Archimedes Principle Applied

[smilingsteph]

Homework Statement

A lead weight with a volume of 0.69x10^-5 m^3 is lowered on a fishing line into a lake to a depth of 1.0m. What tension is required in the fishing line to give the weight an upward acceleration of 1.8m/s^2?

Homework Equations

T=F-mg F=ma D=mv D of lead= 11.34gcm^3

The Attempt at a Solution

I have tried solving it (first changing density into m, to be compatible with my volume value). Then I found the mass of the lead weight (using the given volume and measured density). But still not sure if I'm going through the proper means to arrive at the tension. Any suggestions?

 

[HallsofIvy]

Where have you used Archimedes' principal that you cite in your title? It tells you that there is an bouyancy force equal to the weight of water with the same volume as the lead weight.

 

[Moetasim]

As a scientist, it is important to follow a systematic approach to problem solving. In this case, we can use Archimedes' Principle, which states that the buoyant force acting on an object submerged in a fluid is equal to the weight of the fluid displaced by the object.

First, we can calculate the weight of the lead weight using the formula W = mg, where m is the mass and g is the acceleration due to gravity. We can use the given density of lead (11.34 g/cm^3) to convert the volume (0.69x10^-5 m^3) into mass. This gives us a mass of approximately 0.781 g.

Next, we can calculate the weight of the displaced water using the density of water (1 g/cm^3) and the volume of water displaced by the lead weight (0.69x10^-5 m^3). This gives us a weight of approximately 0.069 N.

Since the lead weight is accelerating upwards with an acceleration of 1.8 m/s^2, we can use the formula F=ma to calculate the force required to give it this acceleration. This gives us a force of 0.0014 N.

According to Archimedes' Principle, this force (0.0014 N) must be equal to the buoyant force acting on the lead weight (0.069 N). Therefore, the tension in the fishing line must be 0.069 N + 0.0014 N = 0.0704 N.

In conclusion, the tension required in the fishing line to give the lead weight an upward acceleration of 1.8 m/s^2 is approximately 0.0704 N.