For safety in climbing mountaineers use a nylon rope that is 50m long (L) and 0.1 m in diameter. When supporting a 900 N climber the rope stretches 1.6 m (AL) under tension. Find the Young's Modulus (Y) for the nylon rope.
same as the last one
Y= [(Force)(Length of rope)]/Area*(change in rope length)
Area= [(pi)(diameter^2)]/4
I can't understand
To find the Young's Modulus of the nylon rope, we can use the formula:
Y = (F * L) / (A * ∆L)
Where:
Y = Young's Modulus
F = Force applied to the rope (weight of the climber) = 900 N
L = Original length of the rope = 50 m
A = Cross-sectional area of the rope = π * r^2 (r is the radius of the rope)
∆L = Change in length of the rope = 1.6 m
To solve for Y, we need to determine the cross-sectional area of the rope.
Given:
Diameter of the rope = 0.1 m
Radius (r) = diameter / 2 = 0.1 m / 2 = 0.05 m
Now, we can calculate the cross-sectional area.
A = π * r^2 = π * (0.05 m)^2 = 0.00785 m^2
Substituting the given values into the formula, we get:
Y = (900 N * 50 m) / (0.00785 m^2 * 1.6 m)
Simplifying the equation, we have:
Y = 570428.95 N/m^2
Therefore, the Young's Modulus for the nylon rope is approximately 570428.95 N/m^2.