A rope can withstand a maximum tension of 75 N before snapping . What maximum speed can you spin a 6.0 kg rock in a vertical circle of radius 1.5 m without breaking the rope?
My answer:
At the bottom of the spin:
Fnet=ma
Ft-Fg=m(v^2/r)
75-58.8=6(v^2/1.5)
v=2.01m/s
Is this correct? thanks for your help.
Yes, it is correct.
Thanks for showing your work!
I wish more students would follow your example.
Thanks!
Where did you get 58.8?
Oh you multiplied the force of gravity by the mass I see. . .
To determine the maximum speed at which the rock can be spun in a vertical circle without breaking the rope, you correctly used the equation Ft - Fg = mv^2/r, where Ft is the tension in the rope, Fg is the force due to gravity, m is the mass of the rock, v is the speed, and r is the radius of the circle.
You correctly plugged in the values: Ft = 75 N, Fg = 6 kg * 9.8 m/s^2 = 58.8 N, m = 6 kg, and r = 1.5 m.
However, there is a slight mistake in your calculation. The correct equation is:
75 - 58.8 = (6 * v^2) / 1.5
Simplifying this equation, you'll get:
16.2 = 4v^2
Now, divide both sides by 4 to isolate v^2:
4.05 = v^2
Finally, take the square root of both sides to solve for v:
v = √4.05 ≈ 2.01 m/s
So, your answer of v = 2.01 m/s is correct!