A 0.500 kg particle moves in a circle of R=0.0150 m at constant speed. The time for 20 complete revolutions is 31.7 s. What is the period T of the motion? What is the speed of the particle? What is the centripetal acceleration of the particle? What is the centripetal force on the particle?
Sorry just re-learning after 30+ years.I had part of it answered however, the 4th and 5th question info was pertaining to questions 3 and 4 so I had to ask the question from the beginning. My answer was T = 1.585 s.
for speed I calc 0.942/1.585s=0.594...right?
my real problem was I thought Ac of particle...use Ac= v2/r? Right? And not sure on force...Thanks
force=mass*centripetal acceleration
Ok so F=MA thanks, I do appreciate especially since I am going to 35th reunion and went back to school. Much harder than I remembered. Again thanks
Well, let's address those questions one by one, shall we?
First up, the period T of the motion is simply the time it takes for one complete revolution. Since we're given that the time for 20 complete revolutions is 31.7 seconds, we can find the period by dividing that time by 20: T = 31.7 s / 20 = 1.585 s.
Now, to find the speed of the particle, we need to remember that the formula for speed is distance (in this case, the circumference of the circle) divided by time. Since the particle moves in a circle of radius R = 0.0150 m, its speed can be calculated as follows: speed = (2 * π * R) / T = (2 * 3.14 * 0.0150 m) / 1.585 s ≈ 0.298 m/s.
Moving on to centripetal acceleration, we know that the formula for centripetal acceleration is given by a = (v^2) / R, where v is the speed of the particle and R is the radius of the circle. Plugging in the values we've already calculated: a = (0.298 m/s)^2 / 0.0150 m ≈ 5.92 m/s^2.
Lastly, the centripetal force on the particle can be found using the equation F = m * a, where m is the mass of the particle and a is the centripetal acceleration. In this case, since the particle has a mass of 0.500 kg and the centripetal acceleration is approximately 5.92 m/s^2, the centripetal force is: F = 0.500 kg * 5.92 m/s^2 ≈ 2.96 N.
So, to recap:
- The period T of the motion is approximately 1.585 s.
- The speed of the particle is around 0.298 m/s.
- The centripetal acceleration of the particle is roughly 5.92 m/s^2.
- The centripetal force on the particle is approximately 2.96 N.
Hope that helps! Let me know if you have any more questions.
To find the period T of the motion, we can use the formula T = time / number of revolutions. In this case, the time for 20 complete revolutions is given as 31.7 s, so we can calculate the period as follows:
T = 31.7 s / 20 revolutions = 1.585 s/revolution
Therefore, the period T of the motion is 1.585 s.
To find the speed of the particle, we can use the formula v = 2πR / T, where R is the radius of the circle and T is the period. In this case, the radius is given as 0.0150 m and the period is 1.585 s. Plugging in these values, we get:
v = (2π * 0.0150 m) / 1.585 s = 0.0946 m/s
Therefore, the speed of the particle is 0.0946 m/s.
To find the centripetal acceleration of the particle, we can use the formula ac = v^2 / R, where v is the speed of the particle and R is the radius of the circle. Plugging in the values, we get:
ac = (0.0946 m/s)^2 / 0.0150 m = 0.60 m/s^2
Therefore, the centripetal acceleration of the particle is 0.60 m/s^2.
To find the centripetal force on the particle, we can use the formula F = m * ac, where m is the mass of the particle and ac is the centripetal acceleration. In this case, the mass is given as 0.500 kg and the centripetal acceleration is 0.60 m/s^2. Plugging in these values, we get:
F = 0.500 kg * 0.60 m/s^2 = 0.30 N
Therefore, the centripetal force on the particle is 0.30 N.
This is pretty simple and straightforward, and I am wondering what your question is.
You are given period: T=31.7s/20
Speed = distance/time=2PI*R/T
Centripetal acceleration? speed^2/R
Frankly, your teacher is to easy.