A force can be a function of position, velocity, or time. Most of the forces we consider in an introduction to dynamics are constant forces, but the text does examine a drag force that is proportional to velocity for a falling object, resulting is a terminal velocity. For this challenge question, imagine a block of mass m sliding across a horizontal surface lubricated with a thick oil, and that the frictional force can be approximated as F, = -bvv If v = vo at time t=0, determine v and x as functions of time. Also show that the maximum distance the block could travel is 2mv3' „3/2 Xmax 3b

A force can be a function of position, velocity, or time. Most of the forces we consider in an introduction to dynamics are constant forces, but the text does examine a drag force that is proportional to velocity for a falling object, resulting is a terminal velocity. For this challenge question, imagine a block of mass m sliding across a horizontal surface lubricated with a thick oil, and that the frictional force can be approximated as F, = -bvv If v = vo at time t=0, determine v and x as functions of time. Also show that the maximum distance the block could travel is 2mv3' „3/2 Xmax 3b

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Similar questions

A body with a mass of 5 kg rests on a rough horizontal table with a coefficient of static friction of 0.9. At a given moment, a horizontal force of 40 N is applied to this body, as shown in the figure. Analyze the propositions and answer the alternative that corresponds to the sum of the correct ones. Adopt g = 10 m/s². (01) With the data presented, we can conclude that the static friction force is 48 N. (02) In the proposed situation, the body will move with an acceleration of 5 m/s2. (04) In the proposed situation, the body will not move. (08) In the proposed situation, the body will be subjected to a frictional force of 40 N. (16) In the proposed situation, the body will be subjected to a frictional force of 45 N. (32) In the proposed situation, the net force in the body is null a) 12 b) 17 c) 19 d) 27 e) 44
A ball of mass m is suspended inside a railroad car, as shown, by two light cords, one horizontal, and one at angle θ to the vertical. Draw a free-body diagram and find the tension in each cord if the railroad car accelerates at to the right. First derive (and simplify) expressions for the tensions in terms of symbols (m, a, θ, and so on). Then, at the end, substitute m = 5.0 kg, θ = 37deg, and a = 2.0 m/s2 to get numerical answers.
Consider what happens if the block is suddenly disconnected from the spring, as shown below. Choose the correct equation for calculating the coefficient of kinetic friction (Uk.) if it takes time t for the block to travel a displacement of Ax down the inclined surface. Note that this displacement is negative in the given rotated coordinate system, and that the acceleration of the block is constant so the motion is described by the four kinematic equations. Hint: remember that Ax = x – x0 - spring is disconnected! Дх 2 Δη gt cos(0) + tan (0) 2 g t² cos(0) + tan (0) Hs = cos (0) + sin (0) gt? 2 Ax + sin (0) Ar 2 sin (0) I t? - sin (0) 2 g t?
block B is on the box A, and both are linked together through a pulley system in which one inextensible rope is used. Knowing that the weight of box A is Pa and the static and the kinetic friction coefficients between all A box A is on an inclined plane which has the configuration shown in the figure below. On another hand, a the contact surfaces are H, and pe, respectively, detemine the minimum weight of the block B for the imminent movement instant. Suggestion: Draw the free body diagram of the box and of the block separately. > Contact surface 1 1 A Contact surface 2
Consider the tension in an elevator cable during the time the elevator starts from rest and accelerates its load upward to some cruising velocity. Taking the elevator and its load to be the system of interest, draw a free-body diagram. Then calculate the tension in the cable. Among the things to consider are the mass of the elevator and its load, the final velocity, and the time taken to reach that velocity.
(a) Demonstrate that six degrees of freedom exist in a rigid body with three or more mass points. Remember to emphasise what makes a rigid body unique and why we need just six dynamical variables to explain the motion. (b) Specifically, what are these six degrees of freedom? (c) Is the selection unusual? In terms of uniqueness, you need examine both the coordinate system and the origin.
Find the particle's horizontal position x(t) and velocity v(x) at any point in a fluid whose drag force is expressed as Fdrag = kmv where, k is a constant, m is the mass of the particle and v is its velocity. Consider that the particle is initially traveling with a velocity vo. Solution: a) To solve for the position as a function of time x(t), we construct the net force in the x-axis as E F=F = m Then: -m v = m since: a - dv/dt then -m v = m by integrating, we obtain the following expression: s voe Further, employing the rules of integration results to the following expression for position as a function of time x= (vo/ - e as t+ 0, the position becomes x= vo/k b) To solve for the velocity as a function of position v(x), construct the net force in the x-axis as follows EF-F sm Then: -m v = m since: a = dv/dt then -m V= m We can eliminate time by expressing, the velocity on the left side of the equation as V= dx/dt Then, we arrive at the following expression = -k By integrating and…
What does my textbook mean by "the coefficient of static friction is a maximum value"? Suppose I have a non-moving box on the ground, does the coefficient change when it's moving vs. when it's non-moving? I also saw this: μkinetic < μstatic. Please explain.
A block of mass m rests on a plane inclined at θ with the horizontal. The block is attached to a spring of constant k as shown in Figure-2. The coefficients of static and kinetic friction between the block and plane are and respectively. Very slowly, the spring is pulled upward along the plane until the block starts to move. (a) Obtain an expression for the extension d of the spring the instant the block moves. (b) Determine the value of such that the block comes to rest just as the spring is in its unstressed condition, that is, neither extended nor compressed.
4.
Consider the scenario in the figure below. The mass of block 2 (hanging vertically) is 72.7 kg. The coefficient of static friction between block 1 and the table is 0.250. Find the minimum mass of block 1 (in kg) for which the system will remain at rest. Assume that the mass of the ropes are al negligible. Hint: apply Newton's 2nd law to block 1, block 2, and the knot. Set every acceleration equal to zero, since nothing is moving! m₁ knot m2 41.0⁰
dler?action=activityBranding&COURSEID=3377&SECTIONID=170728 1 2 1 2 art 1 art 2 $ X R F V 1. Two blocks are connected by a massless rope as shown below. The mass of the block on the table is m, and the hanging mass is m₂. The table and the pulley are frictionless. O 15 % 5 T 2 7 Subpart 1: Draw FBDs In your notebook, draw free body diagrams for m, and m₂ using the template as shown below. The forces acting on the system are weights of the blocks, m₁g, and m₂g, the tension in the string T and the normal reaction N₁ of the table on m₁. ^ B 10 6 Y G H & M- 7 hp U fa J m₁ * 00 8 N M 1 IAA ( 9 K < fo O ► 11 0 O L m₂ f11 3 P ; 22 112 Rain.... ^ 40) @ { + [ ? = 12 ☆ 1 insert ( } ← ] S 4:45 PM 9/27/2022 prt sc backspace pause E