Determine the initial acceleration of a 1 kg solid aluminum chunk (density = 2,700 kg/m3) released from rest by a diver 10 m under the ocean.
Assume water is about 1000 kg/m^3
Force up = 1000 * V *g
Force down = m g = 2700 * V * g
so V = 1/2700
force up = (10/27)g
force down = 1 g
net force down = (1-10/27) g
F = m a
(1 -10/27) g = 1 a
a = 9.81 *(17/27) down
Thank You
To determine the initial acceleration of the aluminum chunk, we can use the concept of buoyancy and Newton's laws of motion.
1. First, let's calculate the buoyant force acting on the aluminum chunk:
Buoyant force = Weight of liquid displaced = Density of liquid × Volume of liquid displaced × acceleration due to gravity
The density of seawater is approximately 1,030 kg/m³, and the density of the aluminum chunk is given as 2,700 kg/m³. The volume of the aluminum chunk can be calculated by dividing its mass by its density (1 kg / 2,700 kg/m³).
2. Next, calculate the weight of the aluminum chunk, which is typically given by:
Weight = mass × acceleration due to gravity
3. Now, with the weight of the aluminum chunk and the buoyant force acting on it, we can apply Newton's second law of motion:
Net force = m × a
where m is the mass of the aluminum chunk and a is the acceleration.
In this case, the net force is the difference between the weight and the buoyant force acting on the chunk.
4. Finally, rearrange the equation to solve for acceleration:
a = (Weight - Buoyant force) / m
Plugging in the values we have calculated, we can determine the initial acceleration of the aluminum chunk.