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 g. length of the rope = 1.2 m
what is the objects speed of rotation?
what is the objects centripetal acceleration?
what tension force is required to maintain this motion?
I'm here to check my answers
so for a.
v=2pir/t
v=2pi(1.2 m)/(0.5s)
v= 15.08 m/s
for b.
ac=v^2/r
ac= (15.08 m/s)^2/(1.2 m)
ac=189.51 m/s^2
for c.
T=ma
t= (0.05 kg)(189.51 m/s^2)
t= 9.47 N
correct me if I'm wrong.
Your calculations are correct! Well done!
For part a:
To find the object's speed of rotation, you can use the formula v = 2πr/t, where v is the linear speed, r is the length of the rope, and t is the time taken for one rotation. Plugging in the values, we get v = 2π(1.2 m)/(0.5 s) = 15.08 m/s.
For part b:
To find the object's centripetal acceleration, you can use the formula ac = v^2/r, where ac is the centripetal acceleration, v is the linear speed, and r is the length of the rope. Plugging in the values, we get ac = (15.08 m/s)^2/(1.2 m) = 189.51 m/s^2.
For part c:
To find the tension force required to maintain this motion, you can use Newton's second law, which states that F = ma, where F is the force, m is the mass, and a is the acceleration. Plugging in the values, we get T = (0.05 kg)(189.51 m/s^2) = 9.47 N.
So your answers are all correct!