Transcript electrostatic practice problems

Electrostatics – Practice Problems
Problem 1 – Lunar Athletes & Apparent Weight
Problem 2 – Electric Field Safety Net
Problem 3 – Lunar Crater Jumping
Problem 4 – Athlete’s Field
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Copyright - Adam Randall
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q = |0.25| C charge on athlete’s suit
m = 72 kg
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athlete’s mass
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In the future, many Olympic athletes will train on the moon because the moon’s
gravitational force field is nearly 1/6th of the Earth’s. Special training facilities will be
built to maintain variable strength / uniform electric fields inside different rooms.
Athletes will wear electrically charged body suits designed to evenly distribute electrical
force. The result will be a unique training environment able to create apparent weights
ranging from 1/6th mg to 2mg.
A. If the athlete above wanted an apparent weight equal to their weight on the Earth,
they would need this type of charge: Positive or Negative?
B. Calculate the electric field (vector) needed to give an athlete an apparent weight equal
to twice their weight on the Earth.
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Answer 1
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The electric field needed to produce an apparent weight equal to
the athlete’s weight on Earth = 5174 N / C directed downward.
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Coulomb’s Lunar Safety Net
A 72 kg Lunar athlete falls from rest, 15 meters above
the ground, wearing a body suit charged with |0.25| C.
As a built in safety measure a photogate placed 5.0
meters above the ground measures the speed of the
falling athlete and turns on the electric force field
safety net.
10. 0 m
The electric force field safety net is designed to
decelerate an athlete in lunar freefall and bring
them safely to rest on the surface of the floor.
A. The net charge on the suit must be this to
save the athlete: Positive or Negative.
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B. Predict the electric field needed in order to
save the athlete by bringing them to rest on the
floor.
5. 0 m
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Photogate
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Coulomb’s Lunar Safety Net
Answers
A. The athlete needs a net negative charge.
B. The electric field needs to be = 1411 N/C
downward in order to bring the athlete
safely to rest on the floor.
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Photogate
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Consider a 120 kg athlete trying to jump the 125 kilometer wide
lunar crater shown below. Their initial velocity is 4.5 m/s at 45
degrees. If the electric field points up and has a strength of
2.5x103 N/C, predict the minimum net charge the athlete must
have on their body suit to jump the crater?
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Hints
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Decompose the initial velocity vector into components.
• Determine the total time in flight.
•Determine the vertical acceleration using ΔY= 0 meters.
• Use Newton’s 2nd Law to find the charge on jumper.
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The athlete must have at least + 7.8 x 10-2
Coulombs of charge to make the 125
kilometer jump.
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Proble
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Imagine four electrically charged athletes standing on the vertices of a
square 2 meters on a side parallel to the surface of the moon. The two
athletes on the top of the square carry -0.25 Coulombs of charge. The two
athletes on the bottom of the square carry +0.25 Coulombs of charge.
A. Determine the electric field at the exact
center of the square.
2 meters
B. Determine the electric force on a 0.1 gram
water drop with 10,000 extra electrons on it, at
the center of the square.
2 meters
C. Could you use the standard equations of
kinematics to predict the motion of the water
drop through space and time?
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Answer
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Answers
A. The Electric Field = 3.1 x 109 N/C Upwards.
2 meters
B. The Electric Force = 5.1 x 10-6 N Downwards
C. No! The force and therefore the acceleration
changes with location. The electric field is nonuniform.
2 meters
Copyright - Adam Randall