Physics

posted by .

A solid sphere and a thin walled spherical she'll, both with a radius R, are set up to roll down a ramp and through a vertical loop of radius r. From what minimum height, h, does each sphere need to be released in order to make it around the loop?
If the loop has a radius of r= 35cm what speed will each sphere have after it has excited the loop

  • Physics -

    let h be the height above the bottom of the loop, so the excess Penergy is mg(h=2r). That energy is converted to KE, both translational and rotational.

    rotational energy=2/3 mr^2*w^2
    were w=v/r
    rotational energy=2/3 m v^2
    translational energy= 1/2 m v^2
    total energy=mg(h-2r)
    7/6 m v^2=mg(h-2r)
    v^2=6/7 g (h-.35)

    to get that velocity, find the velocity at the top.

    now, to stay on the loop,
    gravity=mv^2/r
    mg=mv^2/r
    v^2=g*r
    So finally, in
    v^2=6/7 g (h-.35) solve for h

    now the total energy at the bottom is 1/2 mv^2(top)+mg(2r)=1/2 mvb^2

    solve for vbottom.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. physics

    Two solid spheres A and B are made from the same material. The mass of sphere B is eight times that of sphere A. If the radius of sphere A is 7.50 cm, what is the radius of sphere B?
  2. college physics

    Two solid spheres A and B are made from the same material. The mass of sphere B is eight times that of sphere A. If the radius of sphere A is 7.50 cm, what is the radius of sphere B?
  3. college physics

    Two solid spheres A and B are made from the same material. The mass of sphere B is eight times that of sphere A. If the radius of sphere A is 7.50 cm, what is the radius of sphere B?
  4. Physics

    Four objects - a hoop, a solid cylinder, a solid sphere, and a thin, spherical shell - each has a mass of 4.59 kg and a radius of 0.252 m. (a) Find the moment of inertia for each object as it rotates about the axes shown in the table …
  5. Physics please help!!

    A 1.94 kg solid sphere (radius = 0.105 m) is released from rest at the top of a ramp and allowed to roll without slipping. The ramp is 0.710 m high and 5.17 m long. When the sphere reaches the bottom of the ramp, what is its total …
  6. Physics

    A sphere with a moment of inertia 0.658mr2 and mass m and radius r rolls without slipping along the track shown on a planet where the acceleration due to gravity is g. It starts from rest at a height h = 4.87R above the bottom of the …
  7. physics

    A solid sphere of mass m and radius r rolls with out slipping along the track.it starts from rest with the lowest point of tthe sphere at aheight h above the bottom of the loop of radius R,much larger than r.(a) what is the minimum …
  8. physics

    A hollow cylinder, a solid cylinder, a hollow sphere, and a solid sphere roll down a ramp without slipping, starting from rest. The ramp is 0.25 m high. All the objects have radius 0.035. What are their final speeds?
  9. physics

    solid sphere,thin walled hollow sphere,solid cylinder from above the ground in the same mass and radius which object reach first the ground?
  10. physics

    a block slides down a frictionless ramp. at the bottom of the ramp is a vertical circular loop with a radius of 75 cm. from what minimum height does the block need to be released in order to make it around the loop?

More Similar Questions