physic mechanic

A particle is pushed horizontally by a constant horizontal force of magnitude F, which
starts from the rest at x=0 in the positive ݔ direction. During the movement, it is also
acted by the air resistance force that equivalent to bv, where b is the positive coefficient
and v is the instantaneous velocity of the body.

Find out the acceleration of object at any time t.

  1. 👍
  2. 👎
  3. 👁
  1. F - bv = m a

    a = (F-bv)/m

    1. 👍
    2. 👎
  2. that means

    dv/dt = F/m - (b/m)v
    or
    (b/m) v + dv/dt = F/m

    let v = c (1-e^-kt)
    then dv/dt = cke^-kt
    and
    (b/m)c -(b/m)ce^-kt +cke^-kt = F/m
    when t --> oo, F = bc so c = F/b
    when t = 0, c k = F/m
    so Fk/b =F/m
    so k = b/m
    now
    v = (F/b)( 1-e^-(bt/m) )
    a = dv/dt = (F/b)(b/m)e^-(bt/m)
    or
    a = (F/m)e^-(bt/m)

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. physics

    A 5.3-kg block is pushed 2.3 m up a vertical wall with constant speed by a constant force of magnitude F applied at an angle of θ = 30° with the horizontal, as shown in the figure below. If the coefficient of kinetic friction

  2. Physics

    A 75.0kg bobsled is pushed along a horizontal surface by two athletes. After the bobsled is pushed a distance of 4.5m starting from the rest, its speed is 6.0m/s. Find the magnitude of the net force on the bobsled.

  3. physics

    A 40-kg box is being pushed along a horizontal smooth surface. The pushing force is 15 N directed at an angle of 15° below the horizontal. What is the magnitude of the acceleration (in m/s2) of the crate?

  4. Physics

    A 4.3 kg particle starts from rest and moves a distance of 3.6 m in 2.5 s under the action of a single, constant force. Find the magnitude of the force. Answer in units of N.

  1. college physics

    Two blocks with masses m and M are pushed along a horizontal frictionless furface by a horizontal applied force. The magnitude of the force either of these blocks has on the other is: M being a bigger mass than m of course. I

  2. Physics

    A box has a weight of 120 N and is being pulled across a horizontal floor by a force that has a magnitude of 100 N. The pulling force can point horizontally, or it can point above the horizontal at an angle θ. When the pulling

  3. physics

    A single constant force 18.1 N acts on a particle of mass 2.92 kg. The particle starts at rest at t=0. What is the instantaneous power delivered by the force at t=4.48s? Answer in units of W

  4. physics

    A 5-kg box is pushed across a horizontal floor by a 20-N force that is angled 30 degrees below the horizontal. What is the coefficient of kinetic friction between the box and the floor if the box is pushed at a constant speed?

  1. Physics

    A particle has a charge of +1.5 µC and moves from point A to point B, a distance of 0.18 m. The particle experiences a constant electric force, and its motion is along the line of action of the force. The difference between the

  2. Physics

    A person, sunbathing on a warm day, is lying horizontally on the deck of a boat. Her mass is 59.6 kg, and the coefficient of static friction between the deck and her is 0.696. Assume that she is moving horizontally, and that the

  3. physics

    A 3.90 kg block located on a horizontal frictionless floor is pulled by a cord that exerts a force F=14.1N at an angle theta=32.5degrees above the horizontal, as shown. a.) What is the magnitude of the acceleration of the block

  4. Physics

    A 250-kg crate is being pushed across a horizontal floor by a force P that makes an angle of 30.8 ° below the horizontal. The coefficient of kinetic friction is 0.224. What should be the magnitude of P, so that the net work done

You can view more similar questions or ask a new question.