Let's start with the total amount of energy available for the whole scenario:
Some kind of machine gave the coaster a bunch of potential energy by
dragging it up to the top of a 45m hill,and that's the energy is has to work with.
Potential energy = (M) (G) (H) = (800) (9.8) (45) = 352,800 joules
It was then given an extra kick ... enough to give it some kinetic energy, and
start it rolling at 4 m/s.
Kinetic energy = (1/2) (M) (V)² = (1/2) (800) (4)² = 6,400 joules
So the coaster starts out with (352,000 + 6,400) =<em> </em><u><em>359,200 joules</em></u><em> </em>of energy.
There's no friction, so it'll have <u>that same energy</u> at every point of the story.
=================================
Skip the loop for a moment, because the first question concerns the hill after
the loop. We'll come back to it.
The coaster is traveling 10 m/sat the top of the next hill. Its kinetic energy is
(1/2) (M) (V)² = (400) (10)² = 40,000 joules.
Its potential energy at the top of the hill is (359,200 - 40,000) = 319,200.
PE = (M) (G) (H)
319,200 = (800) (9.8) (H)
H = (319,200) / (800 x 9.8) = <em>40.71 meters</em>
=================================
Now back to the loop:
You said that the loop is 22m high at the top. The PE up there is
PE = (M) (G) (H) = (800) (9.8) (22) = 172,480 joules
So the rest is now kinetic. KE = (359,200 - 172,480) = 186,720 joules.
KE = (1/2) (M) (V)² = 186,720
(400) (V)² = 186,720
V² = 186,720 / 400 = 466.8
V = √466.8 = <em>21.61 m/s</em>
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Now it looks like there should be another question ... that's why they
bothered to tell you that the end is 4m off the ground. They must
want you to find the coaster's speed when it gets to the end.
At 4m off the ground, PE = (M) (G) (H) = (800) (9.8) (4) = 31,360 joules.
The rest will be kinetic. KE = (359,200 - 31,360) = 327,840 joules
KE = (1/2) (M) (V)² = 327,840
400 V² = 327,840
V² = 327,840 / 400 = 819.6
V = √819.6 = <em>28.63 m/s</em> at the end
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If the official answers in class are a little bit different from these,
it'll be because they used some different number for Gravity.
I used '9.8' for gravity, but very often, they use '10' .
If the official answers in class are way way different from these,
then I made one or more big mistakes somewhere. Sorry.
Answer:

Explanation:
The centripetal acceleration of a point moving by circular motion is given by:

where
is the angular velocity
r is the distance from the axis of rotation
The point on the wheel makes 5.0 revolutions per second, so the frequency is

and the angular velocity is

While the distance of the point from the axis of rotation is

Substituting, we find the acceleration:

Answer:
A. Drag
Explanation:
This is because, since friction tends to oppose the motion of an object, and drag affects an object moving in a fluid, the more the friction, the more the drag on the object.
To solve this problem we will use the concepts of the moment of rotational inertia, angular acceleration and the expression of angular velocity.
The rotational inertia is expressed as follows:

Here,
m = Mass of the object
r = Distance from the rotational axis
The rotational acceleration in terms of translational acceleration is

Here,
a = Acceleration
R = Radius of the circular path of the object
The expression for the rotational speed of the object is

Here,
is the angular displacement of the object
The explanation by which when climbing a mountain uphill is changed to a larger pinion, is because it produces a greater torque but it is necessary to make more pedaling to be able to travel the same distance. Basically every turn results in less rotations of the rear wheel. Said energy that was previously used to move the rotation of the wheel is now distributed in more turns of the pedal. Therefore option a and c are correct.
This would indicate that the correct option is D.
Answer:
1.962 × 10⁻³ kW
Explanation:
The energy of a wave of a wave, such as an ocean wave, in regions of considerable water depth given its amplitude in a meter of crest and surface unit is given by the relation;

Where:
ρ = Density of water = 1000 kg/m³
g = Acceleration due to gravity = 9.81 m/s²
A = Wave amplitude = 2 cm = 0.02 m
We therefore have;

The energy is power is the energy per second which is gives;
P = E /second = 1.962 J/s = 1.962 W = 1.962 × 10⁻³ kW.