A bucket hangs from two wires. The left-hand wire makes an angle of 60 with the vertical, and the magnitude of the tension in the wire is 326N. The right-hand wire makes an angle of 45 with the vertical.

Calculate the mass of the bucket, in kilograms, to two significant figures.
(Take the magnitude of the acceleration due to gravity, g, to be 9.8ms^-2)

60o W. of N. = 150o CCW from +x-axis.

45o E. of N. = 45o CCW from +x-axis.

The system is in equilibrium:

326*cos150 = -T2*cos45.
326 = 0.742T2, T2 = 400 N.

Fb = -(T1*sin150+T2*sin45).
Fb = -(326*sin150+400*sin45) = -446 N. = 446 N. Downward.

M*g = 446. M = 446/g = 446/9.8 = 46 kg.

Correction: 326 = 0.816T2, T2 = 400 N.

To calculate the mass of the bucket, we need to use the concept of equilibrium. In this scenario, the bucket is hanging from two wires, so the forces acting on the bucket balance each other out.

First, let's calculate the vertical component of tension for each wire.

For the left-hand wire:
The angle between the wire and the vertical is 60 degrees. We can use trigonometric functions to find the vertical component of tension.

Vertical component of tension on the left-hand wire = Magnitude of tension * sin(angle)
= 326 N * sin(60°)

For the right-hand wire:
The angle between the wire and the vertical is 45 degrees. Again, we can use trigonometric functions to find the vertical component of tension.

Vertical component of tension on the right-hand wire = Magnitude of tension * sin(angle)
= 326 N * sin(45°)

Now, let's equate the sum of the vertical components of tension to the weight of the bucket.

Sum of vertical components of tension = Weight of the bucket

Weight of the bucket = mass of the bucket * acceleration due to gravity

Using the given value of the acceleration due to gravity (g = 9.8 m/s^2), we can now write the equation:

326 N * sin(60°) + 326 N * sin(45°) = mass of the bucket * 9.8 m/s^2

Simplifying the equation, we have:

326 N * √(3)/2 + 326 N * √(2)/2 = mass of the bucket * 9.8 m/s^2

Now, we can solve this equation to find the mass of the bucket.

mass of the bucket = (326 N * √(3)/2 + 326 N * √(2)/2) / 9.8 m/s^2

Calculating this expression will give us the mass of the bucket in kilograms, rounded to two significant figures.