A 2.0 kg mass is attached to a string that is 1.0 m long and moves in a horizontal circle at a rate of 4.0 revolutions per second.
a) What is the centripetal acceleration of the mass?
I converted 4 rev/s to 25.13 rad/s and used the equation: a=rw^2 to get 632 m/s^2
b) What is the tension in the string?
The answer sheet says 1250 N but I have no idea how to get there.
Your problem only has two significant figures accuracy
to two significant figures w = 25
so
r w^2 = 625
F = m a
F = 2 kg * 625 m/s^2 = 1250 N
Thanks. I didn't realize f=ma could be used because of gravity's acceleration.
Gravity is not in this because it says in a HORIZONTAL circle (it must be on a table top or something but 625 is much bigger than g anyway))
Okay, I understand now. Thank you.
To find the tension in the string, we can use the formula for centripetal force. The centripetal force is given by the equation:
Fc = (m * ac) / r
Where:
Fc is the centripetal force
m is the mass of the object (2.0 kg)
ac is the centripetal acceleration (which we found to be 632 m/s^2)
r is the radius of the circle (1.0 m)
Let's substitute the given values into the equation and solve for Fc:
Fc = (2.0 kg * 632 m/s^2) / 1.0 m
= 1264 N
Therefore, the tension in the string is 1264 N. It seems there was a mistake in the answer sheet, as the correct value should be 1264 N, not 1250 N.