Answer:
μ=0.329, 2.671 turns.
Explanation:
(a) ln(T2/T1)=μβ β=angle of contact in radians
take T2 as greater tension value and T1 smaller, otherwise the friction would be opposite.
T2=5000 lb and T1=80 lb
we have two full turns which makes total angle of contact=4π radians
μ=ln(T2/T1)/β=(ln(5000/80))/4π
μ=0.329
(b) using the same relation as above we will now compute the angle of contact.
take greater tension as T2 and smaller as T1.
T2=20000 lb T1=80 lb μ=0.329
β=ln(20000/80)/0.329=16.7825 radians
divide the angle of contact by 2π to obtain number of turns.
16.7825/2π =2.671 turns
Answer: At time 18.33 seconds it will have moved 500 meters.
Explanation:
Since the acceleration of the car is a linear function of time it can be written as a function of time as
![a(t)=5(1-\frac{t}{15})](https://tex.z-dn.net/?f=a%28t%29%3D5%281-%5Cfrac%7Bt%7D%7B15%7D%29)
![a=\frac{d^{2}x}{dt^{2}}\\\\\therefore \frac{d^{2}x}{dt^{2}}=5(1-\frac{t}{15})](https://tex.z-dn.net/?f=a%3D%5Cfrac%7Bd%5E%7B2%7Dx%7D%7Bdt%5E%7B2%7D%7D%5C%5C%5C%5C%5Ctherefore%20%5Cfrac%7Bd%5E%7B2%7Dx%7D%7Bdt%5E%7B2%7D%7D%3D5%281-%5Cfrac%7Bt%7D%7B15%7D%29)
Integrating both sides we get
![\int \frac{d^{2}x}{dt^{2}}dt=\int 5(1-\frac{t}{15})dt\\\\\frac{dx}{dt}=v=5t-\frac{5t^{2}}{30}+c](https://tex.z-dn.net/?f=%5Cint%20%5Cfrac%7Bd%5E%7B2%7Dx%7D%7Bdt%5E%7B2%7D%7Ddt%3D%5Cint%205%281-%5Cfrac%7Bt%7D%7B15%7D%29dt%5C%5C%5C%5C%5Cfrac%7Bdx%7D%7Bdt%7D%3Dv%3D5t-%5Cfrac%7B5t%5E%7B2%7D%7D%7B30%7D%2Bc)
Now since car starts from rest thus at time t = 0 ; v=0 thus c=0
again integrating with respect to time we get
![\int \frac{dx}{dt}dt=\int (5t-\frac{5t^{2}}{30})dt\\\\x(t)=\frac{5t^{2}}{2}-\frac{5t^{3}}{90}+D](https://tex.z-dn.net/?f=%5Cint%20%5Cfrac%7Bdx%7D%7Bdt%7Ddt%3D%5Cint%20%285t-%5Cfrac%7B5t%5E%7B2%7D%7D%7B30%7D%29dt%5C%5C%5C%5Cx%28t%29%3D%5Cfrac%7B5t%5E%7B2%7D%7D%7B2%7D-%5Cfrac%7B5t%5E%7B3%7D%7D%7B90%7D%2BD)
Now let us assume that car starts from origin thus D=0
thus in the first 15 seconds it covers a distance of
![x(15)=2.5\times 15^{2}-\farc{15^{3}}{18}=375m](https://tex.z-dn.net/?f=x%2815%29%3D2.5%5Ctimes%2015%5E%7B2%7D-%5Cfarc%7B15%5E%7B3%7D%7D%7B18%7D%3D375m)
Thus the remaining 125 meters will be covered with a constant speed of
![v(15)=5\times 15-\frac{15^{2}}{6}=37.5m/s](https://tex.z-dn.net/?f=v%2815%29%3D5%5Ctimes%2015-%5Cfrac%7B15%5E%7B2%7D%7D%7B6%7D%3D37.5m%2Fs)
in time equalling ![t_{2}=\frac{125}{37.5}=3.33seconds](https://tex.z-dn.net/?f=t_%7B2%7D%3D%5Cfrac%7B125%7D%7B37.5%7D%3D3.33seconds)
Thus the total time it requires equals 15+3.33 seconds
t=18.33 seconds
Answer:
As the asteroid falls closer to the Earth's surface its <u>Gravitational</u> <u>Potential</u> energy <em>decreases</em> and its <u>Kinetic</u> energy <em>increases</em>.
Answer:
momentum
Explanation:
Mass - Mass is a measurement of how much matter is in an object. It is usually measured in kilograms. Momentum is equal to the mass times the velocity of an object. Momentum is a measurement of mass in motion
Answer:
Because with this test you can determine complex material parameters like Young’s modulus, yield strength, ultimate strength and elongation at break. This is important because it provides us with the factor of safety that needs to be built-in the products using these materials.
Explanation:
This test consists in place the material between to tweezers to subdued the material into a stress-strain test. The figure shows the procedure.
In the x axe the strain and the y axe the stress.