The gravitational potential energy of the brick is 25.6 J
Explanation:
The gravitational potential energy of an object is the energy possessed by the object due to its position in a gravitational field.
Near the surface of a planet, the gravitational potential energy is given by
where
m is the mass of the object
g is the strength of the gravitational field
h is the height of the object relative to the ground
For the brick in this problem, we have:
m = 8 kg is its mass
g = 1.6 N/kg is the strenght of the gravitational field on the moon
h = 2 m is the height above the ground
Substituting, we find:
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To solve this problem it is necessary to apply the concepts related to the Force from Hooke's law, the force since Newton's second law and the potential elastic energy.
Since the forces are balanced the Spring force is equal to the force of the weight that is
Where,
k = Spring constant
x = Displacement
m = Mass
g = Gravitational Acceleration
Re-arrange to find the spring constant
Just before launch the compression is 40cm, then from Potential Elastic Energy definition
Therefore the energy stored in the spring is 63.72J
Answer:
See the explanation below
Explanation:
To better understand this problem, a cylinder sketch is attached before and after the cut, we see that after the cut, the shape of this resembles that of a right triangle.
We can find, the centroid in the xy plane, knowing that the centroid for a triangle is located a third of its base.
In the z axis there is no displacement of the centroid.
To solve this problem we will use the kinematic equations of angular motion in relation to those of linear / tangential motion.
We will proceed to find the centripetal acceleration (From the ratio of the radius and angular velocity to the linear velocity) and the tangential acceleration to finally find the total acceleration of the body.
Our data is given as:
The angular speed
The angular acceleration
The distance
The relation between the linear velocity and angular velocity is
Where,
r = Radius
Angular velocity
At the same time we have that the centripetal acceleration is
Now the tangential acceleration is given as,
Here,
Angular acceleration
r = Radius
Finally using the properties of the vectors, we will have that the resulting component of the acceleration would be
Therefore the correct answer is C.
