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.)
A)an ice cube
1) To determine for which of the objects the buoyant force will be greater than its weight, we need to compare the density of each object with the density of water. If an object is less dense than water, it will experience a buoyant force greater than its weight, causing it to float. If an object is more dense than water, the buoyant force will be less than its weight, causing it to sink.
A) Ice Cube: Ice has a lower density than water, so it will experience a buoyant force greater than its weight and float.
B) Frozen Glycerin: Glycerin has a density greater than water, so it will experience a buoyant force less than its weight and sink.
C) Gold Ring: Gold is denser than water, so it will experience a buoyant force less than its weight and sink.
D) Aluminum Foil: Aluminum has a lower density than water, so it will experience a buoyant force greater than its weight and float.
Therefore, the answers are A) an ice cube and D) a piece of aluminum foil.
2) To find the mass of the cup, we can use the concept of buoyancy. Since the cup sinks when it is full of wine initially, it means that the weight of the cup plus the wine is greater than the buoyant force acting on it.
When the cup is full, the buoyant force is equal to the weight of the displaced wine. Let's denote the mass of the cup as mc and the mass of the wine as mw. The total volume of the cup is 400 cc (cubic centimeters), and the specific gravity of the wine is 1.04. Specific gravity is the ratio of the density of a substance to the density of a reference substance (usually water). Since the specific gravity of the wine is 1.04, its density is 1.04 times the density of water.
The volume of the wine is 400 cc, so we can calculate its mass using the formula:
mw = Volume × Density = 400 cc × (1.04 × Density of Water)
Now, when you drink at least 1/4 of the wine, the cup starts to float. This means that the buoyant force on the cup is now greater than its weight. The buoyant force is equal to the weight of the displaced volume of water.
So, the weight of the cup plus the remaining wine must be equal to the weight of the displaced water. The remaining volume of wine is 3/4 of the initial 400 cc, which is 300 cc.
Using the equation mc + mw = Volume × Density of Water, we can substitute the values and solve for mc:
mc + mw = 300 cc × (Density of Water)
mc = 300 cc × (Density of Water) - mw
Therefore, to find the mass of the cup, subtract the mass of the remaining wine from the calculated mass:
mass of the cup (mc) = 300 cc × (Density of Water) - mw
3) To find the force exerted on the fluid in the input tube to hold the car up, we can use Pascal's law, which states that the pressure applied to an enclosed fluid is transmitted equally in all directions.
The force exerted on the fluid in the input tube is equal to the pressure applied multiplied by the surface area of the input tube.
The mass of the car is given as 2000 kg, and it is held at a height of 1.8 meters. We can calculate the gravitational potential energy (PE) stored in the car using the formula: PE = m × g × h, where m is the mass, g is the acceleration due to gravity (approximately 9.8 m/s^2), and h is the height.
PE = 2000 kg × 9.8 m/s^2 × 1.8 m = 35,280 J (joules)
This gravitational potential energy is equal to the work done by the force exerted on the fluid in the input tube. We can calculate the work (W) using the formula: W = F × d, where F is the force and d is the distance.
W = F × d = 35,280 J
The surface area of the piston inside the lift is given as 300 cm². We need to convert it to square meters by dividing by 10,000 (since 1 m² = 10,000 cm²): 300 cm² / 10,000 = 0.03 m².
To find the force (F), we rearrange the equation W = F × d to solve for F: F = W / d.
F = 35,280 J / 0.03 m² = 1,176,000 N (newtons)
Therefore, the force exerted on the fluid in the input tube to hold the car up is 1,176,000 N.