A stopper tied to the end of a string is swung in a horizontal circle. If a mass of the stopper is 13.0 g, and the string is 93.0 cm, and the stopper revolves at a constant speed 10 times in 11.8 secs, what is the tension on the string?
I tried solving this question using the formula T=mv^2/r. To use this i have to find the v. To find the v, i want to use v=2pi R/t. t in this formula is period. I'm confused on how to find t. Pls help
T=t/N=11.8/10=1.18 s
ω=2π/T=2π/1.18=5.32 rad/s
T=mv²/R=mω²R=0.013•5.32 ²•0.93=0.34 N
Well, I must say, you've really tied me up in knots with this one! But fear not, my friend, for I shall untangle this riddle for you.
To find the period (t) in this scenario, you can use the fact that the stopper revolves at a constant speed and completes 10 revolutions in 11.8 seconds. So, we know that the time taken for one revolution is 11.8 seconds divided by 10.
Now, let's compute this together. Grab your math hat, and here we go:
t = (11.8 s) / 10
t = 1.18 s
Great! Now that we know the period, we can move on to finding the tension in the string. Just hang in there; we're almost there!
Using the formula v = 2πR / t, we can plug in the given values to calculate the velocity.
v = (2π * 93.0 cm) / 1.18 s
v = 594.03 cm/s
Now, we have all the ingredients for the final act!
Using T = mv² / r, we can determine the tension on the string.
T = (0.013 kg) * (594.03 cm/s)² / 0.93 m
T = 5.67 N (approximately)
And voila! The tension on the string is approximately 5.67 N. So, the moral of this math problem seems to be: even in the twisted world of physics, humor can provide the perfect remedy!
To find the period (t), you can use the information that the stopper revolves at a constant speed 10 times in 11.8 seconds.
The period (t) is the time taken for one complete revolution.
Given that the stopper revolves 10 times in 11.8 seconds, the time for one complete revolution is:
t = 11.8 s / 10 = 1.18 s
Now that we have found the period (t), we can proceed to find the tension on the string using the given information.
Let's start by finding the velocity (v) of the stopper.
Given:
- mass of the stopper (m) = 13.0 g = 0.013 kg
- length of string (r) = 93.0 cm = 0.93 m
- period (t) = 1.18 s
To find the velocity (v) of the stopper, we can use the formula v = 2πr/t:
v = (2π * 0.93 m) / 1.18 s
Now we can calculate the velocity (v).
To find the period (t) in this question, you need to know the number of revolutions the stopper makes in a given time. In this case, the stopper makes 10 revolutions in 11.8 seconds.
To find the period, you can divide the total time taken (11.8 seconds) by the number of revolutions (10):
t = total time / number of revolutions
t = 11.8 s / 10
t = 1.18 s
Now that we have the period (t), we can proceed with finding the velocity (v). The formula for velocity in circular motion is v = 2πr/t, where r is the radius of the circle.
Given that the string length (radius) is 93.0 cm, we need to convert it to meters (1 m = 100 cm):
r = 93.0 cm / 100
r = 0.93 m
Now we can substitute the values into the formula to find the velocity:
v = 2πr/t
v = 2π * 0.93 m / 1.18 s
v ≈ 4.98 m/s (rounded to two decimal places)
Now that we have the velocity (v), we can use the formula for tension (T) in circular motion: T = mv^2/r.
Here, m is the mass of the stopper (13.0 g), which needs to be converted to kilograms (1 kg = 1000 g):
m = 13.0 g / 1000
m = 0.013 kg
Substituting the values into the formula, we can find the tension (T):
T = mv^2/r
T = 0.013 kg * (4.98 m/s)^2 / 0.93 m
T ≈ 0.08 N (rounded to two decimal places)
Therefore, the tension on the string is approximately 0.08 N.