This is a classic example of conservation of energy. Assuming that there are no losses due to friction with air we'll proceed by saying that the total energy mus be conserved.
Now having information on the speed at the lowest point we can say that the energy of the system at this point is purely kinetic:
Where m is the mass of the pendulum. Because of conservation of energy, the total energy at maximum height won't change, but at this point the energy will be purely potential energy instead.
This is the part where we exploit the Energy's conservation, I'm really insisting on this fact right here but it's very very important, The totam energy Em was
It hasn't changed! So inserting this into the equation relating the total energy at the highest point we'll have:
Solving for h gives us:
It doesn't depend on mass!
To solve this problem we will apply the concept of Impulse. Which is described as the product between the Force and the change in time. Mathematically this can be described as
Where,
F = Force
= Time
Our values are given as,
F = 1450N
Replacing we have,
Therefore the impulse delivered to the soccer ball is 
or 
Answer:
Explanation:
The acceleration due to gravity on earth is regardless of the mass of the object. This means, in the absence of air resistance, both a 3000 kg object and a 300 kg will accelerate at the same rate of towards earth.
The reason the acceleration due to gravity is the same for all masses is that by grace of nature, the inertial mass 
of the object from 
equals the gravitational mass from 
, resulting
which is the acceleration that only depends on the mass of earth and its radius, and not on the mass of the object.
Answer:
(D) Vega must produce more energy than HR 4374.
Explanation:
The apparent visual magnitude is defined as the luminosity of a star seen from earth. The Greek astronomer Hipparcos was the first who invent a numerical scale to describe how bright a star appear to be in the sky to the naked eye, so he gave an apparent magnitude of 6 to the faintest star in the sky and an apparent magnitude of 1 to the brigthest one. Since the arrive of the telescope era this range was expanded to negative numbers for the most luminous one.
The human eye has a logaritmical response to the luminosity of stars, so as an example, if one star has an apparent magnitude of 6 and another one has an apparent magnitude of 1, the second one will be 100 times brigther than the first one. In the other hand, for a star that has apparent magnitude of 1 it will appear to be 2.512 times brigther than a star with apparent magnitude of 2.
The apparent magnitude of a star can variate as a consecuence of the distance from earth or for its energy production.
With all these facts clear enough described above, it is easier to conclude that as the two star are at the same distance the apparent visual magnitude will depend in the energy production. In the case of Vega it has an apparent visual magnitude of 0.03, while HR 4374 has an apparent visual magnitude of 4.87. According with the scale stablished for Hipparcos, Vega will be more luminous than HR 4374. This means that Vega produce more energy than HR 4374.
Answer:
Let f be force of friction on the blocks kept on inclined plane. T be tension in the string
For motion of block on the inclined plane in upward direction
T - m₁gsin40 - f = m₁a
f = μ m₁gcos40
For motion of hanging block on in downward direction
m₂g - T = m₂ a
Adding to cancel T
m₂g - - m₁gsin40 - μ m₁gcos40 = a ( m₁+m₂ )
a = g (m₂ - - m₁sin40 - μ m₁cos40) / ( m₁+m₂ )
Putting the values
a = 9.8 ( 4.75 - 2.12-1.045) / 7.6
2.04 m s⁻²
M₂ will go down and M₁ will go up with acceleration .
Explanation:
