A test projectile was fired horizontally at v0 velocity into a viscous liquid. Since the decelerating force is directly proportional to the square of the velocity, the value of the acceleration is a = - kv2 Here k is a constant. Derive a relation for each of the distance D traveled in the liquid until the intensity of the velocity drops to v0 / 2, and the time t in the meantime. Ignore any vertical movement.

A test projectile was fired horizontally at v0 velocity into a viscous liquid. Since the decelerating force is directly proportional to the square of the velocity, the value of the acceleration is a = - kv2 Here k is a constant. Derive a relation for each of the distance D traveled in the liquid until the intensity of the velocity drops to v0 / 2, and the time t in the meantime. Ignore any vertical movement.

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

Given that the velocity of a particle in rectilinear motion varies with the displacement xaccording to the equation = v=bx^-3 where: b is a positive constant, find the force acting on the particle as a function of x.(Hint: F= ma= mv dv/dx.)
A firefighter, whose mass (including clothing and equipment) is m = 105kg, hears the alarm and slides down the pole with a constant downward acceleration of magnitude a = 3.92 meters per squared second.What would the expression for the magnitude of the force F, exerted on the firefighter by the pole be? Especially in terms of the variables from the problem statement as well as g for the acceleration due to gravity.
A 4.0 kg object has a velocity of 3i m/s at one instant. Eight seconds later, its velocity is (8i + 10j) m/s. Assuming the object was subject to a constant net force, find (a) the components of the force and (b) its magnitude. show complete solution
Consider the 63 kg ice skater being pushed by two others shown in the figure. The coefficient of static friction is μs=0.4 and kinetic is μk=0.02.Randomized Variablesm = 63 kgF1 = 238 NF2 = 175 N Find the magnitude of Ftot, the total force exerted on her by the others, given that the magnitudes F1 and F2 are 238 N and 175 N, respectively in Newtons. Find the direction of Ftot (in degrees relative to the horizontal), the total force exerted on her by the others, given that the magnitudes F1 and F2 are 238 N and 175 N, respectively .What is the maximum value of the static friction force, in Newtons, that can act on the skater before she moves? What is her acceleration assuming she is already moving in the direction of Ftot in m/s2?
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.
If the vector components of the position of a particle moving in the xy plane as a function of time are x(t) = bt2 and y(t) = ct3, where b and c are positive constants, b has dimensions of length per time squared, and c has dimensions of length per time cubed, when is the angle between the net force on the particle and the x axis equal to 45°? (Use the following as necessary: b, c. Enter an answer greater than 0.)
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.
A block of mass M with a contact area A slides down an inclined plane with a coefficient of friction of 0.4 and travels a distance L in time T. How long would it take another block with the same mass and composition , but with contact area 2A to slide at the same distance L?
A block with mass m1 = 9.2 kg rests on the surface of a horizontal table which has a coefficient of kinetic friction of μk = 0.58. A second block with a mass m2 = 10.8 kg is connected to the first by an ideal string passing over an ideal pulley such that the second block is suspended vertically. The second block is released from rest, and motion occurs. Using the variable T to represent tension, write an expression for the sum of the forces in the y-direction, ΣFy, for block 2. Using the variable T to represent tension, write an expression for the sum of the forces in the x-direction, ΣFx for block 1. Block 1 accelerates along the tabletop, in the horizontal direction, while block 2 moves vertically. With the coordinate system provided in the drawing, we may write a⃗ 1=a1i^a→1=a1i^ and a⃗ 2=a2y^a→2=a2y^. Write an expression that relates the vertical component of the acceleration of block 2 to the horizontal component of the acceleration of block 1. Write an expression using the…
A block with mass m1 = 9.2 kg rests on the surface of a horizontal table which has a coefficient of kinetic friction of μk = 0.58. A second block with a mass m2 = 10.8 kg is connected to the first by an ideal string passing over an ideal pulley such that the second block is suspended vertically. The second block is released from rest, and motion occurs. Using the variable T to represent tension, write an expression for the sum of the forces in the y-direction, ΣFy, for block 2. Using the variable T to represent tension, write an expression for the sum of the forces in the x-direction, ΣFx for block 1. Block 1 accelerates along the tabletop, in the horizontal direction, while block 2 moves vertically. With the coordinate system provided in the drawing, we may write a⃗ 1=a1i^a→1=a1i^ and a⃗ 2=a2y^a→2=a2y^. Write an expression that relates the vertical component of the acceleration of block 2 to the horizontal component of the acceleration of block 1. Write an expression using the…
Recall that Newton’s Equation of Motion for a Body of Mass, m, is F = m(dv/dt). Assume the Initial Velocity of the Projectile is v0, and the Gravitational Acceleration Constant is g, where the Gravitational Force is Fg = -mg. Note that the Maximum Height will Occur at a Time, tm, when the Velocity Goes to Zero, v(tm) = 0. a) Simply Solve the Equation of Motion for the Velocity as a Function of Time, and Determine the Time it Takes the Projectile to Reach the Maximum Height, tm, As a Function of the Given Parameters. b) Include a Force of Air Resistance that is Proportional to the Velocity of the Form Fr = -kmv. Again, Solve the Equation of Motion for the Velocity as a Function of Time, by Direct Integration or by Choosing an Appropriate Ansatz Form for the Solution. Again, Determine an Expression for the Time it Takes the Projectile to Reach the Maximum Height, tm, As a Function of the Given Parameters. c) Finally, Compare the Two Results by First Checking that they Agree for a Small…
A particle of mass 0.75 kg is subject to a force that is always pointed towards the East but whose magnitude changes linearly with time t. The magnitude of the force is given as F = 5t, and has units of newtons. Let the x-axis point towards the East. Determine the change in the velocity Δv, in meters per second, of the particle between t = 0 and t = 1.2 sec. Determine the change in x-coordinate in meters of the particle Δx between t = 0 and t = 1.2 if the initial velocity is 13.4 m/s, and pointed in the same direction as the force.