Answer: 0.048 J
Explanation:
The described situation is better understood with the attached figure.
Let's assume that when the mass is released after being lifted up, it starts performing simple harmonic motion with an amplitude L. Then, the maximum speed of this hanging mass is fulfilled at the equilibrium position and its given by the following equation:
(1)
Where:
is the spring constant which can be calculated by the Hooke's law: being the acceleration due gravity and the length the spring is streched.
is the mass
is the amplitude
So, (2)
Substituting (2) in (1):
(3)
(4)
On the other hand, the kinetic energy is given by the following equation:
(5)
(6)
Hence:
Answer:
The value is
Explanation:
From the question we are told that
The depth of the bottom of the trench is
The depth considered is
Generally the pressure is mathematically represented as
Here is the density of water with value
=>
=>
Converting to atmosphere
=>
=>
The density is determined on the steepness of the slope. The greater the density is bases upon the steepest slope. To conclude, I'd say Line A has the steepest slope therefore has the greatest density.
Answer:
Explanation:
The forces acting on the crates when the train starts stopping are their weights, the normal force from the train, the static frictional force and the fictional force that is produced by the deceleration of the train. As the gravitational force, this fictional force is equal to the mass of the crates multiplied by the magnitude of the acceleration of the train. So, the equations of motion of the crates will be:
Since the static frictional force is , we get:
So we have a limit to the acceleration of the train. Now, we have to know the distance traveled by the train when it is stopping. Then, we use the kinematic formula:
Now we solve for the acceleration to combine this equation to the inequality we got before:
And solve for x:
Since we are looking for the minimum value for x, we consider the case in which that inequality becomes an equation:
Before we finish, we have to convert the unities of the initial velocity to meters per second:
Finally, we plug in the known values to get :
It means that the train can be stopped at a minimum distance of 36.2m at constant acceleration without causing the crates slide over the floor.