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 at with a velocity v0.

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 at with a velocity v0.

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter5: More Applications Of Newton’s Laws

Section: Chapter Questions

Problem 29P

See similar textbooks

Related questions

Q: which one of these factors does not influence the 'drag force' acting on the object? 1.)…

A: Drag force is given by where, FD is the the drag force CD is the the drag coefficient A is the…

Q: When a parachutist jumps from an airplane, he eventually reaches a constant speed, called the…

A: As a parachute jumps from an airplane, his velocity is increasing. This time, there will be…

Q: Mona tion m2 An object of mass m1= 6kg placed on a frictionless, horizontal table is connected to a…

Q: A tennis ball is thrown at 25 m/s on a day when the wind speed is 0 m/s. What is the drag force…

Q: Write down Newton's Second Law for translation along the direction of the slope, calling this the…

A: Given Data: Friction →fs Weight →Mg Reaction force →FN Radius →R Inclination height →h Inclination…

Q: A paratrooper and his 8-m-diameter parachute weigh 950 N. Taking the average air density to be 1.2…

Q: If the net, external force acting on a body is zero, then a. The body is accelerating at a small…

A: We know that Force = mass x acceleration In this question it is given that net external force is…

Q: A 60 kg skydiver can be modeled as a rectangular "box" with dimensions 22 cm × 40 cm × 1.8 m. What…

A: The expression for terminal speed is vT=2mgρACd Area of the sky driver experience the air resistance…

Q: The terminal velocity of a raindrop that is 4.00 mm in diameter is approximately 8.50 m/s under…

A: Radius, R = d/2 = 4/2 = 2 mm = 0.002 m Volume of the drop is given by: V…

Q: Friction force between two surfaces in contact is independent of the surface area O relative motion…

A: Answer The force due to friction is generally independent of contact area between two surfaces. This…

Q: A friend on skis stands still on level ground, covered with dry snow at 08 C. How hard would you…

Q: 2. Ropes AB and AC are thrown to a boater whose canoe has capsized. If a = 25° and the magnitude of…

A: α = 25oFR = 95 lb θR = 10oθAC = 40o

Q: When an object is accelerating in a fluid due to an applied force, the velocity where the magnitude…

A: Introduction: The terminal velocity is the maximum attainable velocity when it acceleration through…

Q: A skydiver of mass 65.0 kg including parachute, floats downward suspended from his parachute having…

A: Given data : Mass, m = 65 kg Area, A = 25.06 m 2 density of air, ρ=1.25 kg/m3…

Q: The large block shown is x = 48 cm wide, y = 36 cm long, V3 and z = 6.0 cm high. This block is…

A: The drag force is, Fd,1=12ρv2CDA=121.43 kg/m38.01 m/s20.8320.48 m0.06 m=1.099 N The drag force is,…

Q: Frozen rain with spherical shape falls from 3.00 km, what is its velocity if the diameter is 0.3 mm?…

Q: When a force F stretches a rope of mass per unit length p, the veloci wave in the rope is given by V…

A: Givenv=Fρwheremass per unit length ρ

Q: A 4.0 kg object has a velocity of 3i m/s at one instant. Eight seconds later, its velocity is (8i +…

A: Write the first kinematic equation to determine the acceleration.

Q: two identical, uniform, and frictionless spheres, each of mass m, rest in a rigid rectangular…

Q: The large block shown is x = 16.0 cm wide, y = 21.0 cm long, and z = 28.00 cm high with a mass of…

Q: The total mass of a rod 2 meters long is 18 kg. If the linear density varies directly as the cube of…

Q: In an experiment to determine the viscosity of some oil, a ball is dropped into the oil. The…

A: At t= 0 , we have : y(0) = 0.07 m Vy(0) = 0 ay(0) = 0.03 m/s2 Vy(∞) = 0.45 m/s To find = A , B , C…

Q: Recall that Newton’s Equation of Motion for a Body of Mass, m, is F = m(dv/dt). Assume the Initial…

A: Given that:F=mdvdtFr=-kmvFg=-mg

Q: What is the terminal speed of a 6.00 kg spherical ball that has a radius of 3.00 cm and a drag…

Q: Find the particle's horizontal position x(t) and velocity v(x) at any point in a fluid whose drag…

A: (a) Suppose a particle is traveling with initial speed v0 and enters a region where it experiences a…

Q: Find the velocity of the Aircraft if you know that, the density of the air ( f 1200 kg/m3) ,P total…

A: Given value --- density = 1200 kg/m3 . Ptotal = 1400 Pa . Pstatic = 1100 Pa . We have to…

Q: A rod of length 59 cm and mass 1.8 kg is suspended by two strings which are 41 cm long, one at each…

A: When the string on the side B is cut, there will be initial rotation of the rod about the point…

Q: Consider two blocks connected by a string (call this the internal string) and being pulled…

A: (a) The acceleration of the system be given as,…

Q: Legend has it that Archimedes was asked by King Hiero of Syracuse to determine whether a crown was…

A: Weight of crown (WC)=8.3 N Tension in the string (T)=7.81 N

Q: The force on an object moving through a viscous fluid (like honey) is F = -bv, where v is the speed…

A: Given data: Force on an object F = -bv Here, v = speed of the object Required: SI unit of b

Q: A bird of mass 2 kg is flying at 10 m s horizontal and vertical components of the Coriolis force…

A: Coriolis force is a velocity dependent force and this is given by F→=-2mω→×v→where ω is the angular…

Q: A ball is falling through air. Calculate the terminal speed (a positive number, in m/s) if these…

A: Mass of the ball, Acceleration due to gravity, Coefficient of air resistance,

Q: A fish is swimming through water at a terminal velocity (constant maximum velocity) of 0.5 m/s…

A: At terminal velocity, the net force is equal to zero. Fnet=Fpush-Fdrag0=Fpush-FdragFpush=Fdrag The…

Q: What does F stand for in the following equation? Gm,m2 F = O a. Friction O b. Gravitational force c.…

Q: Newton's Third Law states that: O a) A particle remains at rest or continues to move with a uniform…

A: Required: The statement of the Newton's Third Law

Q: A racquetball has a radius of 0.0295 m. The drag coefficient of the ball is 0.35, and the density of…

Q: What is the net external force on an object in freefall on Earth if you were to neglect the effect…

A: Dear student Under free fall there acts an acceleration fue to gravity on the object by earth's…

Q: A diver has a mass of 91 kg and a volume of 0.04 m^3. What is the downwards acceleration, in m/s^2,…

A: Draw the free body diagram of the diver. Here, B represents the buoyancy force, W represents the…

Q: A rod of length 60 cm and mass 1.8 kg is suspended by two strings which are 40 cm long, one at each…

Q: Find the particle's horizontal position x(t) and velocity v(x) at any point in a fluid whose drag…

A: Consider a particle initially moving with speed v0 encounters a drag force Fdrag.

Concept explainers

Newton’s Third Law of Motion

The horse pulls the cart and the cart pulls the horse in response as per Newton third law. So the big question is, “Don’t the two forces cancel each other? How does the cart accelerate?”

Question

100%

Find the particle's horizontal position x(t) and velocity v(x) at any point in a fluid whose drag force is expressed as

F_drag = 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 at with a velocity v0.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step by step

Solved in 4 steps with 4 images

SEE SOLUTION Check out a sample Q&A here

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

Like friction, drag force opposes the motion of a particle in a fluid; however, drag force depends on the particle's velocity. Find the expression for the particle's velocity v(x) as a function of position at any point x 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. Assume that the particle is constrained to move in the x-axis only with an initial velocity v0. Solution: The net force along the x-axis is: ΣF = -F = m then: -mv = m Since acceleration is the first time derivative of velocity a = dv/dt, -mv = m We can eliminate time dt by expressing, the velocity on the left side of the equation as v = dx/dt. Manipulating the variables and simplifying, we arrive at the following expression / = -k "Isolating" the infinitesimal velocity dx and integrating with respect to dx, we arrive at the following: = v0 - which shows that velocity decreases in a linear manner.
Problem Like friction, drag force opposes the motion of a particle in a fluid; however, drag force depends on the particle's velocity. Find the expression for the particle's velocity v(x) as a function of position at any point x 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. Assume that the particle is constrained to move in the x-axis only with an initial velocity vo- Solution: The net force along the x-axis is: ΣF-F = m then: mv = m Since acceleration is the first time derivative of velocity a = dv/dt, mv = m We can eliminate time dt by expressing, the velocity on the left side of the equation as v = dx/dt. Manipulating the variables and simplifying, we arrive at the following expression = -k "Isolating" the infinitesimal velocity dx and integrating with respect to dx, we arrive at the following: = vo - which shows that velocity decreases in a linear manner.
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 v0.
A spherical particle falling at a terminal speed in a liquid must have the gravitational force balanced by the drag force and the buoyant force. The buoyant force is equal to the weight of the displaced fluid, while the drag force is assumed to be given by Stokes Law, Fs = 6πrηv. Show that the terminal speed is given by v = (2R2 g/9η) . (ρs − ρ1) , where R is the radius of the sphere, ρs is its density, and ρ1 is the density of the fluid, and η the coefficient of viscosity.
Kayaking is a great example of multiple drag forces. Where a person has to deal with currents in the water and air to propel themselves forward. In this problem, the water is moving at a velocity of 1.7 m/s directly in the direction you are trying to row. When considering this water, the area in contact with the water is .05 m^2, the drag coefficient is 1.02 with normal water density. You are moving at a velocity of 3 m/s, while the air is blowing against you with a velocity of 2.7 m/s (head wind). For the air, you have an area in contact of .5 m^2, and a drag coefficient of 1.75. Normal air density is present. In order to accomplish your time goal, you need a net force propelling you downstream of 175 newtons, how much force are you applying with the paddle to achieve this goal?
An object is released from rest while immersed within a fluid. The terminal speed of the object is measured to be 8.34 m/s. What was the speed of the object 1.551 s after being released? Let the resistive force be given by R = -bv (Assume that the gravitational force also acts)
What is most nearly the terminal velocity of a 50mm diameter solid aluminum sphere falling in air? the sphere has a coefficient of drag of 0.5, density of aluminum is 2650 kg/m^3 , and density of air is 1.225 kg/m^3.Answer: 53 m/s
The drag force, D, on a plate moving with a velocity of (40.0 ± 0.2) km/h through air of density p = ( 1.200 ±0.010) kg/m3, with a surface area of (100.00 ± 0.5mm) x (30.00 ± 0.05cm) is given by D = Cd p AV² where Ca= 2.1 is a non-dimensional constant. What is the drag force D? 30.00 cm 100.00mm O D = 9.33 ± 0.233 N D = 8.9±0.2kg D =0.89±0.22 N D = 9.33 ± 2.33 x 101 N D = 9.3 ± 0.2 N
Prove that in Fluid Mechanics we have : V² (V.v) V = v (5) - v × (v × v)
An 0.90-m-diameter, 1.1-m-high garbage can is found in the morning tipped over due to high winds during the night. Assuming the average density of the garbage inside to be 150 kg/m3 and taking the air density to be 1.25 kg/m3, estimate the wind velocity during the night when the can was tipped over. Take the drag coefficient of the can to be 0.7.
A diving pool that is 4 m deep and full of water has a viewing window on one of its vertical walls. Find the force on a window that is a circle, with a radius of 2 m, tangent to the bottom of the pool. Use 1000 kg/m³ for the density of water and 9.8 m/s² for the acceleration due to gravity. Using the center of the window as the origin, find the width function w(y) for each value of y on the face of the window. w(y) =
Find the terminal velocity (in m/s) of a spherical bacterium (diameter 1.89 µm) falling in water. You will first need to note that the drag force is equal to the weight at terminal velocity. Take the density of the bacterium to be 1.10 ✕ 103 kg/m3. (Assume the viscosity of water is 1.002 ✕ 10−3 kg/(m · s).)