How Far Does the Ball Travel After the String Is Cut?

[Lamnia]

Homework Statement

A 140g ball on a 60 cm long string is swung in a vertical circle about a point 200 cm above the floor. The tension in the string when the ball is at the very bottom of the circle is 6.9 N. At the very bottom of the circle, a very sharp knife is suddenly inserted to cut the string directly below the point of support.

How far to the right of where the string was cut does the ball hit the floor?
Express your answer using two significant figures.

Homework Equations

F_r net = T = (m*v^2)/r
F_z net = 0 = n - m*g (I'm under the impression that this equation isn't necessary to solve the problem as we are (rather, I am) not needing to find a friction force.)

s_1 = s_0 + v_0t + 1/2at^2

The Attempt at a Solution

T = 6.9N
m = 0.140kg
r = 0.60m

6.9N = (0.140kg*v^2)/0.60m
v = 5.43769 m/s

y_1 = 0
y_0 = 2m - 0.6m = 1.4m
v_0 = 0
a = g = 9.80m/s^2

1.4m = .5*9.80m/s^2*t^2
t = 0.534522s

x_0 = 0
v_0 = 5.43769 m/s
a = 0
t = 0.534522s

x_1 = 5.43769 m/s * 0.534522s
x_1 = 2.9m

Above is my 5th attempt at this problem. It, too, is incorrect. I thought that determining the velocity through the sum of radial forces, and then using projectile motion kinematics would finally prove the correct approach. I have one more attempt to receive any credit for my work. Any input would be most appreciated.

 

[LowlyPion]

Homework Statement

A 140g ball on a 60 cm long string is swung in a vertical circle about a point 200 cm above the floor. The tension in the string when the ball is at the very bottom of the circle is 6.9 N. At the very bottom of the circle, a very sharp knife is suddenly inserted to cut the string directly below the point of support.

How far to the right of where the string was cut does the ball hit the floor?
Express your answer using two significant figures.

Homework Equations

F_r net = T = (m*v^2)/r
F_z net = 0 = n - m*g (I'm under the impression that this equation isn't necessary to solve the problem as we are (rather, I am) not needing to find a friction force.)

At the bottom of the loop, you don't think that gravity might not also add to the tension on the string?

 

[Lamnia]

So... when I took F_r net = T = m*g + (m*v^2)/r, my calcs proved spot on. Thanks, again, LowlyPion :)

 

[LowlyPion]

Cheers.