrow_forward
- In procedure 2, you found the coefficient of kinetic friction by measuring the acceleration of a cart under the influence of the combined forces of friction, normal force, gravity, and tension in string from which masses were hanging. Suppose you add more masses to the hanging weight, therefore increasing the tension and hence the acceleration for this system to double (2 x) its original value. How many times of the old value of the coefficient of kinetic friction will the new value be?arrow_forwardConsider two blocks connected by a string (call this the internal string) and being pulled vertically upward by another string (the external string) attached to block A. Suppose that blocks A and B have masses of 3.0 kg and 2.0 kg, respectively, and suppose that the external string’s tension has a magnitude of 55 N. The internal string’s mass is 100 g. Find the acceleration of the system, the magnitude of the tension force on block B, and the difference in the magnitudes of the tension forces exerted by each end of the string. The acceleration of the system is ______ m/s2. The tension force on block B is ____ N. The difference in the magnitudes of the tension forces exerted by each end of the string is ______ N.arrow_forwarda block of mass m = 10.2 kg sitting on a ramp that makes an angle θ = 21° with the horizontal. This block is being pushed by a horizontal force F = 212 N. The coefficient of kinetic friction between the two surfaces is μ = 0.49. Write an equation for the acceleration of the block up the ramp using variables from the problem statement together with g for the acceleration due to gravity. Find the acceleration of the block up the ramp in m/s2.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Classical Dynamics of Particles and SystemsPhysicsISBN:9780534408961Author:Stephen T. Thornton, Jerry B. MarionPublisher:Cengage Learning
Classical Dynamics of Particles and Systems
Physics
ISBN:9780534408961
Author:Stephen T. Thornton, Jerry B. Marion
Publisher:Cengage Learning
Newton's Third Law of Motion: Action and Reaction; Author: Professor Dave explains;https://www.youtube.com/watch?v=y61_VPKH2B4;License: Standard YouTube License, CC-BY