URGENT PHYSICS HELp NEEDED - Please Please -Rock on Strings?

Question

A 540 gm rock is whirled on the end of a string 45 cm long which will break under a tension of 32 N.
a) What is the highest speed the rock can reach before the string breaks? (Neglect gravity.)

vmax = m/s
b) If two other strings identical to the first were attached to the rock, how fast could the rock be whirled before the three strings would break?

v'max = m/s
Next the rock is held by two of the same 45 cm strings with ends 63 cm apart and whirled in a circle between them. Neglect gravity.

c) What is the radius of the circle of motion?

R = cm
d) Now what is the maximum speed the rock can have before the string breaks?

v''max = m/s

Answer 1

ignoring gravity, the rock will spin in a plane perpendicular to the support of the string and the force on the string is
F=m*v^2/R
m=0.54 kg
R=0.45 m
v=sqrt(32*.45/0.54)
5.16 m/s

b)v=sqrt(3*32*.45/0.54)
8.94 m/s

c) This motion is in a radius that is circle when the following triangle is revolved:

hypotenuse is 45 and one side is 63/2. That makes the radius of the circle
sqrt(45^2-63^2/4)
32.1 cm

d) Looking at a FBD, the tension is the string is
related to the angle
th=atan(63/90)

The centripetal force is
m*v^2/R=2*T*cos(th)
setting T=32, solve for v
v=sqrt(64*cos(atan(63/90))*.321/0.54)
5.58 m/s

j