A .5kg ball on the end of a string is revolving uniformly in ahorizontal circle of radius 1m. The ball makes 2 revolustion in a second.
a) determine the linear (tangential) speed of the ball.
For this part of the question would I do this:
v=d/t
=1m/.5s
=2m/s
b)determine the ball's centripetal acceleration
a_c=v^2/r
=2m/s^2/1
=4m/s^2
c)determine the force a person must exert on the opposite end of the string.
F_c=mv^2/r
=.5kg(2m/s)^2/1
=2N
Is this correct? The only thing i'm not too sure about is part a). Thanks in advance for your help.
The distance around the circle is 2PI*radius, v= distance/time You have distance equal to radius.
The centripetal force is indeed v^2/r, your numbers are of course wrong.
part A messes up part b, c.
Yes, you got the correct answers for parts (b) and (c). However, there is a small mistake in part (a). Let me guide you through the correct calculation.
a) To determine the linear (tangential) speed of the ball, you can use the formula:
v = 2πr / T
Where v is the linear speed, r is the radius of the circle, and T is the time taken to complete one revolution.
Given that the ball makes 2 revolutions in 1 second, the time taken for one revolution (T) is 1/2 second.
Substituting the values into the formula:
v = 2π(1m) / (1/2s)
v = 4π m/s
So, the correct linear (tangential) speed of the ball is 4π m/s.
b) For the centripetal acceleration, you correctly used the formula:
a_c = v^2 / r
Substituting the values:
a_c = (4π m/s)^2 / 1m
a_c = 16π^2 m/s^2
So, the centripetal acceleration of the ball is 16π^2 m/s^2.
c) To determine the force a person must exert on the opposite end of the string, you correctly used the formula:
F_c = m * a_c
Substituting the values:
F_c = 0.5kg * (16π^2 m/s^2)
F_c = 8π^2 N
So, the correct force a person must exert on the opposite end of the string is 8π^2 N.
Overall, you had the right approach, but there was a small calculation error in part (a), which I have corrected for you.