when a wire of length 5m & radius 0.5mm is stretched by a load of 49N the elongation produced in the wire is 0.1cm find the energy stored per unit volume of the wire?
energy=forcepulling* distance pulled
= 49*.001 joules
volume=length*PIr^2
use elongated length
To find the energy stored per unit volume of the wire, we can use the formula for strain energy.
The strain energy stored in a wire is given by:
U = (1/2) * F * l
Where:
U is the strain energy stored
F is the force applied on the wire
l is the elongation produced in the wire
First, convert the units of length from centimeters to meters:
l = 0.1 cm = 0.1/100 m = 0.001 m
Now, substitute the values into the formula:
U = (1/2) * 49 N * 0.001 m
Calculate the value:
U = 0.5 * 49 N * 0.001 m
U = 0.0245 N·m
The energy stored per unit volume is given by the formula:
Energy per Unit Volume = U / V
Where V is the volume of the wire.
The volume of a wire can be calculated using the formula:
V = π * r² * l
Where:
V is the volume
r is the radius of the wire
l is the length of the wire
First, convert the radius from millimeters to meters:
r = 0.5 mm = 0.5/1000 m = 0.0005 m
Now substitute the values into the volume formula:
V = π * (0.0005 m)² * 5 m
V = π * 0.00000025 * 5 m³
V = 0.00000125π m³
Now substitute the values into the energy per unit volume formula:
Energy per Unit Volume = 0.0245 N·m / 0.00000125π m³
Calculate the value:
Energy per Unit Volume ≈ 6203 N·m⁻³
Therefore, the energy stored per unit volume of the wire is approximately 6203 N·m⁻³.