a student connects an object with mass m to a rope with a length r and then rotates the rope around her head parallel to the ground. the object takes 0.5 seconds to complete one rotation.
mass= 50 kg. length of the rope = 1.2 m
what is the objects speed of rotation?
what is the objects centripetal acceleration?
Just want to check my answers
I'm pretty sure the first question answer is 15.08 m/s and the second answer is 189.51 m/s^2
Correct me if I'm wrong.
s = 2 π r / t = 2 * π * 1.2 / .5 = 15.08
a = s^2 / r = 15.08^2 / 1.2 = 189.51
there are issues with significant figures
... the 5 figure result for c.a. when the best data number has 2 figures
... same case for speed
So would that make the tension required 9.47 N by any chance. That's what I got for the tension.
the tension supplies the force for the centripetal acceleration
f = m a = 50 * 189.51 = ?
you seem to be off by a factor of 100
the mass does not seem realistic for a person to swing around
To find the object's speed of rotation, we can use the formula:
speed = circumference / time
The circumference of the object's path is equal to the length of the rope which is given as 1.2m. The time taken to complete one rotation is given as 0.5 seconds. Substituting these values into the formula, we get:
speed = 2 * π * r / t
speed = 2 * 3.1416 * 1.2 / 0.5
speed = 7.54 m/s
Therefore, the object's speed of rotation is 7.54 m/s.
To find the object's centripetal acceleration, we can use the formula:
acceleration = (velocity^2) / radius
Where velocity is the speed of rotation and radius is the length of the rope. Substituting the values we have:
acceleration = (7.54^2) / 1.2
acceleration = 45 / 6
acceleration = 7.5 m/s^2
Therefore, the object's centripetal acceleration is 7.5 m/s^2.
Based on your calculations, it seems you made some errors. The correct values are:
- The object's speed of rotation is 7.54 m/s.
- The object's centripetal acceleration is 7.5 m/s^2.
I hope this explanation helps!