Combined Linear and Quadratic Drag in One Dimension Consider object that is coasting horizontally (positive x direction) subject to a drag force farag = -f(v)v with f(v) = bu+cu2. Write down the differential equation from Newton's second law for this object and solve for v by separating variables. Sketch the behavior of v as a function of t. Explain the time dependence for t large. (Which force term is dominant when t is large?) an

Combined Linear and Quadratic Drag in One Dimension Consider object that is coasting horizontally (positive x direction) subject to a drag force farag = -f(v)v with f(v) = bu+cu2. Write down the differential equation from Newton's second law for this object and solve for v by separating variables. Sketch the behavior of v as a function of t. Explain the time dependence for t large. (Which force term is dominant when t is large?) an

Classical Dynamics of Particles and Systems

5th Edition

ISBN:9780534408961

Author:Stephen T. Thornton, Jerry B. Marion

Publisher:Stephen T. Thornton, Jerry B. Marion

Chapter2: Newtonian Mechanics-single Particle

Section: Chapter Questions

Problem 2.9P: Consider a projectile fired vertically in a constant gravitauonal field. For the same initial...

See similar textbooks

Similar questions

A 2 kg box is initially at rest on the smooth horizontal surface. When the box is subjected to horizontal force P= 4 N. Compute the following: What is the resulting acceleration of the box? ______________ How fast is the box moving after 1 second? _______________ How far has it moved after 1 second? ____________________
Consider two peoplepushing a toboggan with four children on it up a snowcovered slope. Construct a problem in which you calculatethe acceleration of the toboggan and its load. Include a freebody diagram of the appropriate system of interest as thebasis for your analysis. Show vector forces and theircomponents and explain the choice of coordinates. Amongthe things to be considered are the forces exerted by thosepushing, the angle of the slope, and the masses of thetoboggan and children.
A block, initially at rest, has a mass m and sits on a plane inclined at angle theta. It slides a distance d before hitting a spring and compresses the spring by a maximum distance of xf. If the coefficient of kinetic friction between the plane and block is uk, then what is the force constant of the spring?
can u also add a free body diagram if applicable?
Just answer problem number 3, and dont forget to write the given, what is required, sketch of the given, free-body diagram and the solution.
What must be the minimum force P such that no motion occcurs? (Refer to the illustrtion below)
Show that the acceleration of any object down an incline where friction behaves simply (that Is, where fk=kN ) is a=(sinkcos) . Note that the acceleration Is independent of mass and reduces to the expression found in the previous problem when friction becomes negligibly small (k=0) .
A projectile of mass [m] is launched with initial velocity [v0] at angle [theta] from the +x direction. From the origin, the projectile is connected toa massless spring with force constant k, as shown. From the equations of motion, one can show that the horizontal and vertical positions of the mass as functions of time can be written asx(t) = A cos wt + B sin wty(t) = C cos wt + D sin wt + Eprovided that the coefficients satisfy the conditions that initially, x(0) = y(0) = 0,vx (t = 0) = v0 cos [theta], and vy (t = 0) = v0 sin [theta]. Determine the coefficients A,B,C,D, and E in termsof the given variables.
A 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.
If we want to find the size of the force necessary to just barely overcome static friction (in which case fs=μsN), we use the condition that the sum of the forces in both directions must be 0. Using some basic trigonometry, we can write this condition out for the forces in both the horizontal and vertical directions, respectively, as: Fcosθ−μsN=0 Fsinθ+N−mg=0 In order to find the magnitude of force F, we have to solve a system of two equations with both F and the normal force N unknown. Use the methods we have learned to find an expression for F in terms of m, g, θ, and μs (no N) What are the steps to solve this?
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.
Q 1: Find the outcome of the convergent forces system in the form below