Question

What is the tension in a wire supporting a 1250.0 N underwater camera submerged in water? The volume of the camera is 8.3x10-2 m3.

Please give me a simple explanation. Thank you!

Answer 1

Tension = `436.6N` because the net force on the camera is zero.

Explanation:

The sum the forces on the camera should be zero because the camera is supported an not accelerating.

The forces acting upward include the tension in the string lifting up the camera and the force of buoyancy (which is why things float in water). The force acting downward is the weight due to the mass of the camera. These should sum to zero. If we set the upward forces as positive forces and the downward forces as negative forces (this way they can mathematically cancel), we come up with this equation.

`F = Tension + Buoyancy - Weight`

But the forces should sum to zero so that net force `F = 0`

`0N = Tension + Buoyancy - Weight`

We are given the weight is `1250N`

`0N = Tension + Buoyancy - 1250N`

To find Buoyancy, we use the equation. Force of Buoyancy = density times volume times gravity. `F = p*v*g`. Since the density of water is `1000 (kg)/m^3`, the volume (of the amount of water displaced by the camera) `= 0.083m^3` and `g = 9.8m/s^2`, we can times these together to get buoyancy `= 813.4N`. Plugging this back into our equation we get:

`0N = Tension + 813.4 - 1250N`

Solving for tension we get Tension `= 436.6N` in the upward direction.