Suppose you want to use your knowledge of electric charge and potential to build

Question

Suppose you want to use your knowledge of electric charge and potential to build a
homemade launcher for the ball you chose in Full Solution 1. The launcher would essentially
be a parallel-plate capacitor with a hole in the middle of one plate, connected to a stack of
batteries to provide whatever potential difference is needed to launch the ball at the desired
speed. Released from a position near the positive plate, the ball accelerates towards the
negative plate and is launched through the hole.
Question
Could such a launcher be built, in principle? Decide by calculating how many batteries (of
your choice) would be required to make the launcher work.
Assumptions
1. The ball carries the maximum possible charge (found in Sol 1)
2. The ball is launched from rest
3. Air resistance and gravity can be ignored
4. The total mechanical energy of the ball is conserved while being launched
5. The voltages of the batteries powering the launcher add up; e.g., three 1.5-V batteries
supply a total potential difference of 3(1.5 V) = 4.5 V
You'll need to find the mass of the ball (measure it for yourself, or consult 2+ sources online),
choose the type of battery (household, car, etc.) you want the launcher to use, and choose a
launch speed.
The launch speed is totally up to you, so long as you briefly explain why you chose it.
Suggested: choose a speed typical for the sport the ball comes from. For example, what
should the speed be for a ping-pong ball launcher used to train someone to return gentle
serves (or fast serves)? This kind of information can be looked up online, and should be
checked against common sense.


diameter of a standard golf ball is 42.67 mm or 4.267 X 10-2m
The charge needed to have an Electric Field of 3 X 106 N/C can be found by...
E = kq/r2
q = Er2/k = (3 X 106)(2.1335 X 10-2)2/(9 X 109)
q = 1.52 X 10-7 C
F = (9 X 109)(1.52 X 10-7)2/(4.267 X 10-2)2
F = .114 N

Explanation / Answer

Taking the golf ball into consideration. The typical mass of a golf ball is 45.93 grams, which is 4.593 X 10-2 kg. Additionally, a typical amatuer golfer can generate a ball speed of between 100 mph to 140 mph when Driving a Golf Ball off of a Tee. Taking an average of that, we can say that a typical speed for a golf ball at club impact on the tee is 54m/s

Then, we can determine the typical KE that a golf ball can have right after club impact.

KE = .5mv2 = (.5)(4.593 X 10-2)(54)2 = 66.97 J

So, can you build a launcher to provide that much energy

Electrical Energy from a voltage is found by...

Energy = qV

We are told that q = 1.5 X 10-7 C

so...

66.97 = (1.5 X 10-7)(V)

V = 4.46 X 108 V

That would take 49.61 million 9 volt batteries to provide that power. So in principle, yes, that can be built. But practically, I wouldn't be so sure.

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.