Rotational Dynamics Homework: Velocity Vector & Wire Strength

[ataglance05]

Homework Statement

A 10kg objects rotates on a point on a wire 3 meters long at the rate of 120 rad/sec without breaking the wire.

1) What is the numeric value (and units) of the velocity vector and 2)what angle does it make with the tangent at any point? and 3) What's the minimum tensile strength of wire asumming that is has a 50% safety factor? (Minimum tensile strength of the wire is 1.5 times the working tensile strength)

Please answer or help me with atleast 1 and 2

Homework Equations

or V=ωr or θ=S/r

The Attempt at a Solution

V=ωr
V=120(3)= 360 m/sec

α=v^2/r
α=129600/3
α= 43200

t= (Vf-Vi)/a
t=(360/43200)
t=.00833 seconds

theta=ω(t)
theta=120(.00833)= 1

please help.

 

[Doc Al]

The Attempt at a Solution

V=ωr
V=120(3)= 360 m/sec

That's the correct approach and answer for question 1.

α=v^2/r
α=129600/3
α= 43200

That's the centripetal acceleration. Now apply Newton's 2nd law to work out the tension.

t= (Vf-Vi)/a
t=(360/43200)
t=.00833 seconds

theta=ω(t)
theta=120(.00833)= 1

No clue what you are doing here.

 

[m2003]

1) The velocity vector can be calculated using the formula V=ωr, where ω is the angular velocity in radians per second and r is the radius of rotation. In this case, V=120(3)=360 m/s. Therefore, the numeric value of the velocity vector is 360 m/s.
2) The angle that the velocity vector makes with the tangent at any point can be calculated using the formula θ=S/r, where S is the distance traveled along the arc and r is the radius of rotation. In this case, θ=1/3=0.333 radians or approximately 19.1 degrees.
3) The minimum tensile strength of the wire can be calculated by first determining the working tensile strength, which is the maximum amount of stress the wire can withstand without breaking. Assuming a safety factor of 50%, the minimum tensile strength would be 1.5 times the working tensile strength. Without knowing the specific material and properties of the wire, it is not possible to calculate the minimum tensile strength. This value would depend on the type and quality of the wire used.