Answer:
(c) 10.29 J
(d) 113.19 J
(e) 113.19 J
(f) 10061 N/m
Explanation:
15 cm = 0.15 m
Let g = 9.8 m/s2
(c) The work done by gravitational force is the product of gravity force and the distance compressed
(d) By using law of energy conservation with potential energy reference being 0 at the maximum compression point. As the ball falls and come to a stop at the compression point, its potential energy is transferred to elastic energy, which is the work that the mattress does on the ball:
where h = 1.5 + 0.15 = 1.65 m is the vertical distance that it falls.
(e) Before the compression, the potential energy of the mattress is 0. After the compression, the potential energy is 113.19J. So it has increased by 113.19J due to the potential energy transferred from the falling ball.
(f)
Answer:
a)
Now we can replace the velocity for t=1.75 s
For t = 3.0 s we have:
b)
And we can find the positions for the two times required like this:
And now we can replace and we got:
Explanation:
The particle position is given by:
Part a
In order to find the velocity we need to take the first derivate for the position function like this:
Now we can replace the velocity for t=1.75 s
For t = 3.0 s we have:
Part b
For this case we can find the average velocity with the following formula:
And we can find the positions for the two times required like this:
And now we can replace and we got:
