The Jokerfish has set a devious trap for Batpenguin, using his own son Nemo as bait. The Jokerfish attaches a very heavy

[answerhappygod]

The Jokerfish has set a devious trap for Batpenguin, using his
own son Nemo as bait. The Jokerfish attaches a very heavy bowling
ball of mass M = 300kg to a long wire of length ℓ=30.0m,
then attaches the other end of the wire to the incredibly vaulted
ceiling of his Jokertower so that the bowling ball hangs at rest
just above the ground without touching. The Jokerfish then pulls
the bowling ball sideways along its arc of constant radius from the
ceiling until it touches the side wall, where Jokerfish attaches it
with an electromagnet. Jokerfish then puts Nemo in a big plastic
bag with water in it and places him on the floor directly beneath
the ceiling attachment of the wire, where the bowling ball had been
hanging at rest. He then lies in wait for Batpenguin to arrive.
1. Since the wire is so long, the bowling ball attached to the
wall is still hanging at a small angle of 0.34 radians
from its vertical equilibrium point. How far is Nemo away from the
wall where the bowling ball is attached (in meters)?
2. Batpenguin is only 0.5 m tall and has flippers that only
reach up to the top of her head, but she can jump 1.0 m off the
ground. Can Batpenguin reach where the bowling ball has been
attached to the wall? (True = Yes, False = No. Explain your answer
in your write-up.)(T/F)
3. The Jokerfish is planning to use his trusty jokerremote
to release the bowling ball from the wall so that it swings down
like a pendulum to bash Batpenguin as she is finding a way to save
Nemo from the bag of water. How long does Batpenguin have (in
seconds) to save Nemo after Jokerfish pushes the release button on
the remote? (Hint: What fraction of a pendulum period does the
bowling ball have to travel to reach the bottom of its arc? Assume
small enough angles for the pendulum to oscillate
harmonically.)
4. How fast will the bowling ball be moving (in meters per
second) when it reaches the bottom of its arc where Nemo is?
(Hint: Think about energy conservation for a simpler solution,
though you can also think about torque and angular
acceleration.)
5. When the bowling ball reaches the bottom of its arc
where Nemo is, the tension in the wire will be (explain your answer
carefully in your write-up):
A. Less than the tension in the wire when the bowling ball was
hanging at rest.
B. Greater than the tension in the wire when the bowling ball
was hanging at rest.
C. Palpable.
D. Equal to the tension in the wire when the bowling ball was
hanging at rest.
6. Batpenguin suspected foul play from the Jokerfish so
secretly arrived at the jokertower earlier and climbed up the side
to the top. When Jokerfish is not looking, Batpenguin opens a
secret hatch in the ceiling and hangs upside down next to where the
wire is attached and unhooks it. Not wanting to drop the wire and
cause a ruckus, Batpenguin loops it over a frictionless pulley
attached to the ceiling where the wire used to be attached
directly, then attaches it to another 300kg bowling ball that
happened to be on the top of the tower. Once attached, Batpenguin
lets the second bowling ball hang from one side of the pulley while
the original bowling ball still hangs from the other side while
still attached to the side wall. The 20 kg Batpenguin then hangs
upside down from the bottom of the newly attached bowling ball and
screeches loudly, which startles the Jokerfish into pressing the
button on the remote.
Explain carefully what you think will happen when the
electromagnet releases the original bowling ball from the side
wall. Is Nemo safe? Defend your answer with good pictures and
reasoning.
(Hint: This problem is challenging to solve exactly, but you
should be able to estimate what will happen using good diagrams and
by thinking through how the motion changes over a sequence of time
steps. Do you best to tell a convincing story! I want to see how
you are reasoning through the problem here, not necessarily whether
you manage to get the correct answer.)