A bodybuilder is holding a 20-kg steel barbell above her head. How much force would she have to exert if the barbell were lifted underwater?
You will need to look up the density of steel.
The weight of the barbell under water will be
20 kg * g - V *(densityH2O)* g
V * g [densitysteel) - densityH2O)
The weight in water will be the weight in air (20 g = 196 Newtons) multiplied by [1 - (densityH2O/densitysteel)]
To determine how much force the bodybuilder would have to exert if the barbell were lifted underwater, we need to consider the effects of buoyancy.
1. Calculate the weight of the steel barbell underwater:
- The weight of an object is given by its mass multiplied by the acceleration due to gravity (W = m * g).
- The weight of the barbell underwater is equal to the weight of the water displaced by the barbell.
- The upward buoyant force equals the weight of the water displaced by the barbell.
- In this case, the barbell's mass is 20 kg, and the acceleration due to gravity is approximately 9.8 m/s^2.
- So, the weight of the barbell underwater is 20 kg * 9.8 m/s^2 = 196 N.
2. Calculate the force the bodybuilder needs to exert:
- The force exerted by the bodybuilder must counteract the weight of the barbell underwater and allow for its upward motion.
- The force will be the sum of the weight of the barbell underwater and the force required to accelerate it against gravity.
- In this case, the weight of the barbell underwater is 196 N, and the upward force required to accelerate it against gravity is also 196 N.
- Therefore, the total force exerted by the bodybuilder should be 196 N + 196 N = 392 N.
Hence, the bodybuilder would need to exert a force of 392 Newtons if the 20-kg steel barbell were lifted underwater.
To determine the force the bodybuilder would have to exert to lift the barbell underwater, we need to understand the concept of buoyancy.
Buoyancy is the upward force exerted by a fluid on an object immersed in it. It is equal to the weight of the fluid displaced by the object.
The weight of the fluid displaced is given by the Archimedes' principle. This principle states that the buoyant force on an object immersed in a fluid is equal to the weight of the fluid displaced by the object.
In this case, the barbell would displace a volume of water equal to its own volume. Since the barbell is made of steel, its density is greater than that of water. This means that the barbell will sink in water.
To find the amount of force the bodybuilder needs to exert to lift the barbell underwater, we can use Newton's second law of motion, which states that the force exerted on an object is equal to its mass multiplied by its acceleration.
First, we need to calculate the buoyant force on the barbell. This is equal to the weight of the displaced water, given that the density of water is approximately 1000 kg/m³.
Buoyant force = weight of displaced water = density of water * volume of water displaced * acceleration due to gravity
Since the volume of water displaced is equal to the volume of the barbell (since it is completely submerged), we simply need to find the volume of the barbell.
To calculate the volume of the barbell, we need to know its dimensions. Once we know the dimensions, we can calculate its volume using the formula:
Volume = length * width * height
Once we have the volume of the barbell and the known density of steel (approximately 7850 kg/m³), we can calculate its mass using the formula:
Mass = density * volume
Once we have the mass of the barbell, we can use Newton's second law to calculate the force needed to lift it underwater:
Force = mass * acceleration due to gravity
Substituting the mass of the barbell and the acceleration due to gravity (approximately 9.8 m/s²) into the equation will provide us with the answer.