My oscillating punching bag

Electricity and Magnetism Level 2

I attached my punching bag from the ceiling of my training room by a spring having a force constant 'T' ,Then I attached my longest sword with it(horizontally). The combined mass of the punching bag and the sword measured out to be 'Z' .The sword could slide without friction along two vertical parallel poles which were 'A' distance apart .After setting this all up ,I attached a capacitor of known capacitance 'C' to the poles using some connecting wires . At last I turned on the magnetic field 'S' of that room. Find the time period 'TRP' of the vertical oscillations of my punching bag.

Neglect the electrical resistance of the sword and all the wires.

My training room

P.s. I'm a pacifist and it's just to scare away my nemesis:P

2π\sqrt{\dfrac{Z+C.S^{2}.A^{2}}{T}}

2π\sqrt{\dfrac{Z^{2}+C.S.A}{T}}

2π\sqrt{\dfrac{Z^{2}+C.S^{2}.A^{2}}{T}}

Not enough info. provided

1 solution

Tom Engelsman
May 2, 2021

This will be a very lazy solution. Given that $T$ has units of $N/m = (kg \cdot m)/(m \cdot s^2) = kg / s^2$ and $Z$ has units of $kg$ , the quantity $CS^{2}A^{2}$ must also have units of $kg.$ This yields units $2\pi \cdot \sqrt{(kg)/(kg/s^{2})} = 2\pi \cdot \sqrt{s^2} = seconds$ for the time period.

Choice $\boxed{A}$ is the solution.

Lazy but time efficient 😎👍

Agent T - 1 month, 1 week ago

Definitely a weird contraption pictured above, Agent T.......anyhoot, it's a nice problem that tests your dimensional analysis acumen! Have a great day :)

tom engelsman - 1 month, 1 week ago

Haha , it's to scare away my nemesis :P

Btw you too have a wonderful day! :D

Agent T - 1 month, 1 week ago

My oscillating punching bag

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