Dynamics

A particle of mass m starts from rest and slides on a polished track around a vertical circular loop of radius a as shown. Show that the minimum starting height h above the bottom of the loop in order that the particle will leave the track at any point is h=5a/2.

  1. 👍 0
  2. 👎 0
  3. 👁 226
  1. at top of loop centripetal acceleration = g or it leaves the track

    g = v^2/a

    height at top of loop = 2 a
    potential energy at top of loop = m g h = 2 m g a
    total energy at top of loop = .5 m v^2 + 2 m g a
    = .5 m g a + 2 m g a
    = 2.5 m g a
    so
    h = 2.5 a

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. Physics

    A 2.0 kg mass starts from rest and slides down an inclined plane 8.0 X 10^-1 m long in .50s. what net force is acting on the mass along the incline. I have no idea how to do this I don't know why they just didn't say .8m the back

  2. Physics

    I need help with this question with explanation. Thanks A particle of mass m starts from rest at position x = 0 and time t = 0. It moves along the positive x-axis under the influence of a single force Fx = bt, where b is a

  3. physics

    Two forces, 1 = (3.85 − 2.85) N and 2 = (2.95 − 3.65) N, act on a particle of mass 2.10 kg that is initially at rest at coordinates (−2.30 m, −3.60 m). (a) What are the components of the particle's velocity at t = 11.8 s?

  4. Physics

    A ball of mass 522 g starts at rest and slides down a frictionless track, as shown below. It leaves the track horizontally, striking the ground a distance x = 0.81 m from the end of the track after falling a vertical distance h2 =

  1. physics

    A block of mass 0.78kg starts from rest at point A and slides down a frictionless hill of height h. At the bottom of the hill it slides across a horizontal piece of track where the coefficient of kinetic friction is 0.29. This

  2. Physics (Algebra-based)

    A block starts at rest and slides down a frictionless track except for a small rough area on a horizontal section of the track.It leaves the track horizontally, flies through the air, and subsequently strikes the ground. gravity=

  3. Physics

    A boy starts at rest and slides down a frictionless slide as in the figure below. The bottom of the track is a height h above the ground. The boy then leaves the track horizontally, striking the ground a distance d as shown. Using

  4. physics

    In Figure 8-50, a block slides along a track from one level to a higher level after passing through an intermediate valley. The track is frictionless until the block reaches the higher level, where a frictional force stops the

  1. Physics

    A small block of mass m = 1.3 kg slides, without friction, along the loop-the-loop track shown. The block starts from the point P a distance h = 54.0 m above the bottom of the loop of radius R = 19.0 m. What is the kinetic energy

  2. Physics

    A particle of mass m1 = 2.5 kg moving along the x axis collides with a particle of mass m2 = 4.9 kg initially at rest. The incoming particle is deflected in the direction 22 degrees above the x axis, whereas the target particle

  3. physics

    A m = 2.51 kg mass starts from rest and slides a distance d down a frictionless theta = 34.6° incline. While sliding, it comes into contact with an unstressed spring of negligible mass. The mass slides an additional 0.220 m as it

  4. PHysics!!

    Starting from rest at a height equal to the radius of the circular track, a block of mass 25 kg slides down a quarter circular track under the influence of gravity with friction present (of coefficient μ). The radius of the track

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