A 20.0kg solid gold statue is raised from the sea bottom. What is the tension in the hoisting cable (assumed massless) when the statue is accelerating upward at 2m/s^2? (assume the statue is still completely underwater) The density of gold is 19.6x10^3kg/m^3
To find the tension in the hoisting cable, we need to consider the forces acting on the gold statue.
Step 1: Determine the weight of the statue
The weight of the statue can be calculated using the formula:
weight = mass x acceleration due to gravity
Given:
mass of the statue (m) = 20.0 kg
acceleration due to gravity (g) = 9.8 m/s^2
weight = 20.0 kg x 9.8 m/s^2
weight = 196 N
Step 2: Determine the buoyant force acting on the statue
The buoyant force is equal to the weight of the fluid displaced by the object. In this case, since the statue is still completely underwater, the buoyant force will be equal to the weight of the statue. Therefore, the buoyant force is also 196 N.
Step 3: Determine the tension in the hoisting cable
To find the tension in the cable, we need to consider the net force acting on the statue.
Net force (F_net) = tension in the cable - buoyant force - weight
Given:
acceleration of the statue (a) = 2 m/s^2
Since the statue is accelerating upward, the net force acting on it is equal to its mass multiplied by its acceleration:
F_net = mass x acceleration
F_net = 20.0 kg x 2 m/s^2
F_net = 40 N
Now, we can calculate the tension in the hoisting cable:
tension in the cable = F_net + buoyant force + weight
tension in the cable = 40 N + 196 N + 196 N
tension in the cable = 432 N
Therefore, the tension in the hoisting cable is 432 N.
To find the tension in the hoisting cable, we need to consider the forces acting on the solid gold statue.
First, let's calculate the volume of the statue. We can use the density of gold to determine its volume by dividing the mass of the statue by the density of gold:
Volume = mass / density = 20.0 kg / (19.6 x 10^3 kg/m^3)
Next, we need to consider the buoyancy force acting on the statue due to it being submerged in water. The buoyancy force is equal to the weight of the water displaced by the statue. The weight of an object is given by the formula:
Weight = mass x acceleration due to gravity
Since the statue is still completely underwater, the entire statue's volume is displacing water. So the buoyancy force is:
Buoyancy force = Weight of water displaced = mass of water displaced x acceleration due to gravity
Now, let's calculate the volume of water displaced:
Volume of water displaced = Volume of the statue
To find the weight of water displaced, we need the density of water. The density of water is approximately 1000 kg/m^3.
Weight of water displaced = Volume of water displaced x Density of water x acceleration due to gravity
Finally, we can calculate the tension in the hoisting cable using Newton's second law:
Tension = Weight of the statue - Buoyancy force
Now let's plug in the values and calculate the tension.
Given:
Mass of statue (m) = 20.0 kg
Density of gold (ρ) = 19.6 x 10^3 kg/m^3
Density of water (ρw) = 1000 kg/m^3
Acceleration due to gravity (g) = 9.8 m/s^2
Acceleration of the statue (a) = 2 m/s^2
Step 1: Calculating the volume of the statue
Volume = mass / density = 20.0 kg / (19.6 x 10^3 kg/m^3)
Step 2: Calculating the weight of water displaced
Volume of water displaced = Volume of the statue
Weight of water displaced = Volume of water displaced x Density of water x acceleration due to gravity
Step 3: Calculating the tension in the hoisting cable
Tension = Weight of the statue - Buoyancy force
By plugging in the values and performing the calculations, you should be able to determine the tension in the hoisting cable.