To solve this problem we will apply the concepts related to energy conservation. From this conservation we will find the magnitude of the amplitude. Later for the second part, we will need to find the period, from which it will be possible to obtain the speed of the body.
A) Conservation of Energy,
Here,
m = Mass
v = Velocity
k = Spring constant
A = Amplitude
Rearranging to find the Amplitude we have,
Replacing,
(B) For this part we will begin by applying the concept of Period, this in order to find the speed defined in the mass-spring systems.
The Period is defined as
Replacing,
Now the velocity is described as,
We have all the values, then replacing,
Answer:
Explanation:
This is a recoil problem, which is just another application of the Law of Momentum Conservation. The equation for us is:
![[m_av_a+m_ev_e]_b=[m_av_a+m_ev_e]_a](https://tex.z-dn.net/?f=%5Bm_av_a%2Bm_ev_e%5D_b%3D%5Bm_av_a%2Bm_ev_e%5D_a)
which, in words, is
The momentum of the astronaut plus the momentum of the piece of equipment before the equipment is thrown has to be equal to the momentum of all that same stuff after the equipment is thrown. Filling in:
![[(90.0)(0)+(.50)(0)]_b=[(90.0)(v)+(.50)(-4.0)]_a](https://tex.z-dn.net/?f=%5B%2890.0%29%280%29%2B%28.50%29%280%29%5D_b%3D%5B%2890.0%29%28v%29%2B%28.50%29%28-4.0%29%5D_a)
Obviously, on the left side of the equation, nothing is moving so the whole left side equals 0. Doing the math on the right and paying specific attention to the sig fig's here (notice, I added a 0 after the 4 in the velocity value so our sig fig's are 2 instead of just 1. 1 is useless in most applications).
0 = 90.0v - 2.0 and
2.0 = 90.0v so
v = .022 m/s This is the rate at which he is moving TOWARDS the ship (negative was moving away from the ship, as indicated by the - in the problem). Now we can use the d = rt equation to find out how long this process will take him if he wants to reach his ship before he dies.
12 = .022t and
t = 550 seconds, which is the same thing as 9.2 minutes
The total energy (also called mechanical energy) is the sum of the kinetic energy and potential energy:
For this pendulum, we see that at t=0.60 s the total energy is TE=0.918 J while the potential energy is 0.054 J, so the kinetic energy (the missing value in the table) is
When the angle of the ramp increases, the weight of the box acting perpendicular to the ramp decreases.
<h3>
Normal reaction of the box</h3>
The normal reaction of the box is due to weight of the box acting perpendicular to the ramp.
Fn = Wcosθ
<h3>when the angle of the ramp = 30⁰</h3>
Fn = Wcos(30)
Fn = 0.866W
<h3>when the angle of the ramp = 45⁰</h3>
Fn = W x cos(45)
Fn = 0.7071W
Thus, when the angle of the ramp increases, the weight of the box acting perpendicular to the ramp decreases.
Learn more about normal reaction here: brainly.com/question/18292235
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We will determine the magnitude of the final component as follows:
So, the magnitude is approximately 8.36.
And the direction will be approximately 57.8° counter-clockwise.
This can be seeing as follows:
