A student was trying to find the relationship between mass and force. He placed four different masses on a table and pulled them
2 answers:
You might be interested in
Answer:
a) It is moving at when reaches the ground.
b) It is moving at when reaches the ground.
Explanation:
Work energy theorem states that the total work on a body is equal its change in kinetic energy, this is:
(1)
with W the total work, Ki the initial kinetic energy and Kf the final kinetic energy. Kinetic energy is defined as:
(2)
with m the mass and v the velocity.
Using (2) on (1):
(3)
In both cases the total work while the objects are in the air is the work gravity field does on them. Work is force times the displacement, so in our case is weight (w=mg) of the object times displacement (d):
(4)
Using (4) on (3):
(5)
That's the equation we're going to use on a) and b).
a) Because the branch started form rest initial velocity (vi) is equal zero, using this and solving (5) for final velocity:
b) In this case the final velocity of the boulder is instantly zero when it reaches its maximum height, another important thing to note is that in this case work is negative because weight is opposing boulder movement, so we should use -mgd:
Solving for initial velocity (when the boulder left the volcano):
Please find attached photograph for your answer. Please do comment whether it is useful or not
Answer:
Explanation:
The heaviside function is defined as:
so we see that the Heaviside function "switches on" when, and remains switched on when
If we want our heaviside function to switch on when , we need the argument to the heaviside function to be 0 when
Thus we define a function f:
The term inside the heaviside function makes sure to displace the function 5 units to the right.
Now we just need to add a scale up factor of 240 V, because thats the voltage applied after the heaviside function switches on. ( when
, so it becomes just a 1, which we can safely ignore.)
Therefore our final result is:
I have made a sketch for you, and added it as attachment.
