How much force does it take to stretch a 15-m-long, 1.0 cm -diameter steel cable by 6.0mm ?
I know f/a divided by change in length/l
knowns are diameter 1.0cm, change in lngth 6.0mm, length 15 m. Convert all to meters.
To find the force required to stretch the steel cable, you can use Hooke's Law, which states that the force needed to stretch or compress an elastic material is directly proportional to the change in length.
First, let's convert all the measurements to meters to ensure consistent units.
The diameter of the steel cable is given as 1.0 cm. Since the diameter is twice the radius, we can calculate the radius by dividing the diameter by 2:
Radius (r) = 1.0 cm / 2 = 0.5 cm = 0.005 m
The change in length (Δl) is given as 6.0 mm, which is equal to 0.006 m.
The original length (L) of the cable is given as 15 m.
To calculate the cross-sectional area (A) of the cable, we can use the formula for the area of a circle:
A = πr^2
Plugging in the values, we get:
A = π(0.005 m)^2
Now, let's calculate the force (F) using the formula:
F = (f/A) / (Δl/L)
Plugging in the known values:
F = (f / [π(0.005 m)^2]) / (0.006 m / 15 m)
Simplifying the equation, we can cancel out the meters in the denominator:
F = (f / [π(0.005 m)^2]) / (0.006 / 15)
Now you can rearrange the equation to solve for the force (f):
f = F * [π(0.005 m)^2] * (0.006 / 15)
Substituting the given value for F, and solving the equation will give us the required force to stretch the steel cable.