A thin, light wire 75.8cm long having a circular cross section 0.560mm in diameter has a 25.5kg weight attached to it, causing it to stretch by 1.12mm .
what is the stress?
To calculate the stress on the wire, we first need to understand what stress is. Stress is defined as the force acting on an object per unit area of the object. In this case, the force acting on the wire is the weight attached to it, and the area is the cross-sectional area of the wire.
First, let's calculate the cross-sectional area of the wire using the diameter. The diameter of the wire is given as 0.560 mm. To find the radius, we divide the diameter by 2:
Radius = 0.560 mm / 2 = 0.280 mm
Now, we need to convert the radius to meters by dividing it by 1000:
Radius = 0.280 mm / 1000 = 0.000280 m
To calculate the area of the wire, we use the formula for the area of a circle:
Area = π * radius^2
Plugging in the values:
Area = π * (0.000280 m)^2
Now, let's calculate the stress. Stress is defined as force divided by area. The force is the weight attached to the wire, which is given as 25.5 kg. However, we need to convert this to Newtons (N) using the formula:
Force = mass * acceleration due to gravity
Acceleration due to gravity is approximately 9.8 m/s^2:
Force = 25.5 kg * 9.8 m/s^2
The stress is then:
Stress = Force / Area
Stress = (25.5 kg * 9.8 m/s^2) / [π * (0.000280 m)^2]
Calculating this expression will give us the stress on the wire.