Physics-Mechanics

posted by .

A poorly designed playground slide begins with a straight section and ends with a circular arc as shown in the figure below.
img716.imageshack.us/img716/8381/25746193.jpg
A child starts at point P and slides down both sections of the slide. At some point on the circular arc, the normal force goes to zero and the child loses contact with the ramp.
Assuming the forces of friction are negligible, at what height from the ground will the child become airborne?
Answer in units of m.

  • Physics-Mechanics -

    relate the change in PE from the vertical fall to changes in KE

    KE change: 1/2 m v^2
    height change: 4.9-radius+ radius(1-CosTheta)
    PE change: mg*height change

    check that
    where theta is the angle measured from the point on the circle to the center and the x axis.

    Now, the object flies off when the normal component of weight (mgSinTheta) is equal to centripetal force (mv^2/r)
    set the equal.
    from setting PE change=KE change, you should be able to solve for v^2. Put that into the equation with the forces, and solve for angle.

  • Physics-Mechanics -

    Hi,

    I am confused on the height change.
    By 4.9 did you mean 4.8? and if so do I set it equal to zero to solve?

    is the v in the centripetal force different from the v in KE?

  • Physics-Mechanics -

    yes, 4.8 I was using my memory of the pic as 4.9

    KEchange=PE change
    1/2 m v^2=mg(4.8 - radius+ radius(1-cosTheta)

    solve for v^2
    then put that v^2 in this:
    mv^2/r=mgSinTheta
    and solve for Theta
    You may have some tricky algebra.

    It is the same v in KE, and force.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Physics

    I need help with this physics problem: A child slides down a playground slide; the coefficient of kinetic friction is uk=0.25, and angle that the slide makes with the horizontal is 28.0 degree. She begins from rest and slides through …
  2. Physics

    At a playground, a 18.7 kg child plays on a slide that drops through a height of 2.07 m. The child starts at rest at the top of the slide. On the way down, the slide does a nonconservative work of -318 J on the child. What is the child's …
  3. Physics

    At a playground, a 18.7 kg child plays on a slide that drops through a height of 2.07 m. The child starts at rest at the top of the slide. On the way down, the slide does a nonconservative work of -318 J on the child. What is the child's …
  4. Physics

    A 18 kg child slides down a 4.0 m-high playground slide. She starts from rest, and her speed at the bottom is 2.8 m/s. What is the change in the thermal energy of the slide and the seat of her pants?
  5. physics

    At a playground, a 19.8 kg child plays on a slide that drops through a height of 2.13 m. The child starts at rest at the top of the slide. On the way down, the slide does a nonconservative work of -319 J on the child. What is the child's …
  6. physics

    At a playground, a 19.8 kg child plays on a slide that drops through a height of 2.13 m. The child starts at rest at the top of the slide. On the way down, the slide does a nonconservative work of -319 J on the child. What is the child's …
  7. Physics

    A 17kg child slides down a 2.7m -high playground slide. She starts from rest, and her speed at the bottom is 1.8 m/s. What is the change in the thermal energy of the slide and the seat of her pants?
  8. Physics

    A 17kg child slides down a 2.7m -high playground slide. She starts from rest, and her speed at the bottom is 1.8 m/s. What is the change in the thermal energy of the slide and the seat of her pants?
  9. Physics

    A 17kg child slides down a 2.7m -high playground slide. She starts from rest, and her speed at the bottom is 1.8 m/s. What is the change in the thermal energy of the slide and the seat of her pants?
  10. Physics

    At a playground, a 22kg child plays on a slide that drops through a height of 2.1m. The child starts at rest at the top of the slide. On the way down, the slide does a nonconservative work of -371J on the child. What is the child's …

More Similar Questions