A 4.65 kg object is released from rest while fully submerged in a liquid. The liquid displaced by the submerged object has a mass of 2.60 kg. How far and in what direction does the object move in 0.300 s, assuming that it moves freely and that the drag force on it from the liquid is negligible?
COOL STORY, BRO. NEVER MIND POSTING HOW YOU SOLVED IT.
Anyway, here's how you solve it:
m = mass of liquid displaced
M = mass of object
F(b) = buoyant force
What two vertical forces are acting on this object? The buoyant force pushing up and the weight of the object.
F(b) = mg (pushing up)
F(weight) = Mg (pulling down)
So our net forces can be written as:
F(net) = Mg - mg = (M - m)g
And you also know that the sum of forces equals the mass times acceleration.
F(net) = Ma
So, rewritten:
(M - m)g = Ma
Do some algebra:
(M-m)*g/M = a
And I'm sure you remember the constant acceleration
x = 1/2 * a * t^2
never mind I finally got it after looking at it for almost and hour.
How did you get the answer?
To determine the distance and direction the object moves in 0.300 s, we can apply the principle of buoyancy and Newton's second law.
1. To find the buoyant force acting on the object, we need to calculate the weight of the liquid displaced by the object:
Buoyant force = weight of displaced liquid
Buoyant force = mass of displaced liquid * acceleration due to gravity
Given: mass of displaced liquid = 2.60 kg, acceleration due to gravity = 9.8 m/s^2
Buoyant force = 2.60 kg * 9.8 m/s^2
Buoyant force = 25.48 N
2. With the buoyant force in mind, we can now calculate the net force acting on the object:
Net force = Buoyant force - Weight of the object
Weight of the object = mass of the object * acceleration due to gravity
Given: mass of the object = 4.65 kg, acceleration due to gravity = 9.8 m/s^2
Weight of the object = 4.65 kg * 9.8 m/s^2
Weight of the object = 45.57 N
Net force = 25.48 N - 45.57 N
Net force = -20.09 N (negative because the buoyant force opposes the weight of the object)
3. Now, we can calculate the acceleration of the object using Newton's second law:
Net force = mass of the object * acceleration
-20.09 N = 4.65 kg * acceleration
Acceleration = -20.09 N / 4.65 kg
Acceleration = -4.32 m/s^2 (negative indicating acceleration in the opposite direction of the weight of the object)
4. Finally, we can find the distance the object moves in 0.300 s using the equations of motion:
Distance = (initial velocity * time) + (0.5 * acceleration * time^2)
Since the object is released from rest, the initial velocity is 0 m/s.
Distance = 0.5 * acceleration * time^2
Distance = 0.5 * (-4.32 m/s^2) * (0.300 s)^2
Distance = -0.1956 m
The object moves a distance of 0.1956 m in the negative direction (opposite to the initial position) in 0.300 s.