Question

1. you pull a pendulum up and let go, watching it swing back and forth. ignoring any outside force that would slow the pendulum. select all statements that are true and would explain the kinetic and potential energy of the pendulum at three points of its swing according to the conservation of energy:

a. at the top of the swing
b. halfway from the top to the bottom of the swing.
c. at the bottom of the swing.
(4 points)
the bottom of the swing has all kinetic energy and no potential energy.
the bottom of the swing has some potential energy and some kinetic energy.
the top of the swing has more potential energy and some kinetic energy.
the total energy at the bottom would decrease.
the middle of the swing has some kinetic energy and some potential energy.
the total energy would stay the same throughout the swing of the pendulum.
the top of the swing has all potential energy and no kinetic energy.

Explanation:

• For the bottom of the swing (point C):
• According to the conservation of mechanical energy \(E = E_{k}+E_{p}\) (where \(E_{k}=\frac{1}{2}mv^{2}\) is kinetic energy and \(E_{p} = mgh\) is potential energy, \(m\) is mass, \(v\) is velocity, \(g\) is the acceleration due to gravity, and \(h\) is height). At the lowest point \(h = 0\), so \(E_{p}=0\) and \(E = E_{k}\).
• For the middle of the swing (point B):
• There is a non - zero height \(h\) (so \(E_{p}=mgh>0\)) and a non - zero velocity \(v\) (so \(E_{k}=\frac{1}{2}mv^{2}>0\)), so \(E = E_{k}+E_{p}\) with both \(E_{k}\) and \(E_{p}\) non - zero.
• For the top of the swing (point A):
• At the extreme position (top of the swing), the velocity \(v = 0\) (momentarily at rest), so \(E_{k}=0\) and \(E = E_{p}\) (maximum height \(h\) gives maximum potential energy).
• For the total energy:
• Since there is no non - conservative force (ignoring outside forces that slow the pendulum), by the law of conservation of mechanical energy \(E=\text{constant}\) throughout the motion.

Answer:

• The bottom of the swing has all kinetic energy and no potential energy.
• The middle of the swing has some kinetic energy and some potential energy.
• The total energy would stay the same throughout the swing of the pendulum.
• The top of the swing has all potential energy and no kinetic energy.