Answer:
Energy May be measured in joule
Answer:
Friction and air resistance cause some of his kinetic energy to be “lost”. This makes him slow down.
Explanation:
The law of conservation of energy states that in absence of frictional forces, the mechanical energy of an object (given by the sum of its kinetic and potential energy) is conserved. In such a situation, the skateboarder would never stop his motion, because potential energy is continuously converted into kinetic energy and vice-versa, but the total energy remains the same so he would never stop.
In a real world, however, this is not true. In fact, in a real world some frictional force are present, in particular:
- friction: this force is due to the contact between the skateboard and the surface of the halfpipe, and its direction is always opposite to the motion of the skateboarder
- Air resistance: this force is due to the resistance opposed by the molecules of air that the skateboarder meets during his motion, and its direction is also opposite to the motion of the skateboarder
This two forces are said to be non-conservative forces, which means that they cause some of the mechanical energy of the skateboarder to be "lost", in the sense that it is dissipated as heat and it is no longer available for the skateboarder.
Therefore, the correct option is
Friction and air resistance cause some of his kinetic energy to be “lost”. This makes him slow down.
This is a perfect opportunity to stuff all that data into the general equation for the height of an object that has some initial height, and some initial velocity, when it is dropped into free fall.
H(t) = (H₀) + (v₀ T) + (1/2 a T²)
Height at any time 'T' after the drop =
(initial height) +
(initial velocity) x (T) +
(1/2) x (acceleration) x (T²) .
For the balloon problem ...
-- We have both directions involved here, so we have to define them:
Upward = the positive direction
Initial height = +150 m
Initial velocity = + 3 m/s
Downward = the negative direction
Acceleration (of gravity) = -9.8 m/s²
Height when the bag hits the ground = 0 .
H(t) = (H₀) + (v₀ T) + (1/2 a T²)
0 = (150m) + (3m/s T) + (1/2 x -9.8 m/s² x T²)
-4.9 T² + 3T + 150 = 0
Use the quadratic equation:
T = (-1/9.8) [ -3 plus or minus √(9 + 2940) ]
= (-1/9.8) [ -3 plus or minus 54.305 ]
= (-1/9.8) [ 51.305 or -57.305 ]
T = -5.235 seconds or 5.847 seconds .
(The first solution means that the path of the sandbag is part of
the same path that it would have had if it were launched from the
ground 5.235 seconds before it was actually dropped from balloon
while ascending.)
Concerning the maximum height ... I don't know right now any other
easy way to do that part without differentiating the big equation.
So I hope you've been introduced to a little bit of calculus.
H(t) = (H₀) + (v₀ T) + (1/2 a T²)
H'(t) = v₀ + a T
The extremes of 'H' (height) correspond to points where h'(t) = 0 .
Set v₀ + a T = 0
+3 - 9.8 T = 0
Add 9.8 to each side: 3 = 9.8 T
Divide each side by 9.8 : T = 0.306 second
That's the time after the drop when the bag reaches its max altitude.
Oh gosh ! I could have found that without differentiating.
- The bag is released while moving UP at 3 m/s .
- Gravity adds 9.8 m/s of downward speed to that every second.
So the bag reaches the top of its arc, runs out of gas, and starts
falling, after
(3 / 9.8) = 0.306 second .
At the beginning of that time, it's moving up at 3 m/s.
At the end of that time, it's moving with zero vertical speed).
Average speed during that 0.306 second = (1/2) (3 + 0) = 1.5 m/s .
Distance climbed during that time = (average speed) x (time)
= (1.5 m/s) x (0.306 sec)
= 0.459 meter (hardly any at all)
But it was already up there at 150 m when it was released.
It climbs an additional 0.459 meter, topping out at 150.459 m,
then turns and begins to plummet earthward, where it plummets
to its ultimate final 'plop' precisely 5.847 seconds after its release.
We can only hope and pray that there's nobody standing at
Ground Zero at the instant of the plop.
I would indeed be remiss if were to neglect, in conclusion,
to express my profound gratitude for the bounty of 5 points
that I shall reap from this work. The moldy crust and tepid
cloudy water have been delicious, and will not soon be forgotten.
Answer: D
Height of marble from ground
Explanation:
From the formula of kinetic energy and potential energy,
K.E = 1/2mv^2
While
P.E = mgh
From all the parameters given from the question. You can see that mass is constant, acceleration due to gravity is also constant.
Independent variable must be a value that can varies.
Since Jack rolled a marble down a ramp and recorded the potential energy and kinetic energy of the marble at different positions on the ramp to see the effects on both energies.
This different position must be the height which will produce an effect on the potential and kinetic energy of the marble.
Independent variable always provides an effect for dependent variable. Which are kinetic energy and potential energy in this case.
Height of marble from ground is the right answer.
A = delta v over delta t delta v is calculated with final velocity less initial velocity then delta v is equals to 20 - 0 that is 20m/s and to calculate delta t is like delta v is final time less initial time as initial time always is 0 the delta t is equals to 10s then a = 20/10 then acceleration is 10m/s^2 (remember that is squared)
