Motion Energy
I am writing this so it can be more than 20 letters
Answer:
F = 2,894 N
Explanation:
For this exercise let's use Newton's second law
F = m a
The acceleration is centripetal
a = v² / r
Angular and linear variables are related.
v = w r
Let's replace
F = m w² r
The radius r and the length of the rope is related
cos is = r / L
r = L cos tea
Let's replace
F = m w² L cos θ
Let's reduce the magnitudes to the SI system
m = 101.7 g (1 kg / 1000g) = 0.1017 kg
θ = 5 rev (2π rad / rev) = 31,416 rad
w = θ / t
w = 31.416 / 5.1
w = 6.16 rad / s
F = 0.1017 6.16² 0.75 cos θ
F = 2,894 cos θ
The maximum value of F is for θ equal to zero
F = 2,894 N
T<span>he </span>similarities between compounds<span> and </span>mixtures<span> are that they are both made up of two or more </span>elements<span> and that they could both be separated and then mixed with different </span>elements<span> to make a new </span>mixture<span> and </span>compound<span>.
</span>
Answer:
Question 1)
a) The speed of the drums is increased from 2 ft/s to 4 ft/s in 4 s. From the below kinematic equations the acceleration of the drums can be determined.

This is the linear acceleration of the drums. Since the tape does not slip on the drums, by the rule of rolling without slipping,

where α is the angular acceleration.
In order to continue this question, the radius of the drums should be given.
Let us denote the radius of the drums as R, the angular acceleration of drum B is
α = 0.5/R.
b) The distance travelled by the drums can be found by the following kinematics formula:

One revolution is equal to the circumference of the drum. So, total number of revolutions is

Question 2)
a) In a rocket propulsion question, the acceleration of the rocket can be found by the following formula:

b) 
Answer:
(a) 
(b) 
(c) 1 s
(d) 20 m
(e) 1 m
(f) 
(g) 
(h) 
(i) 
(j) 
(k) 
(l) 
(m) 
Explanation:
Since <em>x</em> is measured in meters and <em>t</em> in seconds, constants <em>a </em>and <em>b</em> must have units that gives meters when multiplied by square and cubic seconds respectivly, so that would mean
for <em>a </em>and
for <em>b</em>.
We can get the velocity <em>v </em>equation by deriving the position with respect to <em>t</em>, which gives:

And the acceleration <em>a</em> equation by deriving again:

Now for getting the maximun position between 0 and 4, we must find to points where the positions first derivate is equal to cero and evaluate those points. That is <em>v=0</em>, which gives

For <em>t = 0</em>,<em> x = 0</em> so the maximun position is archieved at 1 second, which gives <em>x = 1 meter</em>.
For obtaining it's displacement <em>r</em>, we can integrate the velocity from 0 seconds to 4 seconds, which gives the mean value of the position in that interval:

For the remaining questions, we just replace the values of <em>t</em> on the respective equations.