answers
velocity = 7 m/s
tension = 7.644 N
set up equation for velocity
because energy is conserved, the change in potential energy as the potato drops is the same as the change in kinetic energy
U = K
mgh = m[tex]v^2[/tex]/2
gh = [tex]v^2[/tex]/2
[tex]v^2[/tex] = 2gh
v = [tex]\sqrt{2gh}[/tex]
values
g = 9.8 m/s^2
h = 2.5 m (change in vertical distance)
plug in values and solve
v = [tex]\sqrt{2gh}[/tex]
v = [tex]\sqrt{2*9.8*2.5}[/tex]
v = 7 m/s
set up equation for tension
at the lowest point, tension (directly upward) acts in the opposite direction of weight (directly downwards) so
∑F = T - mg
since the potato is in circular motion, the net force is equal to centripetal force
∑F = m[tex]v^2[/tex]/r
∑F = T - mg = m[tex]v^2[/tex]/r
T - mg = m[tex]v^2[/tex]/r
T = mg + m[tex]v^2[/tex]/r
T = [tex]m(g+\frac{v^2}{r} )[/tex]
values
m = 0.26 kg
g = 9.8 m/s^2
v = 7 m/s
r = 2.5m
plug in values and solve
T = [tex]m(g+\frac{v^2}{r} )[/tex]
T = [tex]0.26(9.8+\frac{7^2}{2.5} )[/tex]
T = 7.644 N
