PHYSICS

posted by .

The figure shows a ball with mass m = 0.405 kg attached to the end of a thin rod with length L = 0.516 m and negligible mass. The other end of the rod is pivoted so that the ball can move in a vertical circle. The rod is held horizontally as shown and then given enough of a downward push to cause the ball to swing down and around and just reach the vertically up position, with zero speed there.

(a) What initial speed must be given the ball so that it reaches the vertically upward position with zero speed?
(b) What then is its speed at the lowest point?
(c) What then is its speed at the point on the right level with the initial point?
(d) If the ball's mass were doubled, would the answers to (a) through (c) increase, decrease, or remain the same?

Can I start with h = L - L*cos(theta) = L(1 - cos(theta))? Where do I go from there?

  • PHYSICS -

    (a) Use conservation of energy. To reach the top with zero velocity
    (1/2) M Vo^2 = M*g*L
    Vo = sqrt(2 g L)

    (b) At the lowest point,
    (1/2)MV^2 = (1/2) M Vo^2 + M g L
    V^2 = Vo^2 + 2 g L
    = 4 g L
    V = 2 sqrt(g L)

    (c) What do you think? The P.E. is the same.

    (d) Note that M does not appear in any of the answers above. What does that tell you?

  • PHYSICS -

    Got it, thanks very much!

  • PHYSICS -

    wot m8

  • PHYSICS -

    Ily pls smd

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Physics/Math

    A thin rod, of length L and negligible mass, that can pivot about one end to rotate in a vertical circle. A heavy ball of mass m is attached to the other end. The rod is pulled aside through an angle and released. (a)What is the speed …
  2. Physics

    A thin rod, of length L and negligible mass, that can pivot about one end to rotate in a vertical circle. A heavy ball of mass m is attached to the other end. The rod is pulled aside through an angle and released. What is the speed …
  3. physics

    Figure 8-31 shows a ball with mass m = 1.0 kg attached to the end of a thin rod with length L = 0.56 m and negligible mass. The other end of the rod is pivoted so that the ball can move in a vertical circle. (a) What initial speed …
  4. physics

    Two blocks, each of mass m, are attached to the ends of a massless rod which pivots as shown in Figure 8-40. Initially the rod is held in the horizontal position and then released. Calculate the magnitude and direction of the net torque …
  5. Physics

    The figure below shows a thin rod, of length L and negligible mass, that can pivot about one end to rotate in a vertical circle. A heavy ball of mass m is attached to the other end. The rod is pulled aside through an angle θ and …
  6. Physics

    A thing rod of length L and negligible mass, that can pivot about one end to rotate in a vertical circle. A heavy ball of mass 5.00kg is attached to the other end. The rod is pulled aside through an angle 30.0 degrees and released. …
  7. Physics

    A 2.5 m rod of mass M= 4. kg is attached to a pivot .8m from the left end so that it can rotate vertically. At the left end of the rod is a small object with mass m=1.5kg. A spring with a spring constant k=90N/m is attached to the …
  8. mechanics

    The figure below shows a ball with mass m = 0.299 kg attached to the end of a thin rod with length L = 0.388 m and negligible mass. The other end of the rod is pivoted so that the ball can move in a vertical circle. The rod is held …
  9. Physics

    A mass of 100g is attached to one end of a massless rod, 10cm in length, which is pivoted about the opposite end. The rod is held vertical, with the mass at the top, and released. The rod swings. A. What is the speed of the mass at …
  10. physics

    A rod of length L has a varying density along its length that satisfies: λ(x) =((x^2/L^2)+1)λo where x = 0 is one end of the rod (which has density λo), and x = L is the other end (which has density 2λo). a. Find …

More Similar Questions