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An green hoop with mass mh = 2.8 kg and radius Rh = 0.12 m hangs from a string that goes over a blue solid disk pulley with mass md = 1.9 kg and radius Rd = 0.09 m. The other end of the string is attached to a massless axel through the center of an orange sphere on a flat horizontal surface that rolls without slipping and has mass ms = 3.8 kg and radius Rs = 0.22 m. The system is released from rest. 1) What is magnitude of the linear acceleration of the hoop? m/s2 2) What is magnitude of the linear acceleration of the sphere? m/s2 3) What is the magnitude of the angular acceleration of the disk pulley? rad/s2 4) What is the magnitude of the angular acceleration of the sphere? rad/s2 5) What is the tension in the string between the sphere and disk pulley? N 6) What is the tension in the string between the hoop and disk pulley? N 7) The green hoop falls a distance d = 1.68 m. (After being released from rest.) How much time does the hoop take to fall 1.68 m?

Respuesta :

Answer:

1) F=ma  

a=(mh*g)/(7/5ms+1/2md+mh)

2) same answer as 1 because it is a system

3)a=alpha*R

alpha=a/Rd (use a from 1)

4) similar to 3

alpha=a/Rs

5)F=ma

T=ms*a

T=7/5ms*a (a from 1)  

6)T=mh(g-a)

7)d=1/2at^2 (position formula - starting position and velocity are zero)

t=sqrt(2d/a) (use a from 1)

8)vf^2=vi^2 +2ad (initial velocity = 0)

vf=sqrt(2ad)

9)omega=v/Rs

Explanation:

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