A large suitcase full of gold sits at the bottom of a lake. A team of treasure hunters uses a crane to recover the suitcase and finds that a force of 2.6 105 N is required to lift the suitcase to the surface. What is the volume of the suitcase?
_____m^3
To find the volume of the suitcase, we need to use the concept of buoyancy. The buoyant force acting on an object submerged in a fluid is equal to the weight of the fluid displaced by the object.
1. Determine the weight of the suitcase: Since the force required to lift the suitcase to the surface is given as 2.6 x 10^5 N, this is the weight of the suitcase.
2. Determine the density of water: The density of water is approximately 1000 kg/m^3.
3. Use the formula for buoyant force: Buoyant force = weight of the fluid displaced
Buoyant force = Density of fluid x Volume of fluid displaced x Acceleration due to gravity
Weight of the suitcase = Density of water x Volume of the suitcase x Acceleration due to gravity
4. Rearrange the formula to solve for the volume of the suitcase:
Volume of the suitcase = Weight of the suitcase / (Density of water x Acceleration due to gravity)
Volume = (2.6 x 10^5 N) / (1000 kg/m^3 x 9.8 m/s^2)
5. Calculate the volume:
Volume = 2.6 x 10^5 N / (1000 kg/m^3 x 9.8 m/s^2)
Volume ≈ 26.53 m^3
Therefore, the volume of the suitcase is approximately 26.53 m^3.
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You're more likely to get expert help if you also post your attempts at answering the problems.