Physics - KE/rotation

In Figure 11-32 (which shows a ball at the top of an incline, at the bottom of the incline a loop begins with radius R and Q a point on the loop lined up with the center of the loop), a solid brass ball of mass m and radius r will roll without slipping along the loop-the-loop track when released from rest along the straight section.
(a) From what minimum height h above the bottom of the track must the marble be released to ensure that it does not leave the track at the top of the loop? (The radius of the loop-the-loop is R = 2.16 m. Assume R>>r, and the mass of the ball is 3.2 kg.)
(b) If the brass ball is released from height 6R above the bottom of the track, what is the magnitude of the horizontal component of the force acting on it at point Q?
*My work so far*
for finding I for a sphere I believe that I need to use I = (2/5)MR^2 which is I = 5.97 kg*m^2. Can I use V = sqrt(gR) to find the V...if so, V = 4.6 m/s. I am not sure what to do now. Can I use -Fs = m(-V^2/R)???


To stay on track at the top of the loop, MV^2/R must equal or exceed Mg there. Use conservation of enewrgy to relate the velocity there to the distance of the release point above the bottom of the loop.
The total kinetic energy when the velocity is V is
KE = (1/2) M V^2 + (1/2)(2/5)Mr^2*(V/r)^2 = (3/5) M V^2
If H is the initial height of the ball above the bottom of the loop, then at the top of the loop, 2R from the bottom,
MgH = (3/5) M V^2 + 2 MgR
V^2 = (5/3) gH -(10/3)gR > g
Solve for the minimum required H

  1. 👍
  2. 👎
  3. 👁

Respond to this Question

First Name

Your Response

Similar Questions

  1. Geometry

    the two figures below are congruent. Find the measure of the angle that isn't labeled on either figure. the one on the left shows a 41* degree on the top right, a 86* degree on the bottom right, a 10 in the middle of the left

  2. Physics

    A 6.0 kg block,starting from rest, slides down a frictionless incline of length 2.0 m. When it arrives at the bottom of the incline its speed is vf. At what distance from the top of the incline is the speed of the block .5 vf

  3. Physics

    A 2.0Kg otter starts from rest at the top of a muddy incline 85 cm long and slides down to the bottom in .50s. What net force acts on the otter along the incline?

  4. Physics

    A 10 kg bowling ball sits at the top of a 10 m hill and then slides down its icy hillside. a. What is the speed of the bowling ball when it reaches the bottom of the hill? b. What is the change in kinetic energy of the system as

  1. Physics

    How do you solve this problem? A ball on the end of a string is revolved at a uniform rate in a vertical circle radius of 72.0 cm, as shown in figure. If its speed is 4.00m/s and its mass is .300 kg. Calculate the tension in the

  2. Physics

    Hello can someone please help me with this physics question and show the work so I can understand? A box at the top of a rough incline possesses 981 joules more gravitational potential energy than it does at the bottom. As the box

  3. Physics (A-level)

    A ball was projected horizontally at a speed of 0.52 m s–1 across the top of an inclined board of width 600 mm and length 1200 mm. It reached the bottom of the board 0.9 s later (Figure 4). Calculate: a the distance travelled by

  4. Physics

    A ball in the shape of a uniform spherical shell (like a soccer ball; I = 2/3 mr2) of mass 1.5 kg and radius 15 cm rolls down a 35 degree incline that is 6.0 m high, measured vertically. The ball starts from rest, and there is

  1. physics

    A frictionless incline is 5.00 m long (the distance from the top of the incline to the bottom, measured along the incline). The vertical distance from the top of the incline to the bottom is 4.03 m. A small block is released from

  2. physics

    A solid sphere of weight 36.0 N rolls up an incline at an angle of 30.0o. At the bottom of the incline the center of mass of the sphere has a translational speed of 4.90 m s-1. Isphere = 2/5mr^2. What is the kinetic energy of the

  3. physics

    A 20. kg block is placed at the top of a 10. meter-long inclined plane. The block starts from rest and slides without friction down the length of the incline. (A diagram shows a height of 5.0 m, the 10. m length of

  4. physics

    A small block is released from rest at the top of a frictionless incline. The distance from the top of the incline to the bottom, measured along the incline, is 3.60 m. The vertical distance from the top of the incline to the

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