Answer:
w = √[g /L (½ r²/L2 + 2/3 ) ]
When the mass of the cylinder changes if its external dimensions do not change the angular velocity DOES NOT CHANGE
Explanation:
We can simulate this system as a physical pendulum, which is a pendulum with a distributed mass, in this case the angular velocity is
w² = mg d / I
In this case, the distance d to the pivot point of half the length (L) of the cylinder, which we consider long and narrow
d = L / 2
The moment of inertia of a cylinder with respect to an axis at the end we can use the parallel axes theorem, it is approximately equal to that of a long bar plus the moment of inertia of the center of mass of the cylinder, this is tabulated
I = ¼ m r2 + ⅓ m L2
I = m (¼ r2 + ⅓ L2)
now let's use the concept of density to calculate the mass of the system
ρ = m / V
m = ρ V
the volume of a cylinder is
V = π r² L
m = ρ π r² L
let's substitute
w² = m g (L / 2) / m (¼ r² + ⅓ L²)
w² = g L / (½ r² + 2/3 L²)
L >> r
w = √[g /L (½ r²/L2 + 2/3 ) ]
When the mass of the cylinder changes if its external dimensions do not change the angular velocity DOES NOT CHANGE
Answer:
Power is 1061.67W
Explanation:
Power=force×distance/time
Power=65×9.8×15/9 assuming gravity=9.8m/s²
Power=3185/3=1061.67W
Answer:
I think D sorry if I'm wrong
Answer:
![\displaystyle X_T=66.6\ km](https://tex.z-dn.net/?f=%5Cdisplaystyle%20X_T%3D66.6%5C%20km)
Explanation:
<u>Accelerated Motion
</u>
When a body changes its speed at a constant rate, i.e. same changes take same times, then it has a constant acceleration. The acceleration can be positive or negative. In the first case, the speed increases, and in the second time, the speed lowers until it eventually stops. The equation for the speed vf at any time t is given by
![\displaystyle V_f=V_o+a\ t](https://tex.z-dn.net/?f=%5Cdisplaystyle%20V_f%3DV_o%2Ba%5C%20t)
where a is the acceleration, and vo is the initial speed
.
The train has two different types of motion. It first starts from rest and has a constant acceleration of
for 182 seconds. Then it brakes with a constant acceleration of
until it comes to a stop. We need to find the total distance traveled.
The equation for the distance is
![\displaystyle X=V_o\ t+\frac{a\ t^2}{2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20X%3DV_o%5C%20t%2B%5Cfrac%7Ba%5C%20t%5E2%7D%7B2%7D)
Our data is
![\displaystyle V_o=0,a=0.987m/s^2,\ t=182\ sec](https://tex.z-dn.net/?f=%5Cdisplaystyle%20V_o%3D0%2Ca%3D0.987m%2Fs%5E2%2C%5C%20t%3D182%5C%20sec)
Let's compute the first distance X1
![\displaystyle X_1=0+\frac{0.987\times 182^2}{2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20X_1%3D0%2B%5Cfrac%7B0.987%5Ctimes%20182%5E2%7D%7B2%7D)
![\displaystyle X_1=16,346.7\ m](https://tex.z-dn.net/?f=%5Cdisplaystyle%20X_1%3D16%2C346.7%5C%20m)
Now, we find the speed at the end of the first period of time
![\displaystyle V_{f1}=0+0.987\times 182](https://tex.z-dn.net/?f=%5Cdisplaystyle%20V_%7Bf1%7D%3D0%2B0.987%5Ctimes%20182)
![\displaystyle V_{f1}=179.6\ m/s](https://tex.z-dn.net/?f=%5Cdisplaystyle%20V_%7Bf1%7D%3D179.6%5C%20m%2Fs)
That is the speed the train is at the moment it starts to brake. We need to compute the time needed to stop the train, that is, to make vf=0
![\displaystyle V_o=179.6,a=-0.321\ m/s^2\ ,V_f=0](https://tex.z-dn.net/?f=%5Cdisplaystyle%20V_o%3D179.6%2Ca%3D-0.321%5C%20m%2Fs%5E2%5C%20%2CV_f%3D0)
![\displaystyle t=\frac{v_f-v_o}{a}=\frac{0-179.6}{-0.321}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20t%3D%5Cfrac%7Bv_f-v_o%7D%7Ba%7D%3D%5Cfrac%7B0-179.6%7D%7B-0.321%7D)
![\displaystyle t=559.5\ sec](https://tex.z-dn.net/?f=%5Cdisplaystyle%20t%3D559.5%5C%20sec)
Computing the second distance
![\displaystyle X_2=179.6\times559.5\ \frac{-0.321\times 559.5^2}{2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20X_2%3D179.6%5Ctimes559.5%5C%20%5Cfrac%7B-0.321%5Ctimes%20559.5%5E2%7D%7B2%7D)
![\displaystyle X_2=50,243.2\ m](https://tex.z-dn.net/?f=%5Cdisplaystyle%20X_2%3D50%2C243.2%5C%20m)
The total distance is
![\displaystyle X_t=x_1+x_2=16,346.7+50,243.2](https://tex.z-dn.net/?f=%5Cdisplaystyle%20X_t%3Dx_1%2Bx_2%3D16%2C346.7%2B50%2C243.2)
![\displaystyle X_t=66,589.9\ m](https://tex.z-dn.net/?f=%5Cdisplaystyle%20X_t%3D66%2C589.9%5C%20m)
![\displaystyle \boxed{X_T=66.6\ km}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cboxed%7BX_T%3D66.6%5C%20km%7D)
The force exerted by a magnetic field on a wire carrying current is:
![F=ILB \sin \theta](https://tex.z-dn.net/?f=F%3DILB%20%5Csin%20%5Ctheta)
where I is the current, L the length of the wire, B the magnetic field intensity, and
![\theta](https://tex.z-dn.net/?f=%5Ctheta)
the angle between the wire and the direction of B.
In our problem, the force is F=0.20 N. The current is I=1.40 A, while the length of the wire is L=35.0 cm=0.35 m. The angle between the wire and the magnetic field is
![53 ^{\circ}](https://tex.z-dn.net/?f=53%20%5E%7B%5Ccirc%7D)
, so we can re-arrange the formula and substitute the numbers to find B: