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: EF = -F 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.

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: EF = -F 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.

University Physics Volume 1

18th Edition

ISBN:9781938168277

Author:William Moebs, Samuel J. Ling, Jeff Sanny

Publisher:William Moebs, Samuel J. Ling, Jeff Sanny

Chapter5: Newton's Law Of Motion

Section: Chapter Questions

Problem 77AP: (a) Find an equation to determine the magnitude of the net force required to stop a car of mass m,...

See similar textbooks

Similar questions

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.
Problem 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. Solution: a) To solve for the position as a function of time x(t), we construct the net force in the x-axis as ∑F = -F_____ = m_____ Then: -m_____v = m_____ since: a = dv/dt then -m_____v = m_____ by integrating, we obtain the following expression: _____ = v0e_____ Further, employing the rules of integration results to the following expression for position as a function of time x= (v0/_____)( _____ - e _____ ) as t -> ∞ , the position becomes x = v0/k b) To solve for the velocity as a function of position v(x), we construct the net force in the x-axis as follows ∑F = -F _____= m_____ Then: -m_____v = m_____ since: a = dv/dt then -m_____v = m_____ We can eliminate time by expressing, the velocity…
In the expression of Newton’s second law for a system of constant mass, F=ma : O The vector representing the net force must pass through the center of mass of the system. O The acceleration term represents the acceleration of a particle located at the center of mass. O The internal forces must be considered when calculating the force term. O The force term can be calculated by considering only the external forces.
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 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. To solve for the position as a function of time x(t), construct the net force in the x-axis. Further, employ the rules of integration results to the following expression for position as a function of time. To solve for the velocity as a function of position v(x), we construct the net force in the x-axis, then, eliminate time by expressing, the velocity on the left side of the equation. By integrating and applying the limits, we then shall arrive with a velocity that decreases in a linear maner.
When rebuilding his car's engine, a physics major must continuously exert 1.16 ✕ 102 N of force to insert a dry steel piston as it slides into a steel cylinder. What is the normal force (in N) between the piston and cylinder? A.) (Enter the magnitude.) B.)What force (in N) would he have to continuously exert if the steel parts were oiled? (Enter the magnitude.)
The human head can be considered as a3.3-kg cranium protecting a 1.5-kg brain, with a small amount ofcerebrospinal fluid that allows the brain to move a little bit insidethe cranium. Suppose a cranium at rest is subjected to a force of2800 N for 6.5 ms in the forward direction. (a) What is the finalspeed of the cranium? (b) The back of the cranium then collideswith the back of the brain, which is still at rest, and the two movetogether. What is their final speed? (c) The cranium now hits anexternal object and suddenly comes to rest, but the brain continues to move forward. If the front of the brain interacts with thefront of the cranium over a period of 15 ms before coming to rest,what average force is exerted on the brain by the cranium?
q A .22 rifle bullet, traveling at 350 m/s, strikes a large tree, which penetrates to a depth of 0.130 m. The mass of the bullet is 1.80 g. Assume constant retarding force. (a) How much time is required for the bullet to stop? (b) What force, in newtons, does the tree exert on the bullet?
What net external force is exerted on a 1350-kg artillery shell fired from a battleship if the shell is accelerated at 1.80 ✕ 104 m/s2? (Enter the magnitude.) NWhat is the magnitude of the force exerted on the ship by the artillery shell? N
A person , sunbathing on a warm day, is lying horizontally onthe deck of a boat. Her mass is 59 kg, and the coefficient of staticfriction between the deck and her is 0.70. Assume that the person ismoving horizontally, and that the static frictional force is the onlyforce acting on her in this direction . (a) What is the magnitude of the static frictional force when the boat moves with a constant velocity of +8.0 m/s? (b) The boat speeds up with an acceleration of 1.6 m/s2 and she does not slip with respect to the deck . What is the magnitude of the static frictional force that acts on her? (c) What is the magnitude of the maximum acceleration the boat can have before she begins to slip relative to the deck ?
A person , sunbathing on a warm day, is lying horizontally onthe deck of a boat. Her mass is 59 kg, and the coefficient of staticfriction between the deck and her is 0.70. Assume that the person ismoving horizontally, and that the static frictional force is the onlyforce acting on her in this direction . (a) What is the magnitude of the static frictional force when the boat moves with a constant velocity of +8.0 m/s? (b) The boat speeds up with an acceleration of 1.6 m/s2 and she does not slip with respect to the deck . What is the magnitude of the static frictional force that acts on her? (c) What is the magnitude of the maximum acceleration the boat can have before she begins to slip relative to the deck ? If you have answered this please skip. Please put the correct formulas and process. thanks
a. During a rocket launch, an astronaut experiences a “g-force” (actually anacceleration) of 3.0 gs [upward], which is equal to three times the accelerationdue to gravity. If the astronaut weighs 79.4 kg, what is her apparent weight duringthe acceleration? b. When the astronaut enters the ISS (International Space Station), she is in “freefall,” where the only force acting on her is the force of gravity applied by theEarth. What happens to her true weight and her apparent weight as she entersthe ISS? Explain.