The distance an object falls from rest through gravity is
D = (1/2) (g) (t²)
Distance = (1/2 acceleration of gravity) x (square of the falling time)
We want to see how the time will be affected
if ' D ' doesn't change but ' g ' does.
So I'm going to start by rearranging the equation
to solve for ' t '.
D = (1/2) (g) (t²)
Multiply each side by 2 : 2 D = g t²
Divide each side by ' g ' : 2 D/g = t²
Square root each side: t = √ (2D/g)
Looking at the equation now, we can see what happens
to ' t ' when only ' g ' changes:
-- ' g ' is in the denominator; so bigger 'g' ==> shorter 't'
and smaller 'g' ==> longer 't' .
-- They don't change by the same factor, because 1/g is inside
the square root. So 't' changes the same amount as √1/g does.
Gravity on the surface of the moon is roughly 1/6 the value
of gravity on the surface of the Earth.
So we expect ' t ' to increase by √6 = 2.45 times.
It would take the same bottle (2.45 x 4.95) = 12.12 seconds
to roll off the same window sill and fall 120 meters down to the
surface of the Moon.
Answer:
31.1 N
Explanation:
m = mass attached to string = 0.50 kg
r = radius of the vertical circle = 2.0 m
v = speed of the mass at the highest point = 12 m/s
T = force of the string on the mass attached.
At the highest point, force equation is given as
Inserting the values
T = 31.1 N
K.E1=1/2×100×3²
=50×9
=450J
K.E2=1/2×100×36
=50×36
=1800J
Helium is lighter than air from the lungs.
Explanation:
A balloon filled with the air from lungs will sink to the ground but a balloon filled with Helium floats because helium is lighter than air.
Air is a mixture of many gases.
The air from the lungs is predominantly made up of carbon dioxide and water vapor.
- Gram per mole of carbon dioxide is 44. Water vapor is 18.
- Compared to helium which is 4, we see that the gas is lighter.
- Since the gas is lighter, it will float in air.
- The main component of air around us is nitrogen gas with a gram per mole of 28.
- A balloon filled with more of air from the lungs weigh more than that will filled air around and even far more than helium gas.
- This will cause a helium filled balloon to float.
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Answer:
<em>0.97c</em>
<em></em>
Explanation:
From the relativistic equation for length contraction, we have
= 
where
is the final length of the object
is the original length of the object before contraction
β = 
where v is the speed of the object
c is the speed of light in free space = 3 x 10^8 m/s
The equation can be re-written as
/ = 
For the length to contract to one-fourth of the proper length, then
/ = 1/4
substituting into the equation, we'll have
1/4 =
substituting for β, we'll have
1/4 = 
squaring both side of the equation, we'll have
1/16 = 1 - 
= 1 - 1/16
= 15/16
square root both sides of the equation, we have
v/c = 0.968
v = <em>0.97c</em>
