a bug is sitting on a long playing record going at a constant speed.
Given: The record is turnning at a constatn reate of 33.3 revloutions per minute. The bug, whose mass is 1.4g, is sitting 12cm from the center of the record.
Find;
a. how long does it take the bug to go around once?
I am not sure if i am overthinking this or not but would it be but would it be like this.
d=2pir = 73.36 cm on 1 revolution. so the bug will travel 73.36cmX33.3 rpm=2442.88cm in one minute, than divide 2442.88cm/60 seconds to = 40.71cm a second. than 73.36cm divide by 40.71 cm/sec = 1.8 seconds for the length of ride?
b. how fast is the bug going?
v=d/t or 40.75 cm/second
c. how much centripetal force acts on the bug.
a,b correct.
Centripetal force= mass*v^2/r
You can work this in the cgs system (centimeter, gram, second) and force will be in dynes, however, I recommend converting to SI units (meters, kg, seconds) and force will be in Newtons.
To answer these questions, we can use the formulas related to circular motion. Let's break it down step by step:
a. How long does it take the bug to go around once?
To calculate the time it takes for the bug to go around once, we need to find the circumference of the circular path that the bug travels. The distance around a circle is given by the formula:
Circumference = 2πr
Here, "r" is the radius of the circle, which is the distance from the center of the record to where the bug is sitting.
Given that the bug is sitting 12 cm from the center of the record, the radius (r) is 12 cm. Plugging this value into the formula, we get:
Circumference = 2π(12 cm) = 24π cm
Now, to find the time it takes for the bug to make one complete revolution, we need to use the given rate of 33.3 revolutions per minute. This means that the bug completes one revolution in 1/33.3 minutes.
To convert this to seconds, we multiply by 60:
Time for one revolution = (1/33.3) * 60 seconds = 1.8 seconds
So, the bug takes 1.8 seconds to go around once.
b. How fast is the bug going?
To find the speed of the bug, we divide the distance traveled by the time taken. We found earlier that the circumference of the circular path is 24π cm, and the time for one revolution is 1.8 seconds.
Speed = Distance / Time
= (24π cm) / (1.8 seconds)
≈ 13.3 cm/s
Therefore, the bug's speed is approximately 13.3 cm/s.
c. How much centripetal force acts on the bug?
The centripetal force is the force that keeps the bug moving in a circular path. It can be calculated using the formula:
Centripetal Force = (mass * velocity^2) / radius
Given that the bug has a mass of 1.4 g and a speed of 13.3 cm/s, and the radius is 12 cm, we can plug in these values into the formula and convert them to the appropriate units:
Centripetal Force = ((1.4 g) / 1000) * ((13.3 cm/s)^2) / (12 cm)
= (0.0014 kg) * (1.7689 m^2/s^2) / (0.12 m)
≈ 0.0204 N
Therefore, the centripetal force acting on the bug is approximately 0.0204 N.