This is a simple application of Newton's Law of Universal Gravitation.
The force of gravity is inversely proportional to the distance between the two
centers of mass. We don't need to know the mass of earth or the test mass to
solve this, because we'll be setting up a proportionality, which means that all
controlled variables can be expressed as a proportionality constant which will
eventually cancel. <span>
Set up the following proportionality equation from
Newton's Universal Gravitation:
F = k/d²; where k is the constant of proportionality
Plug in values for F and d, making two
equations:
(9.803 N) = k/r²; where r is the radius of earth,
and
(9.792 N) = k/(r+h)²; where h is the height above
sea level.
Divide one by the other, and you get:
9.803 / 9.792 = (r+h)² / r²; the k cancels
Solve for h:
√(9.803 / 9.792) = (r+h) / r
r √(9.803 / 9.792) = r + h
r √(9.803 / 9.792) – r = h
Look up the value for r (radius of earth) and
evaluate:
(6371 km) √(9.803 / 9.792) – (6371 km) = h
<span>h ≈ 3.58 km</span></span>
Well I must say that's a very interesting machine you've got there. It wouldn't be possible to build a system with an actual mechanical advantage of 2 million. But if you did have such a thing, and you wanted to use it to lift a 2000 pound weight, then you would only need to pull with a force of 1.6% of an ounce ! The bad news is that in order to lift the weight one foot, you'd have to pull about 379 miles of rope through the pulley system !
Answer:
A hypothesis is a limited explanation of a phenomenon; a scientific theory is an in-depth explanation of the observed phenomenon. A law is a statement about an observed phenomenon or a unifying concept
Explanation:
Answer:
the initial velocity of the ball is 17.14 m/s
Explanation:
Given;
maximum height reached by the ball, h = 15 m
let the initial velocity of the ball = u
at maximum height, the final velocity of the ball is zero, v = 0
The initial velocity of the ball is calculated by using the following upward motion kinematic equation;
v² = u² - 2gh
0 = u² - 2(9.8 x 15)
u² = 294
u = √294
u = 17.14 m/s
Therefore, the initial velocity of the ball is 17.14 m/s
Answer: 288.8 m
Explanation:
We have the following data:
is the time it takes to the child to reach the bottom of the slope
is the initial velocity (the child started from rest)
is the angle of the slope
is the length of the slope
Now, the Force exerted on the sled along the ramp is:
(1)
Where 
is the mass of the sled and 
its acceleration
In addition, if we draw a free body diagram of this sled, the force along the ramp will be:
(2)
Where 
is the acceleration due gravity
Then:
(3)
Finding :
(4)
(5)
(6)
Now, we will use the following kinematic equations to find :
(7)
(8)
Where 
is the final velocity
Finding from (7):
(9)
(10)
Substituting (10) in (8):
(11)
Finding :
