Question

3. (20 points) A pendulum of length L is held with its string horizontal, and then released. The string runs into a peg a distance d below the pivot, as shown in Fig. 2. What is the smallest value of d for which the string remains taut at all times? Hints: (a) What is the speed of the mass at the end of the pendulum when the string first touches the peg? (b) What is the speed of the mass when it reaches the highest point when rotating around the peg with the string remaining taut? (Assume that the speed is large enough so that the pendulum actually reaches the highest possible point.) (c) What is the smallest speed that the pendulum must have at the highest point to keep the string taut? L Figure 2:

          3. (20 points) A pendulum of length L is held with its string horizontal, and then released. The string runs into a peg a distance d below the pivot, as shown in Fig. 2. What is the smallest value of d for which the string remains taut at all times?
Hints:
(a) What is the speed of the mass at the end of the pendulum when the string first touches the peg?
(b) What is the speed of the mass when it reaches the highest point when rotating around the peg with the string remaining taut? (Assume that the speed is large enough so that the pendulum actually reaches the highest possible point.)
(c) What is the smallest speed that the pendulum must have at the highest point to keep the string taut?
L
Figure 2:

3. (20 points) A pendulum of length L is held with its string horizontal, and then released. The string runs into a peg a distance d below the pivot, as shown in Fig. 2. What is the smallest value of d for which the string remains taut at all times?
Hints:
(a) What is the speed of the mass at the end of the pendulum when the string first touches the peg?
(b) What is the speed of the mass when it reaches the highest point when rotating around the peg with the string remaining taut? (Assume that the speed is large enough so that the pendulum actually reaches the highest possible point.)
(c) What is the smallest speed that the pendulum must have at the highest point to keep the string taut?
L
Figure 2:

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