Larry and Balky set up an experiment to analyze the motion of a marble as it rolled down an incline. They started the marble at
2 answers:
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To answer the two questions, we need to know two important equations involving centripetal movement:
v = ωr (ω represents angular velocity <u>in radians</u>)
a =
Let's apply the first equation to question a:
v = ωr
v = ((1800*2π) / 60) * 0.26
Wait. 2π? 0.26? 60? Let's break down why these numbers are written differently. In order to use the equation v = ωr, it is important that the units of ω is in radians. Since one revolution is equivalent to 2π radians, we can easily do the conversion from revolutions to radians by multiplying it by 2π. As for 0.26, note that the question asks for the units to be m/s. Since we need meters, we simply convert 26 cm, our radius, into meters. The revolutions is also given in revs/min, and we need to convert it into revs/sec so that we can get our final units correct. As a result, we divide the rate by 60 to convert minutes into seconds.
Back to the equation:
v = ((1800*2π)/60) * 0.26
v = (1800*2(3.14)/60) * 0.26
v = (11304/60) * 0.26
v = 188.4 * 0.26
v = 48.984
v = 49 (m/s)
Now that we know the linear velocity, we can find the centripetal acceleration:
a =
a =
a = 9234.6 (m/)
Wow! That's fast!
<u>We now have our answers for a and b:</u>
a. 49 (m/s)
b. 9.2 * (m/
)
If you have any questions on how I got to these answers, just ask!
- breezyツ
Answer:
We need about 8769 meters of wire to produce a 2.6 kilogauss magnetic field.
Explanation:
Recall the formula for the magnetic field produced by a solenoid of length L. N turns, and running a current I:
So, in our case, where B = 2.6 KG = 0.26 Tesla; I is 3 amperes, and L = 0.57 m, we can find what is the number of turns needed;
Therefore we need about 39312 turns of wire. Considering that each turn must have a length of , where D is the diameter of the plastic cylindrical tube, then the total length of the wire must be:
We can round it to about 8769 meters.