The concept of energy can be calculated in multiple ways. Which units are used for energy? Check all that apply. joules kilogram
1 answer:
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Answer:
The distance the bungee cord that would be stretched 0.602 m, should be selected when pulled by a force of 380 N.
Explanation:
As from the given data
the length of the rope is given as l=30 m
the stretched length is given as l'=41m
the stretched length required is give as y=l'-l=41-30=11m
the mass is m=95 kg
the force is F=380 N
the gravitational acceleration is g=9.8 m/s2
The equation of k is given by equating the energy at the equilibrium point which is given as
Here
m=95 kg, g=9.8 m/s2, h=41 m, y=11 m so
Now the force is
or
So here F=380 N, k=630.92 N/m
So the distance is 0.602 m
All the answers are:
a) The time that will it take to rise to the highest point is 3.06 seconds.
b) The ball will rise to a height of 45.87 meters.
c) The time at which the ball will have a velocity of 10 m/s upward is 2.04 seconds.
The time when the ball has 10 m/s downward is 1.02 seconds.
d) The displacement of the ball will be zero at 6.12 seconds.
e) The time when the magnitude of the ball's velocity is equal to half its velocity of projection is 1.53 seconds.
f) The ball's displacement is equal to half the maximum height to which it rises after 0.90 seconds.
g) In each moment (upward and downward) the magnitude of the acceleration is the value of g (9.81 m/s²) and is a vector in the negative y-direction.
Let's calculate the values for each case.
a) At the highest point, the final velocity is 0, so we can use the following equation.
(1)
Where:
- v(i) is the initial velocity
- v(f) is the final velocity
- g is the acceleration due to gravity (9.81 m/s²)
We know that v(i) = 30 m/s.
Solve it for t:
Hence, the time is 3.06 s.
b) At the highest point, the final velocity is 0, so we can use the following equation.
(2)
We know that the initial velocity is 30 m/s.
Solving it for h we have:
Then, the height is 45.87 m.
c) Using equation (1) we can find the time (t).
So, the time elapsed to get 10 m/s is:
We know the upward time is equal to the downward time. So the time from v=10 m/s to v=0 m/s will be.
This is the time when the ball has 10 m/s downward.
Therefore, the time upward is 2.04 s, and the time downward is 1.02 s.
d) It will be when the ball returns to the ground.
The displacement will be zero after 6.12 s.
e) Here we need to find the time when v(f) is 15 m/s
The time when the v(f) is 15 m/s is 1.53 s.
f) Here, we need to find t when h = 45.87/2 m = 22.94 m
We can use the next equation:
[tex]h=v_{i}t-0.5gt^{2}/tex]
[tex]22.94=30t-0.5*9.81*t^{2}/tex]
Solving this quadratic equation, t will be:
[tex]t=0.90\: s/tex]
Hence, the ball's displacement is equal to half the maximum h, at 0.90 s.
g) In each moment the magnitude of the acceleration is the value of g (9.81 m/s²) and is a vector in the negative y-direction.
Learn more about vertical motion here:
I hope it helps you!