A 4.55 kg object is released from rest while fully submerged in a liquid. The liquid displaced by the submerged object has a mass of 3.20 kg. How far and in what direction does the object move in 0.200 s, assuming that it moves freely and that the drag force on it from the liquid is negligible?
The object will sink, since the buoyancy force is less than its weight.
The net downward force is
(4.55-3.20)g = 12.25 N
Use Fnet = M*a for the acceleration, a.
a = 12.25/4.55 = 2.69 m/s^2
To determine the distance and direction the object moves, we can use Newton's second law. The net force acting on the object is equal to the product of its mass and acceleration.
First, calculate the buoyant force acting on the object. The buoyant force is equal to the weight of the liquid displaced by the object. We can calculate the buoyant force using the formula:
Buoyant force = mass of liquid displaced * gravitational acceleration
Given that the mass of liquid displaced is 3.20 kg and the gravitational acceleration is 9.8 m/s^2, the buoyant force is:
Buoyant force = 3.20 kg * 9.8 m/s^2 = 31.36 N
Next, calculate the net force acting on the object. Since the object is released from rest, there are no other forces acting on it except for the buoyant force. Therefore, the net force is equal to the buoyant force:
Net force = Buoyant force = 31.36 N
Now, we can determine the acceleration of the object using Newton's second law:
Net force = mass of the object * acceleration
Rearranging the equation, we find:
Acceleration = Net force / mass of the object
Acceleration = 31.36 N / 4.55 kg = 6.8846 m/s^2
Finally, we can calculate the distance the object moves using the equation of motion:
Distance = Initial velocity * time + (1/2) * acceleration * time^2
Since the object is released from rest, the initial velocity is zero. Plugging in the values:
Distance = 0 * 0.200 s + (1/2) * 6.8846 m/s^2 * (0.200 s)^2 = 0.1389 m
Therefore, the object moves a distance of 0.1389 meters in the direction opposite to the buoyant force.
To find the distance and direction the object moves in 0.200 s, we can use the principle of buoyancy and Newton's second law of motion. Here's how you can approach the problem:
1. Calculate the buoyant force acting on the object:
- The buoyant force is equal to the weight of the liquid displaced by the object.
- The weight of the liquid is given by the mass of the liquid (3.20 kg) multiplied by the acceleration due to gravity (9.8 m/s^2).
Buoyant force = mass of liquid × acceleration due to gravity
2. Calculate the net force acting on the object:
- The net force is the difference between the object's weight and the buoyant force.
- The weight of the object is given by the mass of the object (4.55 kg) multiplied by the acceleration due to gravity.
Net force = weight of object - buoyant force
3. Calculate the acceleration of the object:
- The acceleration of the object is given by Newton's second law of motion:
Net force = mass of object × acceleration
4. Calculate the distance traveled by the object:
- The distance traveled can be found using the kinematic equation:
Distance = initial velocity × time + (1/2) × acceleration × time^2
Since the object starts from rest, the initial velocity is 0.
5. Determine the direction of motion:
- The sign of the distance will determine the direction of motion. If the distance is positive, it means the object moves in the positive direction. If the distance is negative, the object moves in the negative direction.
By following these steps and performing the necessary calculations, you can find the distance and direction in which the object moves in 0.200 s.