Answer:
hello the diagram relating to this question is attached below
a) angular accelerations : B1 = 180 rad/sec, B2 = 1080 rad/sec
b) Force exerted on B2 at P = 39.2 N
Explanation:
Given data:
Co = 150 N-m ,
<u>a) Determine the angular accelerations of B1 and B2 when couple is applied</u>
at point P ; Co = I* ∝B2'
150 = ( (2*0.5^2) / 3 ) * ∝B2
∴ ∝B2' = 900 rad/sec
hence angular acceleration of B2 = ∝B2' + ∝B1 = 900 + 180 = 1080 rad/sec
at point 0 ; Co = Inet * ∝B1
150 = [ (2*0.5^2) / 3 + (2*0.5^2) / 3 + (2*0.5^2) ] * ∝B1
∴ ∝B1 = 180 rad/sec
hence angular acceleration of B1 = 180 rad/sec
<u>b) Determine the force exerted on B2 at P</u>
T2 = mB1g + T1 -------- ( 1 )
where ; T1 = mB2g ( at point p )
= 2 * 9.81 = 19.6 N
back to equation 1
T2 = (2 * 9.8 ) + 19.6 = 39.2 N
<u />
<span>H(t) = -16t^2 + vt + s
</span><span>Part A:
</span>Using the given data:
H(t)= -16*t² + 60*t + 82;
Part B:
Put H(t)=0
0<span>= -16*t² + 60*t + 82;</span>
Use the quadratic formula to find t.
See the attachment...'t' is replaced with 'x'.
Answer:
a. They will be tie
b. Win the wood cylinder
Explanation:
a.
The both cylinders will reach the bottom at the same time notice the relation in the equation in indepent of the length and both have the same radius and the same rotational inertia.
![I=\frac{1}{2}*m*r^2](https://tex.z-dn.net/?f=I%3D%5Cfrac%7B1%7D%7B2%7D%2Am%2Ar%5E2)
![a=\frac{g*sin(\beta)}{1+I_{com}/m*r^2}](https://tex.z-dn.net/?f=a%3D%5Cfrac%7Bg%2Asin%28%5Cbeta%29%7D%7B1%2BI_%7Bcom%7D%2Fm%2Ar%5E2%7D)
So both will be tie
b.
![a_{brass}=\frac{g*sin(\beta)}{1+I_{brass}/m*r^2}=a_{wood}=\frac{g*sin(\beta)}{1+I_{wood}/m*r^2}](https://tex.z-dn.net/?f=a_%7Bbrass%7D%3D%5Cfrac%7Bg%2Asin%28%5Cbeta%29%7D%7B1%2BI_%7Bbrass%7D%2Fm%2Ar%5E2%7D%3Da_%7Bwood%7D%3D%5Cfrac%7Bg%2Asin%28%5Cbeta%29%7D%7B1%2BI_%7Bwood%7D%2Fm%2Ar%5E2%7D)
The acceleration of the wood cylinder is larger than the acceleration of the brass cylinder so the cylinder of wood will reach the bottom first
![a_{brass}](https://tex.z-dn.net/?f=a_%7Bbrass%7D%3Ca_%7Bwood%7D)
So the wood win the race