When the following are placed in water, for which of them will the buoyant force be more than as its weight?
A) an ice cube
B) a piece of frozen glycerin
C) a gold ring
D) a piece of aluminum foil
2. Sometimes when I get in my swimming pool I take a plastic cup filled with wine with me. The cup holds 400 cc of wine. I have observed that the cup sinks when it is full of wine, but floats after I have drunk at least 1/4 of it. What is the mass of the cup? Assume that the specific gravity of the wine is 1.04.
3) A car with mass 2000kg is held at a height of 1.8 meters by a hydraulic lift. The surface area of the piston inside the lift is 300cm², and the surface area of the input tube at the bottom of the lift is 6 cm². What force must be exerted on the fluid in the input tube to hold the car up? (Neglect the mass of the fluid itself.)
1) The buoyant force acting on an object when placed in water is equal to the weight of the water displaced by that object. If the buoyant force is greater than the weight of the object, the object will float; if the buoyant force is less than the weight of the object, the object will sink.
To determine for which objects the buoyant force will be greater than its weight:
A) For an ice cube: To determine the weight of the ice cube, you need to know its mass and the acceleration due to gravity. Assuming you have this information, multiply the mass of the ice cube by the acceleration due to gravity to find its weight (W).
Then, determine the volume of the ice cube by measuring its length, width, and height. Multiply these dimensions to calculate the volume (V). Since ice has a density close to 1 g/cm³, which is equivalent to 1 kg/dm³, the mass of the ice cube will also be equal to its volume.
Once you know the volume of the ice cube, you can calculate the weight of the displaced water using the formula W = V * ρ * g, where ρ is the density of water (approximately 1000 kg/m³) and g is the acceleration due to gravity (approximately 9.8 m/s²).
If the weight of the ice cube is greater than the weight of the displaced water, then the buoyant force on the ice cube will be less than its weight, and it will sink. Otherwise, it will float.
B) The same method as for the ice cube can be applied to determine the buoyant force on a piece of frozen glycerin.
C) For a gold ring: The same method as above can be used to determine the buoyant force on the gold ring. Measure the dimensions of the ring to calculate its volume and then compare the weights.
D) For a piece of aluminum foil: Repeat the process by measuring the dimensions of the aluminum foil and comparing the weights.
2) To find the mass of the cup, you need to compare the weight of the cup when it is sinking with the weight of the cup when it is floating. When the cup is sinking, the weight of the cup plus the weight of the wine is greater than the buoyant force acting on it. When the cup is floating, the weight of the cup plus the weight of the remaining wine is equal to the buoyant force acting on it.
You would need to measure the weight of the cup when it is sinking and when it is floating, and then subtract the weight of the remaining wine from the weight of the cup when it is floating. This difference will give you the weight of the cup alone. To convert this weight into mass, divide it by the acceleration due to gravity.
3) To calculate the force exerted on the fluid in the input tube to hold the car up, you can use Pascal's law, which states that a change in pressure applied to an enclosed fluid is transmitted undiminished to every portion of the fluid and the walls of its container.
The pressure exerted by the fluid in the lift is equal to the force exerted on the fluid divided by the surface area of the piston inside the lift (P = F/A). This pressure is also equal to the force exerted on the fluid in the input tube divided by the surface area of the input tube (P = F/A).
Using these two equations, you can set them equal to each other and solve for the force (F) exerted on the fluid in the input tube:
F/A(piston) = F/A(input tube)
F = (A(input tube) / A(piston)) * F
Substitute the known values into the equation to find the force required to hold the car up.