A tow truck is pulling a car out of a ditch by means of a steel cable (Y = 2.0 x 1011 N/m2) that is 9.73 m long and has a radius of 0.550 cm. When the car just begins to move, the tension in the cable is 859 N. How much has the cable stretched?
To find out how much the cable has stretched, we can use Hooke's Law, which states that the force required to stretch or compress a spring (or in this case, a cable) is directly proportional to the amount of stretch or compression.
Hooke's Law equation is given as:
F = k * ΔL
Where:
F is the force applied to the cable (tension)
k is the spring constant (also known as the Young's modulus) of the cable material
ΔL is the change in length (stretch or compression) of the cable
To find the change in length (ΔL), we rearrange the formula as:
ΔL = F / k
Given:
Tension (F) = 859 N
Young's modulus (k) = 2.0 x 10^11 N/m^2
Now, substitute the values into the equation:
ΔL = 859 N / (2.0 x 10^11 N/m^2)
Calculating the value gives:
ΔL = 4.295 x 10^-9 meters (or equivalently, 4.295 nanometers)
Therefore, the cable has stretched by approximately 4.295 nanometers.