Answer:
0.785 m/s
Explanation:
Hi!
To solve this problem we will use the equation of motion of the harmonic oscillator, <em>i.e.</em>
- (1)
- (1)
The problem say us that the spring is released from rest when the spring is stretched by 0.100 m, this condition is given as:
Since cos(0)=1 and sin(0) = 0:
We get
Now it say that after 0.4s the weigth reaches zero speed. This will happen when the sping shrinks by 0.100. This condition is written as:
Since
This is the same as:
We know that cosine equals to -1 when its argument is equal to:
(2n+1)π
With n an integer
The first time should happen when n=0
Therefore:
π = 0.4ω
or
ω = π/0.4 -- (2)
Now, the maximum speed will be reached when the potential energy is zero, <em>i.e. </em>when the sping is not stretched, that is when x = 0
With this info we will know at what time it happens:
The first time that the cosine is equal to zero is when its argument is equal to π/2
<em>i.e.</em>
And the velocity at that time is:
But sin(π/2) = 1.
Therefore, using eq(2):
And so:
The movement of the planets and other celestial bodies in the solar system is actually caused by the sun's gravitational pull or force.
Just like the moon orbits the earth because of the gravitational pull by the earth so does gravitational pull by the sun causes planets' and other celestial bodies' orbit.
Answer:
8.475 x 10^7 Pa
Explanation:
h = 8648 m, g = 9.8 m/s^2, density of water, d = 1000 kg/m^3
Pressure at a depth is defined as the product of depth of water , acceleration due to gravity and density of water.
P = h x d x g
P = 8648 x 1000 x 9.8 = 8.475 x 10^7 Pa
Answer:
64 J
Explanation:
KE = ½mv²
Given m = 8 kg and v = 4 m/s:
KE = ½ (8 kg) (4 m/s)²
KE = 64 J